# I Discrepancy in Hubble's "constant" and its implications

#### Phys12

Summary
Why is the discrepancy in Hubble's "constant" an exciting news which could potentially point to new Physics ( https://www.spacetelescope.org/news/heic1908/ )?
If the Hubble's constant is greater now (to the best of our estimates) than it was in the early universe, doesn't it just imply that the universe's expansion rate is increasing, which was shown by the High-Z Supernova Search team in 1998 that discovered dark energy? Wouldn't this Hubble discrepancy just validate the presence of dark energy, instead of pointing towards new Physics?

#### PeterDonis

Mentor
If the Hubble's constant is greater now (to the best of our estimates) than it was in the early universe
It isn't. It's much smaller.

doesn't it just imply that the universe's expansion rate is increasing
The terminology here is unfortunate, since "expansion rate is increasing" does not mean the Hubble constant is increasing. It just means the Hubble constant is decreasing asymptotically towards a finite positive value, instead of decreasing to zero (and possibly negative values if the universe were going to recollapse).

The root of the problem is that "expansion rate" is ambiguous: it can refer to one of two things: either $\dot{a}$, the rate of change of the scale factor with time, or $H = \dot{a} / a$, the Hubble constant, which is the fractional rate of change of the scale factor with time ("fractional" because of the division by $a$). "Accelerating expansion" means $\dot{a}$ is increasing. But if the accelerating expansion is due to dark energy, then $H$ will be decreasing, not increasing. (This is easy to work out from the Friedmann equations.)

#### Bandersnatch

Science Advisor
If the Hubble's constant is greater now (to the best of our estimates) than it was in the early universe,
As was already mentioned, it's smaller now. Compared with the time when the cosmic microwave background radiation was emitted, by a factor of about 20 000.
I know what's confusing you though. It's true that the measurements using the cosmic microwave background are looking at conditions in the early universe, while those using supernovae at conditions relatively recent. But the conditions from the early era are extrapolated to the present time using a model of expansion (which includes dark energy). The model predicts how the Hubble parameter should be changing over time, given the parameters measured.
The reported discrepancy is between values of the Hubble constant now, obtained by different methods. Not between its values at different times.

#### Mordred

Not surprisingly that article misleads this detail. Wonder if this older version of Jorrie's cosmocalc still works.
$${\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{gen}/c&H/Ho \\ \hline 1090.000&0.000373&0.000628&45.331596&0.041589&0.056714&21.023&22915.263\\ \hline 339.773&0.002496&0.003956&44.183524&0.130038&0.178562&10.712&3639.803\\ \hline 105.913&0.015309&0.023478&42.012463&0.396668&0.552333&5.791&613.344\\ \hline 33.015&0.090158&0.136321&38.051665&1.152552&1.651928&3.200&105.633\\ \hline 10.291&0.522342&0.785104&30.917756&3.004225&4.606237&1.782&18.342\\ \hline 3.208&2.977691&4.373615&18.247534&5.688090&10.827382&1.026&3.292\\ \hline 1.000&13.787206&14.399932&0.000000&0.000000&16.472274&1.000&1.000\\ \hline 0.312&32.884943&17.184900&11.117770&35.666086&17.224560&2.688&0.838\\ \hline 0.132&47.725063&17.291127&14.219438&107.785602&17.291127&6.313&0.833\\ \hline 0.056&62.598053&17.299307&15.535514&278.255976&17.299307&14.909&0.832\\ \hline 0.024&77.473722&17.299802&16.092610&681.060881&17.299802&35.227&0.832\\ \hline 0.010&92.349407&17.299900&16.328381&1632.838131&17.299900&83.237&0.832\\ \hline \end{array}}$$

See S=1090 for roughly CMB time row S=1 for now in the H/H_0 column.

Cool calc still handles the latex pasting.

#### Phys12

The root of the problem is that "expansion rate" is ambiguous: it can refer to one of two things: either $\dot{a}$, the rate of change of the scale factor with time, or $H = \dot{a} / a$, the Hubble constant, which is the fractional rate of change of the scale factor with time ("fractional" because of the division by $a$). "Accelerating expansion" means $\dot{a}$ is increasing. But if the accelerating expansion is due to dark energy, then $H$ will be decreasing, not increasing. (This is easy to work out from the Friedmann equations.)
Why will $H$ be decreasing if the accelerating expansion is due to dark energy? As long as the universe's expansion is accelerating and $\dot{a}$ is increasing, wouldn't $H$ increase too, regardless of the effect of dark energy?

#### George Jones

Staff Emeritus
Science Advisor
Gold Member
Why will $H$ be decreasing if the accelerating expansion is due to dark energy? As long as the universe's expansion is accelerating and $\dot{a}$ is increasing, wouldn't $H$ increase too, regardless of the effect of dark energy?
$H = \dot{a} a^{-1}$ gives
$$\dot{H} = \ddot{a} a^{-1} - \dot{a} a^{-2},$$
so, if the second term dominates, then $\dot{H}$ can be negative when both $\dot{a}$ and $\ddot{a}$ are positive.

#### kimbyd

Science Advisor
Gold Member
2018 Award
Why will $H$ be decreasing if the accelerating expansion is due to dark energy? As long as the universe's expansion is accelerating and $\dot{a}$ is increasing, wouldn't $H$ increase too, regardless of the effect of dark energy?
The rate of expansion is a reflection of the amount of space-time curvature in our universe*. The amount of space-time curvature is a function of the amount of stuff. More stuff = more curvature. Back when the universe was more dense, there was more space-time curvature, and the rate of expansion was higher.

The reason why dark energy causes an accelerated expansion is not because it causes the rate of expansion to increase. Rather, it causes objects in our universe to accelerate away from one another. And that can happen even while the rate of expansion is decreasing.

To see why, consider the case of a constant rate of expansion. A constant rate is a constant velocity per unit distance. Twice the distance, twice the recession velocity. So if a movement moves from its current distance to twice as far away, it will have sped up to twice its current speed.

Currently the rate of expansion is decreasing slowly enough that the distances between galaxies are increasing at an accelerated pace. That fact is fundamentally impossible if normal matter is all there is. Which is where dark energy comes in, or a cosmological constant. Either possibility poses theoretical challenges, but all of the alternatives proposed so far have proven false.

* Slight caveat: the amount of curvature can show up in either spatial curvature, the rate of expansion, or the rate of change of the expansion. Our universe appears to have little to no spatial curvature. The rate of change of expansion is low. So nearly all of the curvature shows up in the expansion itself.

#### PeterDonis

Mentor
Moderator's note: I have deleted an off topic subthread (and made a small edit to one post that remains visible) that is not relevant or necessary to the main discussion.

#### PeterDonis

Mentor
Moderator's note: Some more off topic posts have been deleted, and the poster who started the off topic subthread has been thread banned.

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