Not having read your detailed discussion, this may be slightly off-track; but I have always felt that the simplest explanation of the time-dependent change in the acceleration of the Universe (a gradual slowing of the expansion rate of the Universe from its beginning until about 6 billion years, and a gradual acceleration ever since then can be most easily explained by Einstein's suggestion that an excess of mass compared to empty space tends to slow the expansion, while a deficit of mass compared to empty space tends to speed it up VERY easily explains all that we've observed. When the Universe was much smaller, its mass was larger than the volume of empty space, so the gravity produced by the mass exceeded the critical density, and the Universe slowed. But as it grew the mass remained the same while the volume of empty space, until around the aforesaid 6 billion year ago time the effects of mass became equal to, and is now only about 27% of the amount needed to balance the expansive effect of empty space, so that ever since then the rate of expansion has been increasing, and as the mass to space ratio declines to nearly zero, the rate of expansion will asymptotically approaching its final value. Since the mass to volume ratio is already so small I expect that the final rate of expansion (about 70 km/sec/Mpc) won't be much larger then now (probably between 80 and 90 km/sec/Mpc). This simple view requires no fantasy such as dark energy, which in my view is an abomination invented merely to justify pointless papers, and retain the long-disproved theory that the mass to space ratio was 100% of the "critical" value, albeit in a different form from its original formulation. And it sounds to me (just reading your summary) that what you are proposing is very similar to that, and if so, I would highly recommend it

Note: I strongly believe in Occam's Razor, and as the simplest explanation of the changing rate of expansion is simply to accept Einstein's original thesis, whence the explanation given above.

Courtney SeligmanThank you. Very interesting idea, but how are the values in this derived?

The basic idea comes directly from Einstein's Theory of General Relativity. Specific rates of expansion are determined from observations of the nature of stars in our and nearby galaxies (primarily Cepheid variables for nearby galaxies, and a particular kind of supernova in more distant ones), which allow us to compare the observed recessional rates of galaxies at various distances to their distances determined by "redshift-independent" distances. As you look further out you're looking into the past, and at extremely large distances the RIDE (redshift-independent distance estimates) divided into the recessional velocity yields greater recessional speeds per Mpc, hence the statement that those speeds were once greater than now, and rapidly then gradually slowed down until about 6 Bya (billion years ago), and at closer distances the values get slightly larger, indicating an increase in the rate of recessional since that time. Since measuring the ACTUAL distances is uncertain, dividing them into the CMB (Cosmic Microwave Background) recessional rates (determined by the redshift of spectral lines as a result of the movement of galaxies away from us) is uncertain, but there is no doubt that speeds WERE faster and slowing down early on, but have speeded up a little in the last 6 billion years. The CURRENT rate is 70 km/sec/Mpc, but there are two "firmly" established values, one about 1 1/2 km/sec/Mpc less than that, and the other about the same amount higher than that; so that the average is almost exactly 70 km/sec/Mpc. The reason for the discrepancy between the two values is currently a mystery, but the newest generation of space and (enormous) ground telescopes will hopefully lead to better values for the rate at all distances, and therefore all times.

One problem in interpreting the results is that you need to show the "shape" of the Universe as a whole in order to correct for the delay in the time it takes the light from distant objects to get to us, due to the expansion of the intervening space during that time. There is no doubt that on the largest scale that geometry is "hyperbolic", but the "largest scale" is so much larger than the distance we can see that any given part of the Universe that we CAN see looks essentially "flat" (just as any part of the surface of the Earth LOOKS "flat", even though its overall shape is a globe). So when feeding the observed recessional value into a calculator that takes the expansion of the Universe into account, it's best to use "flat" or Euclidean geometry. You also have to insert the value of the current expansion rate (because of the problems with differing estimates I use 70 km/sec/Mpc in using recessional velocities of distant galaxies to get redshift-based distances, and 27 percent of the "critical" mass for the amount of mass as compared to the amount of empty space (that's based on the rate of rotation of the outer regions of nearby galaxies, and the amount of mass required to keep the galaxies stable at that rate). The 70 is as discussed above accurate to about 1 1/2 out of 70 km/sec, the 27 may be correct, but the observed recessional velocities are relatively accurate except in rich clusters of galaxies, where the gravitational interaction between the galaxies can increase or decrease the "correct" recessional velocities by as much as 1000 km/sec. It would take careful study of many papers and observations to verify this; but summaries of the results of such studies do yield values close to the numbers I quoted above.

One important result of this is that in the EXTREMELY distant future (trillions of years from now), every galaxy further from us than the Virgo Cluster galaxies (of which we are a distant outlier) will be so far away that where they are now will be beyond the Cosmic Horizon then, and not visible at all, so that the Universe will look extremely empty. But of course all life in our galaxy (and probably everywhere else in the Universe) will be long extinct, so there be no one or thing around to observe that; and since even small changes in the view will take billions of years, no life on Earth or in our Solar System will still exist, so all anyone (or any thing) that can ever observe the Universe will see essentially the same thing that we see now).

Hi everyone,

I find it deeply interesting to ask: “What if the cosmological constant were redefined as the average energy density distribution constant of the cosmic vacuum?” I’ve never thought about the cosmological constant this way before, even though I published a paper on “average energy density”—not as a constant, but as a parameter in my model (Mullat, 2016, The Journal of Cosmology, Vol. 26, No. 18, pp. 14992–15015, link), titled “On the Possibility of Replacing Time in Cosmology with the Average Density of Matter.”

However, I’ve recently found what I think is an even better interpretation: considering it as an average absorption coefficient. This idea was inspired by Danilatos’ paper:

Danilatos, G.D. (2020) Novel quantitative push gravity/field theory poised for verification. North Bondi, Australia: ESEM Research Laboratory (link, 8.02.2025).

So, my question is: Would it be reasonable to reinterpret Einstein’s cosmological constant along these lines—as an absorption parameter rather than a fixed constant? If so, that would suggest that my paper (attached) is on the right track, even though some might dismiss it as rubbish.

Best regards,

JM

Courtney Seligman It's good to have ideas, but they need to be compatible with existing theories and well proven

Joseph Emmanuel Mullat Honestly, it's a very obscure read, and I suggest you refer back to similar, high-powered studies to learn from their writing style and wording.

Thank you for your comment. This is my problem. I did not write the article as an academic one. In fact, it is a kind of free style for a layman. However, the mathematics has been tested for many years. Do you have your own articles as examples of style in this direction?

My best wishes. Joseph Mullat

Re any reference, the March 28 issue of New Scientist has an article about various cosmological theories, and notes that based on the expansion rate of the Universe at various past and present time(s) as explained by so-called "dark energy", the actual expansion rate appears to be following the same pattern of changes in the expansion of the Universe as my discussion of Einstein's General Theory of relativity, and suggests that the current expansion rate appears to be asymptotically approaching a fixed value (whereas it was originally assumed that it would continue to grow forever, and might possibly became so extreme as to cause a "Big Rip"). This statement, explained in more detail in the prior part of the afore-mentioned article, appears to justify the supposedly too simplistic version that I proposed, which is based entirely on the prediction by Einstein that if the mass of the Universe exceeded the amount of empty space then it would eventually collapse, but if the empty space exceeded the mass, it would expand (and continue to do so forever). Unfortunately, at that time, what we thought the Universe was, we now was only OUR galaxy, as the existence of other galaxies was not known at that time and remained a debatable topic for another decade, and as a result Einstein concluded that since our Galaxy was obviously stable, there must be something wrong with his theory, hence the execrable constant "lambda" added to force the "Universe" to be stable. As anyone who is familiar with the history since then, when Hubble proved that the Universe of GALAXIES WAS expanding, Einstein said that his invention of lambda was the biggest mistake of his career (although his rejection of quantum mechanics was probably a bigger mistake; but at least that mistake didn't result in the publication of thousands of completely useless papers).

As for the comment criticizing my answer because it doesn't use the grammar, notes and references required for a professionally published paper (though the few papers I published in graduate school DID follow such requirements), my answer was not intended to resemble a "paper", but was meant to be an explanation as simple (yet complete) as possible (as Einstein put it, the best answer to any question was one that even a child could understand, and although I don't consider my answers that simple, or my readers children, I try to follow that philosophy when posting answers on this site).

Note: Since I have spent more time answering this question than I should have, and thereby wasted time that could have been spent on my current work, this will be my last post here, regardless of any further comments condemning my answers, partly because I don't want to devote more time beating a dead horse, and partly because I'm sure that no one now alive will live long enough to see who is right. So although I consider the concept of dark energy a crock invented to keep the mass/space ratio at 100% once it was proven that the ratio is at most around 27% and gradually moving toward zero, I don't expect to live for the millions or gazillions of years for that to be obvious to those anxious to publish papers predestined for the trashbin of history. ( I know it's publish or perish, but we are all going to perish, so I'm not interested in getting on that merry-go-round. )

Dear Courtney Seligman,

I read your comment in the debate and appreciated it—it shows how much interest cosmology sparks in many people. I’ve been fascinated by these questions myself since I was a teenager.

Cosmology, especially when it comes to academic publishing, can be incredibly complex. It doesn’t always follow the traditional path laid out by general relativity, even though many still look to Einstein’s work as a foundation.

I’ve taught myself how to co-author and self-publisher of a high-quality book, serving also as the technical editor. Some of my own ideas are included in it (please see the attachment). You don’t need to read the whole thing to get a feel for it—though I hope you find it both informative and a bit entertaining. One key part is my article on the FLRW metric, which is central to the book.

Here’s one of my main ideas: I see the vacuum of space as a kind of matter, just like regular matter we can see. In my view, what people usually call “dark matter” might simply be vacuum itself. One critique of my paper is that time is necessary to make predictions in cosmology. I disagree—I believe predictions can be made without relying on time as a required factor.

Let me give an example: the Hubble constant (Ho). Despite its name, it’s not actually a constant. Just like the “Big Bang” wasn’t really a bang, I only use these terms because they’re familiar. In my story, Ho started out small, then rapidly increased to a peak of about 87.31, and has since decreased to around 73.8. Some might say this implies a time-based prediction, but I think it’s more like how we say, “It’s going to rain tomorrow.” We accept the prediction without needing an exact time slice when it will happen.

So, what happens next in this Hubble story? According to my theory, Ho will keep decreasing until it reaches about 15 km/megaparsec. This will mark the Universe’s final death phase—the expansion will slow and eventually stop. After that, the Universe’s “dead body,” so to speak, will keep expanding more and more slowly, until everything comes to a halt. This is the speculative tale I developed by solving what I call the Γ-equation.

Of course, no one can currently test or prove my predictions—nor replicate my results in experiments. But speculation is part of science too. Some physicists, even those well-versed in Einstein’s general relativity, believe they’re working with ultimate truths. Sure, general relativity explains things like Mercury’s orbit, but that alone doesn’t make it immune to being questioned—or compared to more imaginative models like mine.

Best wishes,

JM

What if gravity is fundamentally repulsive, and only apparently attractive at smaller scales? Consider how a common sponge liquid is catalyzed and expands into a structure resembling the large-scale structure of the universe, with the only driver being repulsive -- the variable cosmological constant regarding the universe.

https://www.linkedin.com/pulse/derivation-cosmological-constant-warren-frisina-zpvme/?trackingId=o1svCnjCTsiSKJRe%2BtPTcw%3D%3D

Max Li

Yes, in fact the cosmological constant must be redefined as describing the minimum energy density of the cosmic vacuum. It is proportional to the Ricci curvature of a static non inflating universe. This energy density compensates for the negative energy density of gravitational fields. Active stars permanently emit this kind of energy density, because they are full of mass, which gets accelerated.