The redshift-based distance ladder values of the Hubble constant are higher than that inferred by the cosmic microwave background. This discrepancy in the last few years has become highly statistically significant as we have collected more data.

One solution, dubbed early dark energy, posits dark energy making up ~7% of the universe at z~3000 which then turns "suddenly" into radiation. However, could a decay of dark energy during moderate redshifts, i.e. z<10, also reduce or eliminate the Hubble tension? Namely, my dubious logic is if dark energy was stronger in the past, where "past" means z~1-10, it would have given the universe more of a "push" than ΛCDM predicts, accounting for the higher expansion rate today.

We can evolve the Friedman equations with an initial flat-universe condition of T~3000K with the present-day baryon/microwave-photon/other particles ratio but with more dark energy than today (though still negligible until z<~10). I think this gives us enough initial conditions. Each fluid dilutes and contributes density/pressure to the expansion (de)celeration according to its own equation of state. Added to this is a decay of dark energy into radiation or "warm" matter. The rate of decay can be one of many scalar field models, but we are looking at Gyr time-scales. We stop the evolution when our photons hit 2.725K, and measure the Hubble constant.

However, I can't figure out the anisotropies of the CMB play into this picture? So I can't trust my original reasoning.

Edit: I am mainly looking from the perspective of resolving the tension itself rather than the physical plausibility of this occurring. It is possible that the decay is into "dark radiation" which would be hard to detect.


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To throw added confusion into the mix we have this result based on measurements with red giant stars. The use of luminous red giants leads to $H=70\ \mathrm{km/(s\ Mpc)}$ which is in between the CMB and Cepheid variable meter stick results. This suggests we may really have a problem with getting different meter sticks to calibrate together in a consistent way.

The CMB result $H=67\ \mathrm{km/(s\ Mpc)}$ and the Cepheid variable result $H=74\ \mathrm{km/(s\ Mpc)}$, pulling these numbers from memory and they are actually more exact, have stubbornly remained apart. Consider the FLRW energy constraint equation $$ \left(\frac{\dot a}{a}\right)^2=\left(\frac{8\pi G\rho}{3c^2}\right) $$ where the Hubble constant is $H=\left(\frac{\dot a}{a}\right)$. If there were some change in the Hubble constant in the early universe it might then means there is some $\delta\rho$ or mass-energy density. If this density $\rho$ is a vacuum energy then to posit a change would mean that about $10\ \%$ increase of vacuum energy is produced from some other form of energy. This would have happened since the CMB surface of last scatter around $380\,000$ years into the existence of the observable universe. That would be comparable to twice the matter we observe in the universe. So contrary to vacuum energy being decayed it would be increased.

There is some prospect the vacuum energy is not constant. There could be some $$ \dot\rho\sim3(1 + w)\rho $$ where for $w=-1$, which is close to observations from CMB, the vacuum does not change. However, things may be strange. We may have phantom energy that leads do the so-called big rip cosmology. There is also a prospect for pocket worlds in the multiverse interacting which would potentially change vacuum energy.

However, we have to make sure we have resolved issues with calibrating our cosmic meter sticks. Interesting cosmology may be lurking in the wings, but we should not fool ourselves if it turns out our techniques have calibration issues.

  • $\begingroup$ Decaying dark matter (w=0 -> 0<w<1/3) seems to alleviate the problem, see "Dark matter decaying in the late Universe can relieve the H0 tension". Why wouldn't decaying dark energy (w=-1 -> 0<=w<=1/3) accomplish a similar thing, as it also shunts mass/energy from a lower w to a higher w? $\endgroup$ – Kevin Kostlan Jul 20 at 14:54
  • $\begingroup$ I have not heard of such phenomenology proposed, but given that dark matter is proving more enigmatic it is possible. Current data by Reiss et al is for w = -1 with the +/- shifting it a tad more negative. That would correspond to $\dot\rho>0$. Is it possible that dark matter is "decaying" into dark energy? The problem with the question is that we are not entirely clear on how a quantum vacuum makes DE or even what DM is. Then again, maybe something like Verlinde's idea might feed into that. Who knows? $\endgroup$ – Lawrence B. Crowell Jul 20 at 20:12
  • $\begingroup$ There is a difference between phantom and DM -> DE. Namely phantom accelerates the universe (or slows down its deceleration) in the process of creating DE, but DM ->DE doesn't, so DM->DE may not solve the Hubble tension. Mind you early dark energy is the opposite of all this, as it is DE->"dark radiation w=1/3". $\endgroup$ – Kevin Kostlan Jul 21 at 14:57
  • $\begingroup$ @LawrenceB.Crowell, "The CMB result H=74 km/(s Mpc) and the Cepheid variable result H=67 km/(s Mpc)", it's the other way around. Local measurements of Hubble parameter tend to get higher values. $\endgroup$ – MadMax Jul 22 at 14:07
  • $\begingroup$ @ Mad Max, your are right, I got them switched. In fact in what follows I wrote about increasing the vacuum energy, which is what might be happening. $\endgroup$ – Lawrence B. Crowell Jul 22 at 15:23

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