Cosmology at Dr Cormac O’Raifeartaigh’s blog

Professor Cormac O’Raifeartaigh has an interesting blog post about The Cosmological Distance Ladder – the key to understanding the Universe, a lecture given by Micheal Rowan-Robinson, Professor of Astrophysics at Imperial College London.  Rowan-Robinson is author of the textbook Cosmology, which is very good.

I believe that the cosmological distance ladder is the key to understanding the universe, very literally indeed!  So I commented on Professor O’Raifeartaigh’s blog as follows:

Take the Hubble law v/r = H

a = dv/dt = d(Hr)/dt = H*(dr/dt) + r*(dH/dt)

dH/dt = 0, so

a = H*(dr/dt)

= Hv

= H(Hr)

= rH^2

Which predicts a cosmological acceleration at cosmological distances of what is seen in observations, approximately 6*10^(-10) ms^(-2). Smolin’s T.T.W.P. book for example translates the small cosmological constant into an acceleration in units of ms^(-2).

I did this and published it via Electronics World in 1996, well before the cosmological acceleration was discovered by Perlmutter in 1998 and published in Nature.

It’s wrong of Hubble to solely express the recession as v/r = H. Didn’t he know about spacetime?? Distance isn’t meaningful here. The velocity v only correlated to distance r is you are looking back in time as well as distance, because light takes a time of t = r/c to come to you from distance r. During this time, velocity v is quite likely to change!

So Hubble should have expressed recession velocities less ambiguously using the concept of spacetime, where the constant is not v/r, but v/t. If he had done that, he would have noticed that v/t has units of acceleration! (The ratio v/r has units of 1/t, i.e. in general it’s inversely proportional to the age of the universe – and is exactly the inverse of the age of the universe if the universe is flat rather than curved on cosmological scales.)

Once you differentiate Hubble’s law v = Hr to get acceleration a = rH^2, you can do a lot of interesting physics using Newton’s simple laws of motion. E.g., any receding mass m has an outward force from you of F=ma (Newton’s 2nd law of motion), and Newton’s 3rd law of motion then suggests an inward “reaction” force must be directed towards you of equal size F=ma. This reaction force presumably (from the possibilities) is carried by gravitons, and when you calculate with this you find that gravity and all the confirmed aspects of G.R. are reproduced by spin-1 gravitons.

E.g., spin-1 gravitons come inwards towards us from distant receding masses in all directions. The pressure acts on all fundamental particles, and since nearby masses aren’t receding, they don’t have an outward force relative to one another and hence don’t exchange gravitons forcefully with one another. This tells you that the net effect is that nearby particles shield one another and get pushed together. You can predict how much.

This predicts gravity. As Feynman showed in his Lectures on Physics, G.R.’s main difference physically from Newtonian gravity is that there is a contraction radially of spacetime around a mass; the earth’s radius is reduced by (1/3)MG/c^2 = 1.5 millimetres due to the G.R. contraction term. This contraction is the effect of inward graviton force on the earth, shrinking it radially.

The bottom line is that there’s loads of evidence to support the contention that dark energy is spin-1 graviton energy.

Spin-1 graviton exchange between masses on large (cosmological) scales pushes the masses apart, causing the cosmological acceleration as predicted in 1996. It also pushes cosmologically “nearby” masses together (because nearby masses aren’t receding much if at all, there is little or no forceful exchange of gravitons between nearby masses; so the only forceful exchange of gravitons occurs between each of the masses and converging inward gravitons from the surrounding receding masses in the universe, which means that nearby masses get pushed towards one another; gravity).

That’s the answer to “dark energy”. It’s graviton energy!

Sadly, all the stuff above life Hubble’s law, spacetime, differentiation, Newton’s empirical laws of motion, and so on, are rejected when combined to come up with a quantum gravity theory.

The mainstream prefers to believe that two nearby masses only exchange gravitons with one another, which means that for attraction the gravitons would have to have spin-2. They just can’t see that an apple is going to be exchanging gravitons more forcefully with the massive surrounding universe than with the earth; although the earth is closer, the gravitons coming inwards from surrounding masses and hitting the apple are converging inward from the surrounding universe (they’re not diverging outward). So there is no loss due to inverse square law divergence!

It’s so hard to get anybody who believes in spin-2 leprechauns to listen to straightforward physical facts, that I’ve virtually given up!


‘I guess the real question concerns the Hubble equation really means. Is it meaningful to talk about a Hubble graph for one galaxy only? If we measure the distance and velocity of galaxy A, plot it, then measure the distance and velocity of galaxy A again some time later, plot that etc, do we get a straight line of slope H?’ – Cormac

Thanks for responding! If we take a single highly redshifted receding galaxy or supernova, there is evidence that it is accelerating away from us. Perlmutter’s original paper on the discovery of the cosmological acceleration is titled:

Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications published in Nature v. 391, pp. 51-54 (1 January 1998).

By that time, 50 supernova with extreme redshift had been discovered, but the paper dealt with just the first one of extreme redshift, the SN 1997ap which has a redshift of z = 0.83. Thus, the implication from this research is that individual supernovae are indeed accelerating!

So this acceleration of individual masses away from one another isn’t controversial.

If you remember the story, Einstein added the cosmological constant to general relativity a year or so after publishing the basic field equation in November 1915.

He believed that the observed universe was static (Hubble’s analysis of redshifts wasn’t completed until 1929, and is still falsely attacked by some people who have mistaken ideas, as exposed on the excellent page, and that it would collapse unless there was a repulsive force between masses which increased with distance (thus being negligible over small distances) and cancelled out gravitational attraction over a distance equal to the average distance between galaxies.

At smaller distances, Einstein’s cosmological constant produced a repulsive force which was smaller than gravity (so gravity dominated), while over bigger distances it produced a force which was bigger than gravity (so universal repulsion dominated). One immediate problem was that this model would make the universe unstable.

So it was abandoned by Einstein in after Hubble’s results showed that the universe was expanding.

However, in 1998 the cosmological constant (albeit with a much smaller magnitude than Einstein had stipulated) had to be taken back into the field equation to account for the observed lack of gravitational curvature on the largest distances. The exact value is still hazy, but the approximate order of magnitude is well established: it’s certain from the evidence that there is cosmological acceleration on the order of 10^{-10} m/s^2 or so at large redshifts. There is some uncertainty from gamma ray burster evidence over whether the cosmological acceleration actually implies a cosmological constant or an evolving parameter:

So from observational evidence, every receding mass has a small cosmological acceleration away from every other masses. On small distances, gravity dominates over cosmological acceleration, and so the cosmological acceleration only becomes important over large distances.

Going back to your question about testing the applicability of the Hubble law to individual galaxies by measuring the recession and distance of a galaxy at successive times, I fear that we’d have to wait too many lifespans to get statistically significant results. Experimental errors are generally too large to wait short periods of time and detect whether an individual galaxy is accelerating or not. Obviously if we naively apply the Hubble law to predict the motion of an individual galaxy, it fails because as the galaxy recedes to greater distances the Hubble law is describing earlier times after the big bang; when of course the recession will take time so the galaxy will age as it recedes, instead of getting younger. My feeling is that, as Minkowski stated in the quotation above, we have to base physics on observables. The Hubble law is what is observed. Even though an individual galaxy may just be coasting along at constant velocity, or maybe slowing, that doesn’t really matter because all we we see appears to be an acceleration in the frame of reference at our disposal, in which information is carried to us at light speed from times past which increase with distance. Because other effects like gravitons will go at the same velocity as visible light, this observed reference frame is the correct one to be using in making predictions. For gravitational purposes, the apparent spacetime observations of the universe are fine, because the data is coming from the past just at the same velocity that gravitons come at. So the apparent positions and accelerations of masses as seen with visible light are going to be the same as those corresponding to gravitons coming from such receding masses. In any case, from the fact that the universe really is acelerating, I have no problem in deducing from this acceleration that receding individual galaxies themselves do have an effective acceleration in observable spacetime. If we could see them in a reference frame whereby we could see things when the same age after the big bang – without looking backwards in time with increasing distance – then maybe the acceleration would be modified. But we can’t see the universe in reference frame where everything is 13,700 million years old, so it’s unphysical. We have to accept, as Minkowski stated in 1908, that when we look at distant things we’re seeing them as they were at earlier epochs in the big bang.


Dr Chris Oakley:

Thanks! Taking your last point first, the flat universe cosmology has

t = 1/H


H = 1/t

so it does suggest that the Hubble “constant” is falling as the universe expands. But Hubble’s constant is not a time-independent constant, but merely

v/r = H

= 1/t

in flat cosmology, where t is age of universe.

So v is only a “constant” with respect to r as far as Hubble was concerned. H is not a variable as observed in the Minkowsky flat spacetime metric of the universe we see.


v/r = H = 1/t,

your argument (‘so it is Hubble’s “constant”, not the speed of the galaxy that is changing’) suggests that v is constant and in

v/r = 1/t

each denominator (r and t) is increasing in proportion.

That’s a nice simple idea. Unfortunately, it’s completely wrong, because the time t in this formula is the age of the universe, whereas r = cT where T is time past.

The age of the universe, t, is not proportional to time past T = r/c. E.g., the closest star, the sun is T = 8.3 light-minutes away, but the universe is not t = 8.3 minutes old. (We’re just seeing the sun as it was 8.3 minutes in the past.) So you can’t set v/r = H = 1/t and try to get rid of a changing v by saying that r is proportional to t!

Now for your earlier comment above about the explosion analogy. This particular explosion analogy has been tried and criticised. In about 1931, when initial attempts were being made to understand the Hubble law (before the Friedmann-Robertson-Walker metric was dogma), people like Lemaitre were suggesting that the universe was like an explosion in a pre-existing space.

A letter appeared in Nature in I believe 1931 (I think you will find the details discussed in Eddington’s book The Expanding Universe) pointing out that the Hubble law is not what you expect from say a bursting bomb.

Just before the bomb explodes, the compressed hot gas of explosion debris will have a Maxwell-Boltzmann distribution of velocities, which is skewed so that most of the molecules have low velocities, and the above the peak there is a long tailing-off to a small number of molecules with very high velocities: see or

The letter in Nature pointed out that the Hubble distribution is quite different, it is in fact an anti-Maxwell-Boltzmann distribution. In the universe, the greatest number of galaxies have the greatest recession velocities, which is contrary to what the Maxwell-Boltzmann distribution predicts for molecules from a bursting bomb.

‘Afterwards the distance of the fragments from the site of the explosion is proportional to the velocity they set off at, so if you observe at a later time T the distance from the initial point d=vT. So the “Hubble constant” for this is just the inverse time since the explosion. And, because of vector addition of velocities, one gets the same answer in a co-ordinate system comoving with any fragment.’

There’s a graph showing the Hubble law for distribution of air molecule speeds behind the shock front in an explosion, in a paper by Sir G. I. Taylor, ‘The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945’, Proceedings of the Royal Society of London, Series A, v. 201, pp. 175–186.

However, that’s an air burst detonation, not an explosion in space. The die-hard general relativists who believe in curved space (even though the universe has been shown to be flat, and curvature is anyway just an approximation to a lot of quantum graviton interactions), will tell you (falsely) that spacetime in the universe curves back on itself at great distances, so any effort to model the big bang as some kind of explosion is automatically void.

I’m not sympathetic with those people who want to use the authority of popular speculations to rule out the simplest possible physical model. Within seconds, the big bang universe became mainly compressed, ionized hydrogen gas. As in a H-bomb, fusion occurred in the extremely high temperature and pressure but was not complete; the expansion of the universe quenched the fusion rate by reducing the temperature and pressure before all of the hydrogen could fuse into helium, etc.

If you get away from the curved space of general relativity, and move on to a model of gravitation where accelerations result from the exchange of gravitons in discrete interactions (so spacetime curvature is just an approximation for the effect of a large number of discrete interactions), then it might make sense to try to model the late stages of the universe as a 10^55 megatons H-bomb in a pre-existing space. But this won’t address the very early-time physics (less than 1 second after the big bang), where the energies were initially so high that the binding energy of hadrons was trivial by comparison, so there was a quark soup instead. Also, it will annoy all the pacifist physicists who don’t like the morality of using an explosion as any kind of analogy to the big bang. Finally, general relativity indicates that space was created with the big bang, not pre-existing (this is because spacetime is defined by the gravitational field, so where you don’t have such a field there is no spacetime).

I find these arguments vacuous because general relativity is just a classical continuous-field line model for gravitational fields. Because of the clever way it incorporates conservation of mass-energy for fields (something which Newton’s gravity law ignored), it makes checkable predictions that differ from Newtonian gravity, and which is correct. But the evidence supporting general relativity is just supporting the inclusion of conservation of mass-energy by general relativity, it isn’t specifically supporting the classical curved spacetime model of general relativity. Curved spacetime at best is just a classical approximation to many discrete graviton interactions. Sum the Feynman diagram interaction histories for many graviton interactions, and you get something that approximates to the spacetime curvature of general relativity.

A simple physical way to get the observed cosmological acceleration out of big bang is by spin-1 graviton exchange between masses. All masses have the same gravitational charge (say positive gravitational charge), so they all repel by exchanging gravitons. The repulsion makes masses accelerate away from one another, giving the Hubble law. The same effect predicts gravitation with the correct strength (within observational error bars).

‘As for an “accelerating” universe, that observation depends entirely on the redshifts of Type Ia supernovae. Many astrophysicists are not sure their luminosity is constant.’ – Louise Riofrio


In addition to Type Ia supernovae, gamma ray bursters (stars collapsing into black holes) also provide alleged evidence of “acceleration”, albeit an “evolving dark energy” (changing cosmological constant), see the plotted gamma ray burster data at:

However, as Nobel Laureate Philip Anderson has argued,

‘… the flat universe is just not decelerating, it isn’t really accelerating …’ –

The radial recession of galaxies in the Friedmann-Robertson-Walker metric of general relativity is the Hubble recession law with a gravitational slowing down at large distances due to attraction to the mass centred around us (in our frame of reference, which is the frame of reference we’re observing the universe from).

The 1998 results of Perlmutter on Type Ia supernovae suggested that this metric is wrong because there is no observable gravitational slowing down of the expansion.

So the mainstream knee-jerk response was to say that the inward-directed gravitational acceleration (which is only important at large distances, i.e. immense redshifts, according to general relativity) must be cancelled out by an outward-directed acceleration on the order 10^{-10} metres/second^2. The outward-directed acceleration would be due to a universal repulsion of masses, i.e. a small positive cosmological constant.

However, this explanation makes quite a lot of assumptions. As mentioned, gamma ray burster data indicate an evolution of the cosmological ‘constant’. There is also the idea that gravity gets weaker over cosmological distance scales. If you believe that gravity is due to spin-2 gravitons being exchanged directly between the masses which are attracting, then for redshifted masses the gravitons can be expected to be redshifted and thus received in a degraded energy condition, weakening the gravity coupling constant G from that measured in a lab where the masses are not relativistically receding from one another.

But if gravitons have spin-1 rather than spin-2 (and thereby act by pushing masses together instead of pulling them together), the spin-1 graviton exchange actually causes the cosmological acceleration as well as gravity. This makes checkable predictions.

I think one thing to be made clear is that a gravitational field can exist without something actually accelerating. I’m sitting in a gravitational field of 9.81 metres/second^2 and I’m not being accelerated downward, because there’s a normal reaction force from the chair that stopping me.

It’s exactly the same with the cosmological acceleration:

1. The most distant receding galaxies, supernovae and gamma ray bursters etc have an inward-directed gravity-caused acceleration towards us observers on the order 10^{-10} metres/second^2. (This effect is similar in nature to the gravitational slowing down of a bullet fired vertically upward.)

2. Such distant receding matter also has an outward-directed ‘dark energy’ (spin-1 graviton, I argue) caused acceleration away from us on the order of 10^{-10} metres/second^2.

The outward cosmological ‘dark energy’ acceleration cancels out the inward gravitational acceleration, so there is no net acceleration.

This is what Philip Anderson meant when he wrote:

‘… the flat universe is just not decelerating, it isn’t really accelerating …’

In my case, I’m not being accelerated downward by gravity because that acceleration is being cancelled out by an equal upward acceleration due to electromagnetic repulsion of the electrons in me and the electrons in my chair.

In the case of the universe, the cosmological acceleration of the universe is being cancelled out by gravitational attraction.


“In the standard big bang cosmology of yore, its growth was supposed to be decelerating due to the gravitational pull between galaxies. If you believe the current concordance model, it is actually growing faster as time goes by.” – SomeRandomGuy

The Friedmann-Robertson-Walker metric of general relativity up to 1998 predicted that the expansion rate is slowing down, and that this should be observable at extreme redshifts.

Perlmutter simply found that the expansion rate isn’t slowing down in his observations in 1998.  The mainstream interpreted the lack of gravitational (inward-directed) deceleration to imply that gravity is being cancelled out by an outward-directed cosmological acceleration due to some unknown dark energy.

The universe isn’t actually accelerating; there is an acceleration field which isn’t causing matter to accelerate because gravitational attraction is cancelling out that outward acceleration (see Nobel Laureate Phil Anderson’s criticism of “acceleration” on mainstream cosmologist Professor Sean Carroll’s blog as I quoted it in the previous comment; Sean didn’t repudiate this point!).

The cosmological acceleration is a small but universal repulsion between masses.  Gravitation is a universal attraction between masses.  On cosmological distance scales these two opposite accelerations cancel one another out, so there is no net acceleration of matter.



The Lambda-CDM model, which is the mainstream model now (the Cold Dark Matter model with a small positive cosmological constant lambda worked out from the data), involves a repulsive force that increases as a function of distance.

The gravitational deceleration effect decreases with increasing distance.

Therefore at small distances, gravitation predominates, then at a larger distance (on the order 5*10^9 light years) the acceleration of the universe cancels out gravitational deceleration on receding matter, and at still greater distances the cosmological acceleration exceeds gravitation.

The observations of red-shifts made so far from Type Ia supernovae and gamma ray bursters are concentrated in the region where cosmological acceleration (repulsion) is cancelling out gravitational acceleration which is trying to slow the expansion of the universe.

For bigger distances than have currently been well observed, the mainstream Lambda-CDM model suggests an overall net acceleration outward. Whether the model is right is another matter (see the evidence from gamma ray bursters which suggests that the value of Lambda isn’t a constant: ).

This acceleration as an extrapolation from the Lambda-CDM model isn’t a fact or even a scientific prediction, because it’s not really a falsifiable prediction because the small positive Lambda/cosmological constant value is already an ad hoc modification, not a piece of genuine scientific prediction. You can endlessly introduce ad hoc ‘epicycle’ type corrections into a model to make it fit unpredicted effects. Whatever new data comes, they can just find a formula to fit Lambda’s variation (if any) as a function of redshift/distance. But this isn’t real physics.

The real physics concerns the nature of the dark energy. It’s spin-1 gravitons, causing universal repulsion between similar gravitational charge; this causes the cosmological acceleration and also pushes relatively small masses towards one another because they exchange gravitons more forcefully with the large masses in the distant universe than with one another. Both are checkable predictions.

Spin-2 gravitons don’t lead to any checkable predictions. Firstly spin-2 gravitons are based on the bizarre idea that mass A and mass B are solely exchanging gravitons with one another, and not exchanging gravitons with every other mass in the universe, including the immense masses at great distances. Secondly, spin-2 gravitons seem to need some incredibly ugly and extravagant theoretical framework such as string theory with 10 dimensions. (String theory is inherently vague because 6 dimensions are supposed to be too small to probe experimentally, so nobody knows their moduli if they are compactified in a Planck scale Calabi-Yau manifold. Without knowing all the parameters of these extra dimensions, you can’t make falsifiable predictions.)



Thanks for that up to date reference. Normally blog posts are updated or have trackbacks from new posts when updates are made, which makes them more dynamic than the usual literature not less so, but as you point out this is not so for Cosmic Variance. (I’ll avoid linking to posts at Sean’s blog from now on in case they become obsolete and are not updated by a trackback.)

It’s interesting that the latest gamma ray burster data is compatible with an unchanging cosmological constant!


“As an aside, your use of the term “acceleration outward” suggests that you do not yet understand FRW. You really seem to be using a mental image of an ordinary explosion in 3-dimensional space.”


We’re seeing earlier epochs with increasing distances, which is quite different from a purely 3-dimensional Euclidean space. As I explained there, flat spacetime is Minkowski spacetime, where you time changes with distance. This is why the variation in recession velocity with “distance” that Hubble reported is also a variation of velocity with time (conventionally referred to as acceleration).

“Your claim of repulsive “spin-1 gravitons” is of course completely unsubstantiated.”

There is scientific evidence to back it up:

The cosmological acceleration is a univeral repulsion of masses suggesting a spin-1 mediator, and differentiating Hubble’s law, a = dv/dt = d(Hr)/dt gives you a way of making solid predictions of forces, which predicts that the same spin-1 mediators that cause cosmological acceleration also produce gravitation. This is simple physical calculations using long-established empirical laws and observations. It predicted the cosmological acceleration of the universe in a publication in 1996, two years before observational discovery by Perlmutter!

The same calculation predicts gravity parameter G accurately. It doesn’t contain any speculations, unlike string theory. It’s already made falsifiable predictions and been vindicated. So it does seem scientifically accurate, although string theorists have censored it out!



No, I’ve never mentioned a balloon analogy!

Your statement that ‘the whole effect is caused by the expansion of space’ is vague enough to be compatible not only with what you’re thinking (the idea that the vacuum is powering cosmological expansion) but is also compatible with the physics I’ve stated: spin-1 gauge boson exchange between masses in the vacuum causes a repulsive force, giving rise to expansion of the universe (recession of masses) over large distances and pushing matter together on small scales.

Cosmologists don’t know what dark energy is so they don’t mean anything by accelerated expansion, apart from what I explained.

I.e., the cosmological acceleration is an outward radial acceleration (acceleration is a vector so it has direction and can be either outward or inward towards us when it is ascertained from redshifts). It’s needed – as far as cosmologists are concerned – to make the observed redshift data compatible with the predicted gravitational deceleration of the universe which is based on the density of the universe.

If the universe had a high enough density, the gravitational deceleration would not merely slow down the expansion but would cause the universe to begin contracting at some point in the future. I think it’s important to understand that the gravitational deceleration is always a vector, represented by arrows pointed radially inwards towards the observer. The acceleration of the universe by ‘dark energy’ is an acceleration outward, a vector represented by arrow pointed radially away from the observer. Hence the two accelerations oppose each other.

This physical explanation makes clear what is going on. Ideally the quantitative magnitude of the acceleration needs to be explained to people, on the order of 10^{-10} metres/second^2. If all this had been done when the acceleration was discovered in 1998, then there would be less confusion today. E.g., differentiate the Hubble law (v = Hr) and you get

a = dv/dt = d(Hr)/dt = H*dr/dt + r*dH/dt = Hv + 0 = rH^2.

This predicts the acceleration of the universe quantitatively. Mainstream cosmologists can’t predict this, so they don’t really ‘mean’ anything about acceleration. This was predicted in 1996, two years before being confirmed, while I was doing a cosmology course at university. Further calculations predicted gravity accurately. This model is observationally confirmed and predicts not only cosmological acceleration but also gravity accurately, using spin-1 gauge bosons. It debunks spin-2 graviton speculations, which are physically vacuous.

To restate briefly Dr Oakley’s problem:

Hubble law: v/r = H

where H = 1/t,

Chris Oakley argument: v/r = H = 1/t,

hence: v/r = 1/t

where Dr Oakley suggests that r is proportional to t, so v doesn’t vary: “(so it is Hubble’s “constant”, not the speed of the galaxy that is changing)” comment #3.

This is wrong since, as you look to bigger distances (r) you are seeing smaller times (t) after the big bang.

So r definitely is not proportional to age of universe t. In fact, if the age of the universe is that of the observer’s frame of reference, t is fixed at 13,700 million years. Hubble’s point was that v/r = constant = H, regardless of how far away (back in time) you look. This is why I feel that Dr Oakley’s comments (comments #2 and #3) above are in error.

If an Oxford PhD/D.Phil in quantum field theory can make such an error in looking at the very basics of cosmology, and then come back with personal comments ignoring the science, you can see the problem in communicating the fact that there is an acceleration inherent in the Hubble law!


“I can see why people don’t like to get into arguments with you … Hubble’s law is a fit. The velocity of galaxies being proportional to their distance roughly fits the observational data.” – Chris Oakley

You haven’t mentioned the scientific facts at all, you’ve “argued” with me by making personal comments which miss the scientific facts. You’ve ignored entirely everything that I wrote in comment 24.

Look, saying “Hubble’s law is a fit” which we all know doesn’t tell us anything new, because that’s been known since Hubble did it in 1929. I’ve done cosmology and quantum mechanics courses, and I’m studying quantum field theory as time permits.

Hubble’s law: v/r = H. Rearrange: v = rH. Differentiate it and you get an acceleration, from the calculus


= d[Hr]/dt

= H(dr/dt) + r(dH/dt)

= H(dr/dt)

= Hv

= H(Hr)

= rH^2

~ 6*10^(-10) ms^(-2) at extreme redshifts approaching the horizon radius.

This was predicted in 1996, and confirmed in 1998. The calculation above was published before confirmation. I’m very well aware (not just from hostility I receive) that it is not in the textbooks, because if it was well known, I wouldn’t need to point it out to people. I’m not pointing this out because I think it’s well known, but because it isn’t well known. It’s counter intuitive which is why it’s not mainstream thinking. If it was totally obvious, someone else would have predicted the acceleration of the universe this way before me. Yet it’s been borne out by factual evidence. It also leads to a simple prediction of the strength of gravitation, which again turns out to be accurate!



Thirteen years ago I did a cosmology course that included finding solutions such as the Friedman-Walker-Robertson metric and everything else. General relativity doesn’t predict the small positive cosmological constant to fit te observed expansion of the universe. This approach does.

See my calculation in comment 29 above and note it was done in 1996 two years before Perlmutter’s observations of distant supernovae confirmed it. It’s a different calculation from the Friedmann-Robertson-Walker metric. I work from empirical laws towards falsifiable predictions. This isn’t mainstream fundamental physics, which involves starting with a mathematical speculation like general relativity (or even string theory) that can model just about any universe, and fitting the model to the results of observations <i>ad hoc</i>. That’s one reason why I dropped physics and don’t want a degree in physics. Another reason is the general hostility, prejudice, etc., you receive when trying to have a scientific discussion. It’s not particularly healthy. I’m not claiming to be a paid-up member of the orthodoxy, I’m just pointing out facts that made falsifiable predictions which were confirmed.



I did a course in general relativity. Let me explain this to you and also to Chris Oakley very clearly.

Hubble noticed that the ratio v/r = constant = H.

In other words, the velocity of recession increases linearly with distance in spacetime.  Hence, when observing the universe by looking out in space (and back in time) in observable spacetime, dH/dt = 0, but if we <i>don’t</i> do that but instead wait around for H to change and then look again in the telescope, we’ll find that H is varying!

In the context of looking out to bigger distances and earlier times after BB, H is a constant, but when we wait around, we’ll find that H is varying as a function of the age of the universe for the observer (not for the observed).

When I did cosmology, the horizon radius of the universe was supposed (from the FRW metric) to be increasing in proportion not to t but to t^(2/3).  This slower than linear increase was predicted from the gravitational deceleration on the expansion which was predicted by GR without a CC, i.e. a curved universe of critical density.

This implied that the age of the universe was t = (3/2)/H or H = (2/3)/t.

After it was discovered by Perlmutter in 1998 that the mainstream model was wrong and the universe wasn’t decelerating (because the gravitational deceleration was being cancelled by a repulsive-force type acceleration), the flat geometry of the universe meant that the horizon radius wasn’t expanding as t^(2/3) but merely as t, so the age of the universe in flat geometry is simply

t = 1/H.

This has nothing to do with the Hubble constant varying as we look back in time.  It doesn’t!  There is no contradiction between dH/dt = 0 for spacetime where t represents earlier epochs in the universe (because as Hubble observed, H <i>is constant when we look back in time because recession velocities vary in proportion to distances or to times past</i>), and H = 1/t.

dH/dt = 0 applies to looking to greater distances in spacetime where the variation of v with r (or time past) means that v/r = constant = H, so dH/dt = 0.  When you differentiate such a constant you get zero.

But H = 1/t does not apply to looking to greater distances, because t here is the observer’s time, not the time after the big bang for the object being observed.

The only variation of H you get from H = 1/t is when the age of the universe in our frame of reference varies.

E.g., if you wait for a time of 13,700 million years and then re-measured Hubble’s “constant”, H would have halved.

<i>When you look to greater distances, however, H doesn’t appear to vary!</i> That’s because H when observed in spacetime is a ratio of two things which are both varying in sync: v and r. Because recession velocities increase as you look to greater distances (earlier times), you can’t observe any variation in H with distance. This is so simple, it’s depressing that I have to really keep spelling it out. Again, dH/dt = 0 involves spacetime t for the observed galaxy, while H = 1/t involves observer time t.

“But you are quite wrong to call GR “a mathematical speculation”.”

I’ve gone into the details of the speculations in general relativity here:

1. The successful predictions of “general relativity” result directly from the inclusion of mass-energy conservation into the gravitational model.

2. General relativity speculatively assumes that the source of gravity is a continuous distribution, not a quantized one consisting of fundamental particles. So the stress-energy tensor has to be supplied by an unrealistically smoothed distribution of matter like a mathematically “perfect fluid”, instead of discrete particles, to act as the source of smooth curvature.

3. General relativity speculatively and implicitly assumes that acceleration is due to spacetime being smoothly curved, instead of there being a quantum field with a series of discrete interactions with gravitons.

4. General relativity’s Ricci curvature tensor is rank-2, so it’s been argued by Pauli and Fietz in the 1930s that gravity is due to spin-2 gravitons, not spin-1 particles like electromagnetism. Spin-1 particle exchange between similar sign gravitational charges (e.g. two masses) would cause repulsion, whereas since attraction occurs, so you need spin-2 to make gravity attractive between two masses.  The flaw here is that – while the surrounding universe is electrically neutral for electromagnetism charges (equal positive and negative charges) – it definitely can’t be ignored this way for gravity.  Basically you have an immense amount of mass surrounding your apple and Earth, which should be exchanging gravitons with them both.  This can lead to spin-1 gravitons producing gravity by pushing together masses that are small compared the mass of the surrounding universe.  (Feynman points out in “The Feynman Lectures on Gravitation”, page 30, that gravitons are not necessarily spin-2). This is what I find to be the case, resulting in falsifiable predictions that are checked:

5. General relativity can result in a wide range of metrics depending on what assumptions you make in order to derive those metrics: it’s an endlessly adjustable speculative cosmological model that can model flat and curved universes, and in fact with appropriate ad hoc amounts of dark energy and dark matter it can model anything from endless expansion to collapse.

6. The speculative aspect of general relativity was explained even better by Einstein himself, who stated:

‘I consider it quite possible that physics cannot be based on the [smooth geometric] field principle, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air …’ – Albert Einstein in a letter to friend Michel Besso, 1954.


The anonymous commenter then followed Dr Chris Oakley’s approach by ignoring the physics in my comment and writing personal abuse, to which I replied (probably my final reply, since it’s not much use when my comments are ignored and personal abuse is made instead):

No, you are both 1) and 2), because you are confused about the “definition” of the Hubble constant.

(a) Age of universe t = 1/H implies H = 1/t, so the rate of change of H is:

dH/dt = d(1/t)/dt = – 1/t^2

(b) But in spacetime T:

dH/dT = 0

So it’s fundamentally dishonest of you to muddle up the two times!

No amount of confusion and insults against me will make dH/dt = dH/dT. They are not the same. There is not only one possible definition to the Hubble parameter: if you’re dealing with Friedmann’s obsolete law then you have varying H, but if you’re dealing with real physics in real spacetime, you have constant H.

This is because Hubble’s observation was that there is an unvarying ratio v/r = H, it follows H is defined as constant where r = cT, T being time past (if we use capital T for time past to distinguish it from time after big bang). Hubble’s law states:

v/r = v/(cT) = H

= constant regardless of value of T, because v increases in direct proportion to T, keeping observed H in spacetime constant! You still can’t grasp this, and you try to confuse it with Friedmann’s irrelevant (non-spacetime) absolute time since big bang, where H does vary.

Differentiate and you will find that dH/dT = 0 because H is constant as observed in spacetime!

So you’re confusing time after big bang from your obsolete cosmology notes, with spacetime in the Hubble law. The time after big bang is not what we can observe. Please read again what I quoted (maybe on the original blog thread here) from Minkowski wrote in 1908: we have to base physics on spacetime, where distance is proportional to time past because of the speed of light.

Really, for you and others to ignore this and make personal comments based on ignorance about my background or claims that I am being dishonest, is not helpful to the physics! Please understand that the time used in the Friedmann et al metric is not directly observed! Physics calculations in this case needs to be based on observables! Spacetime (i.e. where distance r is related to time past T by r = cT) is observed, and in spacetime the Hubble parameter H is constant because it is the ratio of (velocity)/(radial distance from us, or time past). You seem to be completely confused about this.

Physics needs to build upon facts, not speculative theories. The non-zero dH/dt you get for the Hubble constant varying with absolute time after big bang doesn’t come into what I’m calculating at all, because in spacetime the further the distance, the earlier after the big bang you are seeing. All effects such as light and gravitons will travel to us at velocity c, so in calculating effects we need to treat the physical universe as we observe it, i.e. with time past varying with observable distance. This gives us an effective acceleration for predicting physical facts. The dishonesty and confusion come from the mainstream, I fear.

What your comments – which contain no relevant physics and are just personal attacks based on ignorance – do is to detract attention from the important quantitative success in which the acceleration of the universe was accurately predicted in 1996, years before observation! The kind of confusion you have is not helpful to physics. It’s dishonest to make such comments if you are so confused about the basics. That said, there is a lot of confusion around!



Instead of apologising for your insults, and admitting that you are totally confused and got it wrong, you again just ignore my message and ask a question.

The graph shows that observable distance (double the distance and you’re seeing twice as far back in time) and recession velocity are linearly correlated, i.e. that H = (velocity)/(distance) or H = (velocity)/[(time past)*c] = constant.

Hence, H doesn’t vary because the velocity increases in proportion to distance or to time past. This variation of velocity with time is an effective acceleration.

In my original 1996 8-pages paper predicting the acceleration of the universe, I pointed out Minkowski’s statement that when looking to greater distances we’re seeing the past, and explained that if Hubble in 1929 had tried that he would have predicted the acceleration of the universe.

“The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

– Hermann Minkowski, 1908.

Hubble found (velocity)/(distance) = constant (H) with units of 1/(time). If he had noted that in spacetime (distance) = c*(time past), he would have had the option of finding that (velocity)/(time past) = constant with units of acceleration!

If you want to make the expansion rate of the flat universe absolutely clear in terms of time, it is

v = Hr

= (1/t)*(cT)

= cT/t

where T is time past (which VARIES with observed distance), and t is time after big bang in our frame of reference (so it does NOT vary with distance).

The confusion of youself and Chris is centred on confusing the two times. It’s pretty obvious that you don’t have any real interest in physics, just quoting irrelevant obsolete speculations from your textbook, trying to confuse things, and then handing out insults instead of apologies when your errors are explained to you. But this behaviour is pretty typical in mainstream physics, which is religion.

I remember a fruitless discussion with fellow Electronics World features writer Mike Renardson in 1996. His dismissed it for a different reason to you, because the predicted acceleration of the universe, on the order of 10^{-10} ms^(-2), was extremely small. This prediction and the related prediction of the gravity parameter G was rejected by journals which believed in a large or a zero cosmological constant on the basis of string theory. When it was discovered to be a correct prediction in 1998, people still tried to ignore it and claimed that the small cosmological acceleration of the universe is a “mystery”!

I remember correspondence in which I answered all kinds of concerns Renardson had with the physics in 1996, and then he sent a reply stating “do you really expect me to start believing an unorthodox theory?” I think that this says it all: mainstream physics is a belief-based system, and people need more than factual discussions to convince them of anything new. They need authority as in the stamp of officialdom. Science is supposed to be a matter of facts, but in reality it’s a matter of politics: fame, money, popularity and groupthink. As Chris Oakley wrote above, innovations in physics need sponsorship. Facts don’t speak for themselves. Or people refuse to listen to them unless they come from authority figures, the orthodoxy of religion.


“Right – so if I see a car travelling at 30 kph 30 meters away from me, and one travelling 60 kph 60 metres away from me then it must mean that the nearer one is accelerating and will be travelling at 60 kph when it is 60 meters away – ? I suppose that it is possible … but a much simpler “explanation” is that neither of them is accelerating, but started at the same place (where I am standing) and set off at different speeds. AFAIK we cannot measure galactic acceleration directly so I don’t know how I would prove you wrong. But it certainly is not the most natural explanation.” – Chris comment #37

You’re neglecting the time delay in light coming from more distant objects, which is the whole point for the case of cosmology. For cars, the distances are small enough that the delay time in information coming to you is trivial.
For galaxies billions of light years away, you’re seeing them as they were in the past. In this case, as Minkowski states, you have to accept that seeing an object at distance r is the same thing as looking back in time r/c seconds ago.

Two things are varying as you look to greater distances: distance and time. The car analogy ignores the variation in time, which is trivial. But in cosmology this variation in time past is not trivial, and if we differentiate the Hubble velocity correctly we get acceleration

a = dv/dt = d(Hr)/dt = rH^2

which is an accurate prediction made in 1996. It was confirmed. There is no speculation involved in spacetime, the plot of recession velocity versus distance r (or time past T = r/c), or the rules of differentiation. There is also no speculation involved in dH/dt = 0 for the case of looking to greater distances, because the Hubble constant is a constant when we look to bigger distances: v/r is constant because top and bottom are proportional. The Hubble constant is only not a constant when you get away from spacetime and just consider a variation in absolute time. So there is no speculation in predicting the acceleration.

It’s simple physics and mathematics all the way!


“a = a_0 t^k, H = k t^(k-2), so k = 2/3 implies H ~ 1/t^(4/3).” – SomeRandomGuy

If the universe’s horizon radius increases as

R ~ t^(2/3), [Equation 1]


v = dR/dt = (2/3)t^(-1/3) [Equation 2]

Now, since H = v/R, using Equations 1 and 2 we get:

H = v/R = [(2/3)t^(-1/3)]/[t^(2/3)]

= (2/3)/t

This is my result, H = (2/3)/t. Your result H ~ 1/t^(4/3) is just plain wrong, and I’ve no interest in trying to help you find out why since you are rude and ignorant of physics.


“You do realize, of course, that this means the observed expansion would be geometrically like any explosion in 3D, with a central point where it all started? And that since we observe the same rate of expansion in all directions, we would have to be located at that point, i.e. at the center of the universe, for your picture to work?” – SomeRandomGuy

What I realise is that science is not about prejudice, it’s about facts and making predictions that are subsequently confirmed by observations. If you have a theory based entirely on observed facts that has made checkable unique predictions that have been confirmed, that theory may be correct.

Regarding our place in the universe, I refer you to the largest anisotropy (the cosine variation in the sky) in the microwave background radiation.

In the May 1978 issue of Scientific American (vol. 238, p. 64-74), R. A. Muller of the University of California, Berkeley, published an article about this, titled “The cosmic background radiation and the new aether drift”, stating:

“U-2 observations have revealed anisotropy in the 3 K blackbody radiation which bathes the universe. The radiation is a few millidegrees hotter in the direction of Leo, and cooler in the direction of Aquarius. The spread around the mean describes a cosine curve. Such observations have far reaching implications for both the history of the early universe and in predictions of its future development. Based on the measurements of anisotropy, the entire Milky Way is calculated to move through the intergalactic medium at approximately 600 km/s.”

Most of this 600 km/s velocity is due to our galaxy, the Milky Way, being locally attracted to the larger galaxy Andromeda, so it may be an upper limit on the average speed of the Milky Way mass motion. Now suppose the universe was more like Dr Chris Oakley’s explosion than the curved boundless geometry of mainstream general relativity: since the universe is flat and in any case curvature appears to be a classical approximation to a lot of graviton interactions, if quantum gravity is correct.

Distance is the product of velocity and time, and if we multiply 600 km/s by the age of the universe, we find that the matter in the Milky Way would have moved only 0.3% of the horizon radius of the universe in 13,700 million years.

If the average speed was less than 600 km/s, it would be even closer to the centre of the universe. So it doesn’t pay you to be biased either way. There are lots of problems with multiplying the 600 km/s speed deduced from the major anisotropy in the cosmic microwave background by the age of the universe to obtain our distance from the “centre” or “origin” of the universe. But they can probably all be overcome. Muller’s argument that this is a “new aether drift” in 1978 didn’t catch on, because of relativity. I don’t want to argue about speculations.

I’m mentioning this just as a counter argument to you. I made a fact based prediction that was subsequently confirmed. You then make a comment saying that if it is right it implies we’re at the middle of the universe. Well, I don’t care where we are, only that the prediction works. Copernicus is referred to as a defender of science for arguing that we’re not at the centre of the universe. I think science is quite different to any sort of prejudice: science is not about defending speculations that we are or are not here or there. It’s about establishing facts!


Further support for the result of my calculation in comment #42 above can be found in Marc Lachièze-Rey’s textbook, “Theoretical and Observational Cosmology”, 1999, p 384, available online at:

For horizon radius expansion proportional to t^(2/3), you get H = (2/3)/t.

The same also occurs in Lars Bergström and Ariel Goobar, “Cosmology and Particle Astrophysics”, Springer, 2004, p. 202:

“For a flat, matter dominated FLRW [Friedmann-Leimatre-Robertson-Walker] model, a(t) ~ t^(2/3), (da/dt)/a [this (da/dt)/a = H, since a is radius here] = 2/(3t) …”

I’m very busy now and I hope that no more insulting rubbish from the totally ignorant pseudo physicist SomeRandomGuy will appear.  I won’t have time to respond to it any more.  He doesn’t read anything I write anyway, so what’s the point in trying to explain physics to someone like that?


Before disappearing back to SQL database ASP programming for good, just one more comment about Chris Oakley’s point in comment 37, that we may be seeing stars with different velocities at different distances because stars started from one point and moved with different speeds.  This is something I responded to earlier in comment 4 (unfortunately I didn’t turn off italics at one point, so the while section is in italics as a result).  Eddington discussed that idea in his book “The Expanding Universe”, referring to papers in Nature which discredited it.  The distribution of speeds you need turns out to be contrary to the Maxwell-Boltzmann distribution for a gas like the hydrogen cloud that the universe was soon after the big bang. But let’s assume that is one possibility.  That predicts no cosmological acceleration!  My argument, a = dv/dt = d(Hr)/dt, does predict cosmological acceleration of the right size, which I think is evidence that it might be right.  I then went on to predict the strength of gravity and other things, again using simple facts.

“As an aside, why are your “spin 1 gravitons” causing repulsion only over cosmological distance, and attraction on all scales at least up to galactic? How does that work, exactly, given that exchange of spin 1 bosons is repulsive for equal charges, and you are using mass as charge? Is the mass of the moon of opposite sign to that of Earth?” – SomeRandomGuy

See for the answer.  All masses repel one another by exchanging gravitons.  The more mass, the more repulsive charge.  If you have two small masses, two planets or nearby galaxies, they will repel each other slightly, but they’re being pushed together harder by gravitons exchanged with the surrounding universe, involving bigger masses and a convergence of gravitons.

The outward radial acceleration from us of mass m is a = dv/dt = rH^2.  The second law of motion gives outward force for that mass of F = mrH^2.  The third law of motion suggests that there is an equal reaction force, F = mrH^2, directed radially towards us.  This quantifies spin-1 graviton predictions for low energy, where only the simplest Feynman diagram contributes significantly to the result, so the path integral becomes very simple and can be evaluated geometrically as Feynman did for QED (see for a discussion of how this works).

Now the graviton force F = mrH^2 contains mass m and distance r, so it is trivial for relatively small masses and relatively small distances, but is significant for marge masses and/or larger distances.

Two nearby masses get pushed together because they exchange gravitons more forcefully with the surrounding universe than with each other.  So the fundamental particles in the Moon are pushed towards the Earth repulsion of immense distant masses more than by graviton impacts from gravitons exchanged between the Earth and the Moon. This is very slightly like LeSage’s pictorial gravity from the Newtonian era (it was said to have been first proposed by Newton’s friend Fatio but Newton didn’t like it because at that time it couldn’t be made to work and make checkable predictions), which was generally discredited because:

1. It couldn’t usefully predict anything checkable like G
2. It wasn’t a gauge theory of virtual radiation (graviton) exchange, so the real radiation it postulated as the exchange radiation would cause drag on moving bodies, heat up bodies until they glowed red how, and would also diffuse into geometric “shadows” to make gravity fall off much faster than the inverse-square law.’s_theory_of_gravitation

(I also have a discussion of the errors somewhere on my blog.)

The fact-based calculations you’re talking of differs from the LeSage model in that it’s a gauge theory of quantum gravity, which does make predictions of cosmological acceleration, G, and other things, and which does not have the defects of LeSage’s theory.



I don’t have much time for discussions. If you knew cosmology, you’d have known the fact that t^(2/3) expansion leads to H = (2/3)/t.  You don’t know anything about it. Your calculations are irrelevant and wrong.

“The main points are of course unaffected: you are saying that metric theories of gravity in general and GR in particular are wrong, despite all evidence to the contrary, and should not be used to do cosmology, that spacetime is static and we are located at the center of the universe, and that gravity is mediated by “spin 1 gravitons”, which would make it repulsive between masses of equal sign.”

No, I’m not saying that.  You’re saying that.  What I am saying is a sequence of facts:

Fact 1: the universe is accelerating, confirmed by Perlmutter and others since 1998.

Fact 2: the acceleration was predicted by a = dv/dt = d(rH)/dt = rH^2 back in 1996.

Fact 3: the spin-2 graviton idea relies on a path integral including only two masses: so it forces the exchange of gravitons to have the right spin to cause attraction when exchanged.  It makes no falsifiable predictions (string theory of gravitons has a landscape of 10^500 vacua, which can’t be checked).

Fact 4: If you correct the path integral for gravitons so that you include graviton exchange between all mass-energy(gravitational charge) in the universe, instead of just two masses as Pauli and Fietz did in the 1930s when arguing that gravitons have spin-2, you find that gravitons have spin-1 and the basic graviton interaction is the Feynman diagram of virtual radiation being exchanged by analogy to radiation scattering off charge.

Fact 5: This predicts the strength of gravity, and other things.

Your statement that I’m saying that all metric theories of gravity are wrong is in error.  I’m saying are facts. (Quite a few metrics of general relativity are useful under certain conditions, where they approximate the underlying quantum gravity dynamics very well.) I’ve no interest in arguing with time-wasting bigots about whether approximate metrics are wrong or right.  Life is short and what matters are facts, not uncheckable controversies.


On the speculative nature of conjectures concerning spin-2 (attractive or ’suck’) gravitons, Richard P. Feynman points out in The Feynman Lectures on Gravitation, page 30, that gravitons do not have to be spin-2, which has not been observed.


“My solution (simple version): Yes, Hubble’s Law implies that distant galaxies are accelerating away from one another. However, this has nothing to do with the so-called acceleration of the universe. The latter term refers to the observation that the universe expansion has recently speeded up (an acceleration of the universe acceleration above if you like.)” – Dr Cormac O’Raifeartaigh

Thanks for putting the mainstream official case so eloquently. I think that this is wrong for two reasons: first, the universe isn’t “recently” speeding up.  The acceleration is observed at the greatest distances, i.e. the earliest times after the big bang.  Second, there is no evidence that the “dark energy” causing the acceleration of the universe is evolving with time.  Whatever is causing the cosmological acceleration, it is only a very small acceleration, 6*10^{-10} m/s^2 over immense distances, and you need to look to immense distances to detect it’s effect on recession rates.

Maybe you have Smolin’s book, “The Trouble with Physics”, where Smolin finds that the acceleration of the universe is quantitatively equal to approximately 6*10^{-10} m/s^2.  Smolin found it a coincidence that a = cH or RH^2. Presumably you do too, despite my derivation in 1996 of this acceleration from the Hubble expansion law, v = HR.  a = dR/dt = d(HR)/dt = RH^2.

If you look at Hubble’s law, H = 1/t where t is time since big bang in the observer’s frame of reference in flat spacetime with cosmological acceleration cancelling out gravitational attraction over large distances, and R = cT, where T is time past.

So v = HR = [1/t]*[cT] = cT/t

The whole point of Hubble’s law is that when you look to greater distances R in spacetime, the increase in v is matched by the proportionate increase in R, so v/R = constant = H.  If H = 1/t, when looking out in spacetime, the fact that H is constant makes also t constant.

So t is not a variable in spacetime!  Two variables in the equation v = cT/t are v and T.  Hence, in spacetime, a = dv/dT = d(cT/t)/dT = c/t = cH = 6*10^{-10} ms^{-2}.

This is physically and mathematically legitimate, and makes an accurate prediction.  The only objections I’ve ever received have been based on errors, misunderstandings, or the idea that physics is mainstream orthodoxy and the obnoxious but prevalent idea any new developments based on deeper understanding of the basics must be dismissed as wrong automatically.

This is a very tiny acceleration and is therefore only observable over immense distances.  Perlmutter’s group back in 1999 came up with a computer program to detect the supernova signatures automatically from CCD equipped telescopes, which was an innovation.

The acceleration is only observable over vast distances, corresponding to relatively short times after the big bang.  Therefore I don’t think that you can claim that this acceleration is “recent”.

In spacetime you are looking back to earlier times with bigger distances.  In the time taken for light to travel from a distant star to you, the star will presumably have receded a further distance.  One way to get around the two distance scales is through spacetime, using the travel time of light to measure how far away things are.  If you stop thinking about distances and think about times past instead, then the velocity-distance relationship of Hubble becomes a velocity-time relationship.  The funny thing is that the maths predicts the correctly observed cosmological acceleration.

“My solution (more sophisticated version): … Relativity tells us that that the expansion of the universe is an expansion of space-time (or space expanding as time unfolds). Hence, the common ‘explosion-picture’ of galaxies rushing away from one fixed point is simply wrong. Instead, space itself is expanding and this expansion has a scale factor. The recent evidence of ’acceleration’ simply suggests that the scale factor has increased in the last few million years. (This is a surprise because most cosmologists expected the expansion to slow down, if anything, due to gravitational effects)….” – Dr Cormac O’Raifeartaigh

Your sentence:

“The recent evidence of ’acceleration’ simply suggests that the scale factor has increased in the last few million years.”

I’m worried that your “few million years” timescale is not consistent with Perlmutter’s 1998 discovery of cosmological acceleration, using specifically supernovae at half the age of the universe, i.e. 7,000 million years.

Also, there has been quite a lot of criticism of the concept you mention of “expanding space”:

“Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?

” ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’

“Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept,’ he says. ‘Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.’ ” –—-everyweek-questions-about-the-big-bang-flood-into-the-new-scientist-officesowe-thought-it-was-about-time-to-let-some-experts-loose-on-the-subject-.html

I don’t think that Dr Chris Oakley, SomeRandomGuy, or yourself really grasp this problem.  I think I do after twelve years of battling against ignorance everywhere, although there is always room to improve the communication of facts (although the more forcefully the facts are presented, the more angry the opposition to progress!).