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Vacuum space energy density is related to the speed of light in a vacuum $c$ as:

$$ \Lambda=8 \pi \rho_{v a c} G / c^4=\kappa \rho_{\text {vac }} $$

where $\rho_{v a c}$ is the vacuum energy density currently a constant.

This would also suggest that during the first 1μs of Cosmological inflation (i.e. until the first protons were formed) the speed of light was much larger than the current value $c$ thus superluminous light which is a necessary condition for the cosmological inflation to be happened in the first place. After that first micro second of the BB with the addition of dark energy phenomenon, the speed of light became constant at its current $c$ value up today and the first protons were formed after this first 1μs.

By using a proof of contradiction, if for whatever reason in the future the vacuum energy density changes form its current constant value, which is currently unchanged with expansion of Universe due to dark energy, does this not also mean a variable speed of light in the vacuum proportional to the vacuum energy density?

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    $\begingroup$ Where did you get the idea that the vacuum energy determines the speed of light? This is not the case. $\endgroup$
    – John Rennie
    Commented Sep 10, 2022 at 13:34
  • $\begingroup$ @JohnRennie It is a matter interpretation of the above equation. You may see "c" constant speed. I see c as speed. $\endgroup$
    – Markoul11
    Commented Sep 10, 2022 at 14:22
  • $\begingroup$ @ConnorBehan Of course I am aware that according to theory space can expand faster than c but IMHO you're missing the point here. If your first fermions, atoms, galaxies etc. were created after the inflation from a primordial energy soup that expanded together with space this means that this homogeneous energy must have expanded in the first second of the BB with the same rate as space therefore an energy propagation speed greater than c. Otherwise you would not have a ΛCMB. $\endgroup$
    – Markoul11
    Commented Sep 10, 2022 at 14:29
  • $\begingroup$ Otherwise if we had to wait the primordial energy soup to catch up with space propagating at the c speed we would never have observed galaxies that are 12 Blyrs away from our home planet, The energy primordial soup would have cooled off much sooner forming galaxies not that far away we observe today. $\endgroup$
    – Markoul11
    Commented Sep 10, 2022 at 14:43
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    $\begingroup$ It is not a matter of interpretation. The early history on the universe is described by the same metric (the FLRW metric) as the later history, just with a different energy density, and in the FLRW metric $c$ is a constant. $\endgroup$
    – John Rennie
    Commented Sep 10, 2022 at 15:18

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In SI units the speed of light is fixed at exactly 299792458 m/s. It cannot vary, by definition. Even during inflation, if you are talking about c in SI units then it is fixed by definition.

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  • $\begingroup$ That does not make any sense. If space inflated more or less to the current volume within the first second after the Big Bang then with the current speed of light $c$, energy (light) would not follow the inflation and there would not be any Universe today. Assuming ordinary condensed matter was created after the inflation from the homogeneous energy soup. $\endgroup$
    – Markoul11
    Commented Sep 10, 2022 at 14:06
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    $\begingroup$ @Markoul11 If you want a model of variable $c$, you must first provide a definition of $c$ that allows it to vary, preferably with experimental motivation for that definition. $\endgroup$
    – John Doty
    Commented Sep 10, 2022 at 17:12
  • $\begingroup$ @Markoul11 If the vacuum has a characteristic energy density, then inflation cannot dilute it. And, the model says that it's that energy density driving inflation. $\endgroup$
    – John Doty
    Commented Sep 10, 2022 at 17:16
  • $\begingroup$ @JohnDoty Inflation and the afterward expansion are two separate events. Inflation was created by the BB whereas expansion is driven by dark energy which the vacuum energy density remains constant despite the volumetric expansion of space. Therefore due to the dark energy the vacuum energy is not diluted. $\endgroup$
    – Markoul11
    Commented Sep 10, 2022 at 18:56
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    $\begingroup$ @Markoul11 the physics of the inflation epoch is irrelevant here. The point is that c is a dimensionful constant. As such it’s value depends on your system of units. In SI units c simply cannot change. It is fixed by the definition of the SI units. You probably want to ask a similar question, but about the fine structure constant which is dimensionless and therefore can have a physically meaningful variation. $\endgroup$
    – Dale
    Commented Sep 11, 2022 at 1:33

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