testing the universe's expansion history with supernovae

[notFritzArgelander]

https://phys.org/news/2021-05-expansion ... novae.html

[AntennaGuy]

So, basically they are adding another adjustable parameter, to better fit the data, hmm? I.e., the Hubble "constant" now gets an added rate-of-change parameter: "[M]odels for the expansion of the Universe best match the data when a new time dependent variation is introduced." Whether this is correct or not, it is not very satisfying. But then, we don't get to tell the universe what to do.

[notFritzArgelander]

So, basically they are adding another adjustable parameter, to better fit the data, hmm? I.e., the Hubble "constant" now gets an added rate-of-change parameter: "[M]odels for the expansion of the Universe best match the data when a new time dependent variation is introduced." Whether this is correct or not, it is not very satisfying. But then, we don't get to tell the universe what to do.

There is no way that the Friedmann equations for cosmology permits a zero time derivative for the Hubble parameter. The physics of GR requires that there be a time dependent variation. The changing matter density of the universe alone drives the change. Whether the "cosmological constant" term is non constant is the real problem. See the first 2 equations in the Wiki and you can see that GR demands a time varying Hubble parameter.

https://en.wikipedia.org/wiki/Friedmann_equations

The only thing really at stake here is:

1) Does H0 vary in time as GR with a cosmological constant requires?
2) Is something more exotic than a cosmological constant required to explain the observed variation of H0 with the age of the universe?
3) Are the observations verschimmelt?

I think a deeper look back at SN Ia is a promising try to assess the differences.

[pakarinen]

Excellent! More epicycles!

[turboscrew]

@notFritzArgelander : You have talked about the time dependency of the Hubble "constant". I guess this is observational support for that.

[notFritzArgelander]

Excellent! More epicycles!

Seriously, no. GR requires that that the Hubble parameter varies as the universe ages. It’s about time ( ) some one tries to measure it at more than 2 ages of the universe.

[notFritzArgelander]

@notFritzArgelander : You have talked about the time dependency of the Hubble "constant". I guess this is observational support for that.

It’s a start.

[notFritzArgelander]

The remarks above about measuring the time dependency of the Hubble parameter are humorous but quite wrong.

Using the notation of https://en.wikipedia.org/wiki/Friedmann_equations

the Friedmann metric for a homogenous and isotropic universe is

ds^2={a\left(t\right)}^2ds_3^2-c^2dt^2

The dynamical equation is the second of Friedmann's equations and describes the acceleration or deceleration of the universe's expansion and reads It's the one that corresponds to Newton's equation of motion in gravity.

\ddot{a}(t)/a(t)=-\frac{4piG}{3}(\rho+\frac{3p}{c^2})+\frac{Lambdac^2}{3}

The first of the Friedmann equations contains the Hubble parameter and reads

{(\dot{a}}^2(t)+kc^2)/a^2(t)=\frac{1}{3}(8piG\rho+Lambdac^2)

It can be regarded as energy conservation, a relationship between the energy of motion and the gravitational and other potential energies.

In the above k is -1, 0, or 1 depending on whether the universe is negatively curved, flat or positively curved. For simplicity let’s set k=0 which is the observed universe anyway.

Then from the first of the Friedmann equations we get

{\dot{a}}^2(t)/a^2(t)=H_0(t)^2=\frac{1}{3}(8piG\rho+Lambdac^2)

This makes the time dependence of the Hubble parameter explicit.

Comparing time varying Hubble parameter to epicycles if fair only when new fundamental constants (describing the epicycles) are introduced. No new fundamental constants are necessary here. No epicycles at all. Our measurement technology is improving so we can test the time variation predicted by GR using only G and c. No epicycles.

I'm struggling with the latex feature to get the equations to display right...... Hope it's legible enough.

[pakarinen]

I was being facetious.

[notFritzArgelander]

I was being facetious.

You perhaps were not the only one being facetious.
It’s good to know and hard to tell for sure without that reassurance. Thanks. When unsure, I tend to play straight man for folks making light.