Inverted Neutrino Hierarchy Disfavored By DESI

The DESI collaboration has found that the sum of the three neutrino masses should be less than 0.071 eV at 95% confidence (assuming as a prior only that the sum of the neutrino masses is greater than zero). This disfavors an inverted neutrino hierarchy the demands roughly a minimum of a 0.100 eV sum of neutrino masses, while a normal neutrino hierarchy requires a minimum sum of neutrino masses of only about 0.059 eV. The preference for a normal hierarchy is only about two sigma, however. This estimate is heavily dependent upon the assumed dark energy model, however, and assumes a fixed cosmological constant. 

The upper bound on the sum of the neutrino masses from direct measurements at KATRIN is about 1.35 eV, a cap that is likely to fall by about 0.75 eV to 0.60 eV when the KATRIN experiment is concluded. The upper limit based upon cosmology observations, as of 2020, was about 0.130 eV, and DESI significantly tightens this bound. Of course, direct measurement bounds on the absolute neutrino masses remain much weaker than those from cosmology, and will continue to be weaker for the foreseeable future.

The number of effective neutrino species N(eff) is estimated by DESI to be 3.18 ± 0.16 compared to the expected value of 3.044 if the only neutrinos are the three Standard Model active neutrinos, a possibility that is compatible at the one sigma level. This disfavors a model with four or more neutrinos impacting N(eff) at more than the five sigma level (as well as disfavoring the already ruled out possibility that there are two or fewer neutrino flavors at more than five sigma), consistent with past cosmological estimates of N(eff). This is a slightly higher value of N(eff) than a prior DESI analysis, due to this paper's additional consideration of "full shape" information, but the difference is immaterial given that the number of neutrino flavors is a quantity that changes in integer increments.

The loophole in the N(eff) measurement, however, is that a very massive fourth neutrino species would not register as a neutrino contributing to the number of effective neutrino species.

For example, a 50 GeV mass fourth generation active neutrino would not change N(eff).

In addition to its conclusions about neutrinos, the DESI collaboration concludes that the late time Hubble constant value is 68.40 ± 0.27 in  the usual units, which is closer to the CMB based determination of it of 67.66 ± 0.42, which is consistent with the new DESI estimate at the 1.5 sigma level, than many other efforts to determine the late time Hubble constant have suggested. The DESI results still prefer a non-constant amount of dark energy, however.

The Hubble Tension Considered

When Did We Learn That The Universe Is Expanding?

There is no reasonable doubt that the size of the observable universe has expanded over the last 13.8 billion years or so from time when it was dramatically smaller than it is today called the Big Bang.

Why this happened and the details of the very first moments of it are still the subject of ongoing research, but there is near universal consensus about the broad outlines of this process from Big Bang nucleosynthesis (end about 15 minutes after the Big Bang in a conventional cosmological chronology) to the present.

A 1924 paper by Carl Wirtz, which was one of the earliest to note the astronomy observations now explained with the expansion of the universe and to reach the conclusion that the universe was expanding has been made more widely available in an English translation on the 100th anniversary of its publication. 

Better know cosmologist Edwin Hubble, who read Wirtz's work, reached the same conclusion from the data and improved upon it by proposing "Hubble's Law" which quantified and characterized this expansion with what has come to be known as Hubble's Constant, in 1929.

Quantifying and characterizing any changes in the rate at which the universe has expanded has proven to be a more challenging problem which we are still wrestling with a century later.

General relativity with a cosmological constant is an idea that had been proposed only a few years earlier when Wirtz and Hubble made their early ground breaking conclusions that astronomy observations supported an expanding universe.

Once Hubble's Law was proposed, the race was on to measure Hubble's constant, sometimes producing conflicting results. Some of the early estimates of it (in (km/s)/Mpc units), one of which predated the formal publication of Hubble's law, were as follows (often with significant uncertainties or no estimated uncertainties):

1927  625

1929  500

1956  180

1958    75

early 1970s 55

mid-1970s 100

late 1970s to 1994 50-90

The best fit values for estimates made since 1994 have ranged from 69.8 to 76.9, and the uncertainties in those estimates has more or less steadily fallen to as little as 0.42 for CMB based indirect early time estimates and as little as 1.0 for some late time direct measurements.

Notably, it took less than 30 years from the publication of Hubble's law to get measurements of the value of Hubble's constant that were reasonably close to the modern measured value.

Previous discrepancies between measurements of the Hubble constant which is functionally related to the cosmological constant of general relativity, have had discrepancies and tensions (much bigger in magnitude than the current "Hubble tension") before, but those were always resolved by reducing sources of measurement uncertainty in the differing values of the Hubble constant from different kinds of observations.

The LambaCDM "Standard Model of Cosmology" assumes that this expansion is explained by general relativity with a cosmological constant. The source of  this phenomena due to this cosmological constant in the LambdaCDM model is often called "dark energy."

The Hubble Tension

The simple explanation of this expansion with a constant cosmological constant in general relativity (which by the way, facially, at least, is a gravitational modification and not a new substance or separate force), which leads to a constant value of the Hubble constant, however, has broken down in the last few years. 

Increasingly powerful space telescopes have shown a tension between the high precision determination of the Hubble constant inferred from the Planck cosmic microwave background (CMB) observations early in the universe's history, and late universe measurements of the Hubble constant.

[M]easurements from the Planck mission published in 2018 indicate a lower value of 67.66 ± 0.42 (km/s)/Mpc, although, even more recently, in March 2019, a higher value of 74.03 ± 1.42 (km/s)/Mpc has been determined using an improved procedure involving the Hubble Space Telescope. The two measurements disagree at the 4.4σ level, beyond a plausible level of chance. The resolution to this disagreement is an ongoing area of active research.

The chart below from the same link summarizes some of these recent measurements. 

New late time measurements in the last few years from sources including the James Webb Space Telescope and DESI, since the chart below was made, with one or two exceptions (such as a July 2023 estimate based upon astronomy observations of kilonova that produced a late time value of Hubble's constant of 67.0 ± 3.6) that can't cancel out independent late time measurements to the contrary, have generally strengthened the evidence that the Hubble tension is real and not just a product of observational uncertainty.

Even in the face of the Hubble tension, Hubble's Law is still a good first approximation description of the rate at which the universe is expanding. The difference in the measured values of Hubble's constant, in measurements of its value from times that are up to about 13 billion years apart, is less than 10%. 

This is still highly statistically significant (more than 5 sigma), because the relative uncertainty in the difference between the most precise measurements is less than 2%. But in plenty of astronomy contexts, a field not generally known for its high precision by physics standards, 10% precision is still excellent.

But from a fundamental laws of physics and cosmology perspective, if these results are confirmed, the consequences are profound. 

Any changes to Hubble's constant over time demand that the simple cosmological constant explanation of these observations be discarded, effectively rewriting a part of the equations of general relativity with deep cosmological implications, in favor of a new theory.

Possible Resolutions Of The Hubble Tension

Time will tell how the Hubble tension is resolved.

There are basically three possible resolutions to the Hubble tension (more than one of which could each provide a partial explanation).

1. Indirect Early Universe Estimates Are Wrong. The CMB based determination of Hubble's constant in the early universe (about 380 million years after the Big Bang according to the LambdaCDM model) is flawed somehow, in a way that underestimates the value of the Hubble constant in the early universe. 

McGaugh, for example, has suggested that this is a plausible full or partial explanation.

For example, maybe the Planck collaboration omitted one or more theoretically relevant components of the formula for converting CMB observations to a Hubble constant value that were reasonably believed to be negligible (indeed, it almost certainly did so). But it could be that one or more of the components omitted from the Planck collaboration's calculated value of Hubble's constant from the CMB data actually increase the calculated value by something on the order of 9% because some little known factor makes the component(s) omitted have a value much higher than one would naively expect.

Also, since the indirect determination of the value of Hubble's constant from CMB measurements is model dependent, any flaw in the model used could cause its determination of Hubble's constant to be inaccurate.

An indirect CMB based determination of Hubble's constant is implicitly making a LamdaCDM model dependent determination of how much the universe had expanded since the Big Bang at the time that the CMB arose. If the LambdaCDM model's indirect calculation of Hubble's constant predicts that the CMB arose later than it actually did, then its indirect determination of the value of Hubble's constant would also be too low, and a high early time value of Hubble's constant would resolve the problem.

This is a plausible possibility because the James Webb Space Telescope has confirmed that the "impossible early galaxies problem" is real, implying that there is definitely some significant flaw (of not too far from the right magnitude and in the right direction) in the LambdaCDM models description of the early universe, although the exactly how much earlier than expected galaxies arose in the early universe (which is a mix of cutting edge astronomy, statistical analysis, and LambdaCDM modeling) hasn't been pinned down with all much precision yet.

The impossible early galaxy problem is that galaxies form significantly earlier after Big Bang than the LambdaCDM model predicts that they should. The galaxies seen by the JWST at about redshift z=6 (about 1.1 billion years after the Big Bang) are predicted in the LambdaCDM model to apear at about redshift z=4 (about 1.7 billion years after the Big Bang).

If the CMB arose more swiftly after the Big Bang than the LambdaCDM model predicts it did but the amount by which the universe had expanded at that point was about the same, in much the same way that galaxy formation actually occurred earlier than the LambdaCDM model predicted that it would, then that could fully or partially resolve the Hubble tension.

The relationship between Hubble's constant and the amount of expansion in the universe at any given point in time is non-linear (it's basically exponential). So, figuring out how much of a roughly 55% discrepancy at 1.1 billion years after the Big Bang in galaxy formation time translates into in Hubble constant terms, at about 380 million years after the Big Bang, is more involved than I have time to work out today, even though it is really only an advanced pre-calculus problem once you have the equations set up correctly. But my mathematical intuition is solid enough to suspect that the effect isn't too far from the 9% target to within the uncertainties in the relevant measurements.

2. Late Time Direct Measurements Share A Systemic Error. The multiple different, basically independent, methods of measuring Hubble's constant in the late universe are flawed in a way that causes them to overestimate Hubble's constant in roughly the same amount.

The problem is that since several different methods have been used and reach similar higher values for Hubble's constant in the late universe, so the issue can't be one that is particular to only a single method of determining Hubble's constant.

For example, one explanation that has been explored is that the little corner of the universe around the Milky Way from the perspective of solar system observers has some local dynamics, or has local distortions that impact light at the relevant wavelengths reaching us in the solar system (e.g. due to localized gravitational lensing or local distributions of interstellar gas and dust) that has nothing to do with the expansion of the universe, but is indistinguishable, by the most precise existing methods used to measure Hubble's constant in the late time universe, from an increase in Hubble's constant of about 6.4 (km/s)/Mpc. 

I've bookmarked a number of papers exploring this hypothesis but haven't had the time to analyze them as a group or compile them in a blog post.

3. Hubble's Constant Isn't Constant. The third possibility is that Hubble's constant genuinely isn't constant and the rate of the expansion of the universe attributed to a cosmological constant in the equations of General Relativity is mistaken. Thus, new physics are necessary to explain these observations.

This is, of course, the most exciting possible answer. But I'll save consideration of some of these alternative theories to a cosmological constant for another post (and I won't address them in the comments to this post either). 

Suffice it to say that there are many proposals for alternatives that could resolve the Hubble tension out there in the literature.

GR v. Asymptotically Safe Gravity

One alternative to general relativity, called asymptotically safe gravity, is one of the better established routes to solving the difficult problem of devising a theory of quantum gravity (which is necessary to integrate general relativity with the Standard Model of Particle Physics). 

This approach has a characteristic observable difference from general relativity: its black holes are smaller. But astronomy observations of actual black holes show that unmodified general relativity is a better fit than this alternative. So, this otherwise promising approach to quantum gravity may not be the right one.

According to the asymptotically safe gravity, black holes can have characteristics different from those described according to general relativity. Particularly, they are more compact, with a smaller event horizon, which in turn affects the other quantities dependent on it, like the photon ring and the size of the innermost stable circular orbit. 

We decided to test the latter by searching in the literature for observational measurements of the emission from accretion disk around stellar-mass black holes. All published values of the radius of the inner accretion disk were made homogeneous by taking into account the most recent and more reliable values of mass, spin, viewing angle, and distance from the Earth. We do not find any significant deviation from the expectations of general relativity. Some doubtful cases can be easily understood as due to specific states of the object during the observation or instrumental biases.

Luigi Foschini, Alberto Vecchiato, Alfio Bonanno, "Searching for quantum-gravity footprint around stellar-mass black holes" arXiv:2411.09528 (November 14, 2024).