Is renormalization the answer?
The Hubble tension controversy is a measurement discrepancy of the Hubble constant. This constant is the rate at which the universe is expanding. It is measured in kilometers per second per Megaparsec because the farther two galaxies are from one another, the faster they move apart.
The Hubble constant is measured in two ways: (1) by observations of distant Supernovae that we can see both electromagnetically and, more recently, with gravitational wave detection and (2) by looking at the Cosmic Microwave Background (CMB), the echo of the formation of the universe and the earliest light we can see.
A great deal of progress has been made on both fronts in recent years which has led to the Hubble tension controversy. The value for the Hubble constant measured by observations of distant galaxies is 73.04 +/- 1.04 km/s/Mpc. The value for the CMB, as measured by the Planck spacecraft in 2018, is 67.36 +/- 0.54.
Thanks to improved statistical techniques and measurements correlating electromagnetic imaging with gravitational wave detection, the SH0ES experiment has pushed the first measurement to the point where we can say, with 5 sigma confidence, that this discrepancy is real and not just some experimental flub. This means that there is a one in a million chance that this is just some statistical fluke.
That confidence is the threshold in particle physics for the discovery of a new particle. Congrats, Hubble tension, you are officially real.
Something is fishy in cosmology.
Physics abounds with controversies, some real and some made up. An example of a made up controversy is the black hole information paradox, which is an argument between mathematical approaches to things falling into black holes. The math is real and from a certain perspective it is a controversy but the phenomenon is never observed so you can’t distinguish between solutions.
The Hubble tension is not made up.
The controversy hints at new physics and potential modifications needed to the aging ΛCDM model of the universe. This model assumes that dark energy, responsible for fluctuations in the expansion rate of the universe, arises from a cosmological constant, Λ, in Einstein’s equations of general relativity. This constant is the gravitational effect of empty space itself, which one would expect to be a constant, the density subject only to the expansion of the universe itself.
The Hubble tension, however, suggests that it is not constant at all but may have changed from the early to the later universe.
While the late time SH0ES measurements are model independent, the CMB calculations are based on the vanilla ΛCDM being correct.
The problem is made more interesting because of the absolute consistency of the measurements. CMB measurements all seem to agree with one another whether from the Planck spacecraft or Big Bang Nucleosynthesis (measurements of the formation of light elements in the early universe). Supernovae measurements also agree with one another. Gravitational wave measurements are less reliable but appear to agree with the supernovae ones. You can see that in this plot. The blue band are from measurements of Supernovae while the red band is from CMB.
This means that there is very clear evidence that something fundamental changed from the early to later universe and probably the ΛCDM, which by all other measures is a very accurate model, is wrong.
A review paper on this topic alone published June 2021 includes over 1000 references, indicating this is one of the hottest topics in cosmology in recent years.
In fact the number of competing models to explain the phenomenon is massive. There are dozens of particle models, dark energy models, modified gravity models, inflationary models, and a mixed bag of far out alternative physics.
Here is a good article on the whole controversy.
There are so many it is virtually impossible to go through them in this article, so I will just give you my take which is biased because I work in quantum gravity.
I think it very likely that the cosmological constant is not constant at all but a running constant, which is a well known feature of quantum physics. In this case, the constant was different in the early universe because of quantum effects that we know change constants of nature.
This is called the renormalization group flow approach, which is a terrible name for a phenomenon that arises in all physics. The basic idea is that if you have any model that is even moderately interesting it has scale dependency which means it behaves differently at one scale than another. Obviously, the scale of the universe has changed tremendously since its early days, especially the density.
There is some fundamentally small scale at which physics changes completely in a grand unification and our cosmological constant is implicitly dependent on both that scale and the scale of the universe now (or in the early universe, the scale then). It is the difference in those two scales that causes the constant to change.
I wrote an article on this idea using the stock market as an example.
How a dubious math trick became a law of physics, a stock trading analogy
You can use renormalization in any statistical model as long as it matches what is actually happening under the hood.medium.com
Scale dependency is everywhere in our world. Things that appear to be constants of nature are only so because we observe them at a particular scale. In particle accelerators, we know even supposedly fundamental constants like the interaction strength between charged particles changes with scale.
Let me explain with another example. Suppose you have a city where residents have settled. At first the city was sparsely populated. The city has a law however that says it cannot grow beyond 10 square kilometers. People live in peace and quiet at first.
The city dwellers can speak to one another at normal volumes at first. As more people move in, however, the old houses have to be torn down and apartment buildings put in their place to accommodate all the residents. The city becomes noisier and noisier. The city dwellers have to speak louder and louder to be heard. Eventually, however, no more people can move in and the whole city is torn down and a single giant building put in its place with completely sound proof apartments with telephones lines between units. The city is quiet again and people don’t have to shout.
This is an example of how scale affects things as they become more dense and energetic. The volume people have to speak to be heard is similar to a constant of nature. The tearing down of the whole city is similar to grand unification.
I think it likely that our universe has gone through such a transition and the cosmological constant has changed since the early universe.
This idea may explain the coincidence problem which asks why dark energy density is similar to matter density in the universe now. A running cosmological constant would enforce such a relationship. The denser the matter, the denser the dark energy.
The ΛCDM meanwhile assumes this is just a coincidence of our current epoch. The past matter was much denser, and in the future dark energy will be denser.
The renormalization answer is a good bet because we know that it affects constants of nature and, by all accounts, dark energy appears to be a constant related to the gravity of the vacuum. It would also be a very minor modification to our current model, swallowing it in a quantum theory of gravity without a lot of extra unobserved particle fields or other models.
Moreover, it might explain why vacuum energy is so different from what we expect it to be, by 120 orders of magnitude. (One with 120 zeroes after it.) It turns out that is about size of the observable universe in Planck lengths — the smallest observable length and the length scale at which we expect a grand unified theory to include gravity.
Could it be that if the universe were one Planck length in size the vacuum density would be that of a Planck size black hole?
Renormalization says yes and that at that scale the cosmological constant really is that big.
Further observations will likely only solidify the controversy, but we hope they will shed light on which solutions are wrong. Right now the field of cosmology is too crowded with ideas. We can only hope that one of them is the right one.
Pan, Supriya, et al. “In the realm of the Hubble tension-a review of solutions.” Classical and Quantum Gravity (2021).