The simpler cosmology and astrophysics of the Rh = ct Universe

Updated: Feb 26

In today’s blog we discuss the Rh = ct Universe with Dr. Fulvio Melia, PhD at MIT, Professor of physics, applied mathematics and astronomy, at the University of Arizona, Professorial Fellow at Melbourne University and Distinguished Visiting Professor with the Chinese Academy of Science.

David: My understanding is that you have shown that in R = ct there are regions of the Universe that are causally connected at t*> 0 and that despite t* being small, it is enough to produce the isotropy we observe in the CMB. And the reason why others failed to acknowledge this is due to the incorrect assumption that R = ct implies a physical distance traveled by light, which would make causality impossible for all t > 0. Is this correct?

Fulvio: The Universe we see today appears to be causally connected across the sky, even when we look at opposite sides. The farthest we can see is the surface of last scattering (LSS), where the cosmic microwave background was produced. In the standard model, that corresponds to about 380,000 years after the Big Bang. This gives rise to the so-called "horizon" problem, since the size of the LSS at that time would not have been large enough for it to expand to the size we see around us today. Inflation was invented to generate an exponential spurt very early on in order to expand the LSS sufficiently by 380,000 years to fix this problem.

But the horizon problem exists only for cosmologies that had an early period of deceleration, like LCDM. As long as the Universe expanded at a constant rate, or accelerated, the problem does not exist because the LSS would have been large enough to grow as needed. In the Rh=ct cosmology, the Universe has expanded at a constant rate—the threshold condition for the horizon problem to be eliminated. So in this model, there is no need for inflation to have occurred. And the observations today are starting to show growing tension with the predictions of inflation anyway. So it probably never happened.

David: The R=ct universe must be older than the λCDM universe. This is attractive in overcoming the patchwork super-Eddington accretion solution proposal to the growth of supermassive black holes. Are the highest redshift quasars recently detected still compatible with Eddington-limited accretion in Rh = ct?

Fulvio: Actually, the age of the Universe is pretty much the same in both cosmologies. BUT the redshift dependence of the age would have been different. For example, the Universe would have been about 1.9 Gyr old by redshift 6 in Rh=ct, but only about 940 Myr in LCDM. But the latter would have slowly caught up afterwards, so that their ages today are about the same. HOWEVER, this factor 2 difference prior to z=6 is all that is needed to fix the early appearance of supermassive black holes and galaxies. And yes, Eddington-limited accretion would therefore suffice to explain the appearance and growth of these structures at such early times in the context of Rh=ct. As you know, one instead needs to introduce unproven, exotic mechanisms to create and grow them in the standard model.

David: Is the cause of the expansion in Rh = ct beyond the scope of the model?

Fulvio: Actually no. If one assumes (1) that General Relativity (GR) is correct and (2) that the Universe evolves according to the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime--which happens to be the only known solution to Einstein's equations that can be used for this purpose--then the expansion rate is very firmly constrained. Recent work has shown that the Local Flatness Theorem in GR actually permits the orderly expansion we see with FLRW for only two equations-of-state in the cosmic fluid. These are (i) ρ=p=0, which leads to Minkowski space, and is not at all relevant to the Universe, which obviously has a non-zero ρ (i.e., energy density), and (ii) ρ+3p=0, the so-called zero active mass condition in relativity (see The latter produces the expansion history in Rh=ct. So both the data and this recent theoretical argument are consistently pointing to steady expansion rate emerging in this model. Once an energy budget is given, say at the

Big Bang, the subsequent expansion history of the Universe is then fixed, and apparently needs to correspond to a constant rate, which we infer from a measurement of the Hubble constant. The latter appears to be one of the initial conditions at the time of the Big Bang, so it is not "predictable," but seems to be a variable that was set stochastically when the Universe was born.

David: Resolving the horizon problem in cosmology and the growth of giant black holes in astrophysics are two fundamental problems that defy easy solution in λCDM. A framework that solves both issues should attract attention. Is this feature recognized? What kinds of objections have you received? Are the objections squarely based on scientific arguments or have you experienced hesitation that stems from sociological issues?

Fulvio: This is indeed a very interesting question and I myself have been toying with the idea of writing a memoir about my experience with Rh=ct once I retire. Cosmology is one of the scientific fields with the most inertia. There are many thousands of active workers on this topic, numerous large-scale collaborations and instrument development, and many millions of dollars spent each year. I would estimate that about half of this community is thus not at all interested in entertaining new ideas, and they don't even bother to read the literature. They discount it offhand because they "don't have the time." The other half believes there are problems with the standard model, and many of them do listen, though with a great deal of skepticism. About 1/3 of the community follows the literature of new ideas quite seriously. So it's a mixed bag.

What I would point out is that there's only one way to make serious inroads in a field such as this. One needs to diligently focus on one piece of the puzzle at a time and work it thoroughly to produce a compelling result. This is what we've done over the past 15 years. It's been painstaking, but fruitful. We have now completed and published over 27 different tests, based on over 27 different kinds of data, from low to high redshifts, based on integrated measures (such as the luminosity distance) and differential quantities (such as the redshift-dependent Hubble rate). The examples you quoted above are but two of these 27 cases. And in all of them, the Rh=ct model has accounted for the data better than LCDM. It's becoming increasingly difficult for our stubborn colleagues to hold out. It will be interesting to see how far they can drag their feet.

By the way, so much has now been published about the Rh=ct model, that Taylor & Francis was willing to publish a monograph collating its fundamental tenets and results. There's a link to this book, which came out in November 2020, below.

David: On a separate note, how did your ideas about imaging the Sagittarius A star black hole come about?

Fulvio: Another interesting question! Back in the 1990's we were studying and trying to understand what Sgr A* is and how it produces its observed radiative spectrum. Believe it or not, even as recently as 25 years ago, there was still uncertainty about whether one could convincingly show that it had to be a black hole, as opposed to something like a star made of strange matter, among other possibilities.

Within a span of only 5 years, several key ideas and results emerged, some from theory and others from VLBI observations. Three of these came together by 2000 that allowed us to realize how possible an imaging experiment would be. In summary, these are the key ingredients: (i) The radio spectrum of Sgr A* suggests that the medium surrounding the black hole (where the radiation is produced) is optically thick up to the mm range, but becomes transparent at shorter wavelengths. This is an amazing feature that one could not have optimistically hoped for, but there it is. Nature has given us this window. What it means is that if our telescopes look at radiation shortward of the mm range, we can see photons produced everywhere surrounding the black hole, including from radiating gas behind it. That's the key to producing a "shadow" or a "silhouette." But this is not enough to make the experiment work. There are observational issues to deal with too. And this is where the other two "miracles" come in; (ii) light produced at the Galactic center has to pass through a lot of gas and dust in the plane of our Galaxy to get to us. It is therefore virtually impossible to image anything at that distance for most wavelengths in the mm-m range. But as you can guess, this hindrance is wavelength-dependent and, as it turns out, the size of Sgr A* is just right for us to start seeing through the murky Galactic medium shortward of the mm range; Finally, (iii) Earth's atmosphere absorbs most of the radiation entering from outer space. But it so happens that there's a tiny window where the absorption is virtually zero. It includes the mm and sub-mm range. All in all, the probability of all three of these occurrences happening would have been very small, but all three must be present for the imaging experiment to work.

Incidentally, in the case of M87 (the object imaged first), the second problem is non-existent

because M87 lies out of the plane, so there is far less dust and gas along the line-of-sight. It

is also a thousand times bigger, so the source changes much more slowly, allowing the imaging to be more precise.

Thank you for asking, David. Take good care, and I look forward to staying in touch.

David: Thank you Professor!

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