I The quintessence as variable dark energy

[Jaime Rudas]

TL;DR

Is the quintessence variable in space?

Wikipedia says:

The exact nature of dark energy remains a mystery, and many possible explanations have been theorized. The main candidates are a cosmological constant (representing a constant energy density filling space homogeneously) and scalar fields (dynamic quantities having energy densities that vary in time and space) such as quintessence or moduli.

Does the quintessence really vary in space? Wouldn't that imply violating the cosmological principle? Or perhaps it refers to small-scale variations, while homogeneity would be preserved on large scales?

 

[PeterDonis]

Does the quintessence really vary in space?

"Space" isn't an invariant. It varies in spacetime. Whether that means variation in "space" depends on your choice of coordinates.

Wouldn't that imply violating the cosmological principle?

Potentially, yes, if we take "space" to mean "space in standard FRW coordinates". You would have to look at specific models that have been proposed to see whether that's significant in those particular models.

Or perhaps it refers to small-scale variations, while homogeneity would be preserved on large scales?

Some quintessence models might be like this, yes.

Note that we have no evidence of any variation in spacetime of dark energy, so a cosmological constant is at present the simplest model that's consistent with our evidence. Unless and until we have some evidence that shows variation, any model with variation in it is just speculation, and there's not a lot one can say about it, since in principle a scalar field model, for example, could have any kind of variation in it you like. (Note that that would include variation that, in standard FRW coordinates, is only in time, not space, so that the model would still be spatially homogeneous.)

 

[PAllen]

As far as I know, the common models of quintessence still use the FLRW equation metric, just with particular forms of $a(t)$. In these, the cosmological principle is obeyed, and there is no spatial variation of the quintessence within a slice of constant cosmological time.

 

[Ibix]

As far as I know, the common models of quintessence still use the FLRW equation metric, just with particular forms of $a(t)$. In these, the cosmological principle is obeyed, and there is no spatial variation of the quintessence within a slice of constant cosmological time.

Presumably, however, if one perturbs the initial spatially uniform density of matter/radiation with random fluctuations so that stars and galaxies form then the quintessence density would also fluctuate?

 

[PAllen]

Presumably, however, if one perturbs the initial spatially uniform density of matter/radiation with random fluctuations so that stars and galaxies form then the quintessence density would also fluctuate?

Yeah, but if you are talking about galaxies, you are outside the FLRW idealized model - that has only perfect fluid with different equations of state. So, to the same degree you ignore clumping to use an ideally homogenous model with cosmological constant, you ignore it when modeling a quintessence field with homogeneity over large scales. Within the FLRW equation, you can only play with the density pressure relationship, as they influence a(t).

 

[timmdeeg]

Yeah, but if you are talking about galaxies, you are outside the FLRW idealized model - that has only perfect fluid with different equations of state.

This raises the question to which extent "the FLRW idealized model" is applicable locally? E.g. it is said that voids expand faster because of under density.

 

[PeroK]

This raises the question to which extent "the FLRW idealized model" is applicable locally?

It's not applicable, except on the largest scales. The fundamental assumption is uniform mass and radiation density. Moreover, the model applies to the universe as a whole.

 

[timmdeeg]

It's not applicable, except on the largest scales. The fundamental assumption is uniform mass and radiation density. Moreover, the model applies to the universe as a whole.

That's the reason why I mentioned "voids expand faster because of under density" as an example. That seems to refer to the Friedmann equations. But its a local effect, so why if at all is the conclusion in "" still reasonable?

 

[PeroK]

That's the reason why I mentioned "voids expand faster because of under density" as an example. That seems to refer to the Friedmann equations. But its a local effect, so why if at all is the conclusion in "" still reasonable?

There are no voids in a homogeneous universe. If you want to study a local region of the universe, then you need to set up the equations with the appropriate boundary conditions. You might find that a local region of vacuum expands faster than the universal average; or, you might not. Neither conclusion can be drawn from the global Friedmann equation.

If you pick an atypical region of the universe, the hypotheses for the Friedmann equation do not hold. You cannot directly apply the solutions of the Friedmann equation to a local region.

From a mathematical point of view, there is no difference between a vaccum of one metre cubed and one billion light years cubed. So, you have to be very careful extrapolating a global solution to a local solution - even if the local solution applies to a physically "large" region of space.

 

[Ibix]

That's the reason why I mentioned "voids expand faster because of under density" as an example. That seems to refer to the Friedmann equations. But its a local effect, so why if at all is the conclusion in "" still reasonable?

You can formally model the evolution of fluctuations via perturbation theory. As I understand it, the point isn't really that "voids expand faster", but rather where you've got an overdense region its own self-gravity slows the matter and causes it to collapse (i.e., acquire peculiar velocities inwards), increasing density in the middle but lowering it at the edge. So voids grow as well as expand.

 

[PAllen]

While the FLRW metric, when used for a realistic universe, is purely an emergent approximation at large scales, there is one aspect of if that applies locally. That is, if it suggests that there is a cosmological constant, this applies everywhere and has effects (too small to be observed) within, e.g., the solar system. Similarly, if quintessence is suggested, then this could also have local effects.

 

[javisot]

You can formally model the evolution of fluctuations via perturbation theory. As I understand it, the point isn't really that "voids expand faster", but rather where you've got an overdense region its own self-gravity slows the matter and causes it to collapse (i.e., acquire peculiar velocities inwards), increasing density in the middle but lowering it at the edge. So voids grow as well as expand.

Wasn't that the Timescape model?

 

[PAllen]

I wondered if anyone had ever treated voids using numerical relativity rather than more indirect approximations. I came across the following, which does exactly this:
https://academic.oup.com/mnras/article/536/3/2645/7923505

I note the conclusions are generally in agreement with other methods, which is a good mutual cross check.

 

[timmdeeg]

I wondered if anyone had ever treated voids using numerical relativity rather than more indirect approximations. I came across the following, which does exactly this:
https://academic.oup.com/mnras/article/536/3/2645/7923505

Here is an update of this paper:
https://arxiv.org/pdf/2412.15143

They argue that according to the timescape model the cosmological constant can be replaced:
....
Instead of a matter density parameter relative to average Friedmann-Lemaître Robertson-Walker model (as in ΛCDM), timescape is characterised by the void fraction, 𝑓v, which represents the fractional volume of the expanding regions of the universe made up by voids.
A key ingredient of the timescape model is a particular integrability relation for the Buchert equations: the uniform quasilocal Hubble expansion condition. Physically, it is motivated by an extension of Einstein’s Strong Equivalence Principle to cosmological averages at small scales (∼ 4 – 15 Mpc) where perturbations to average isotropic expansion and average isotropic motion cannot be observationally distinguished (Wiltshire 2008).
....
What I don't get here is the physical motivation, the hint to the Strong Equivalence Principle, which I understand as that feeling gravity is indistinguishable from feeling acceleration in a rocket. But where is the rocket? Everything is in free fall. Obviously the model is based on "expanding regions of the universe made up by voids".

 

[PAllen]

Here is an update of this paper:
https://arxiv.org/pdf/2412.15143

They argue that according to the timescape model the cosmological constant can be replaced:
....
Instead of a matter density parameter relative to average Friedmann-Lemaître Robertson-Walker model (as in ΛCDM), timescape is characterised by the void fraction, 𝑓v, which represents the fractional volume of the expanding regions of the universe made up by voids.
A key ingredient of the timescape model is a particular integrability relation for the Buchert equations: the uniform quasilocal Hubble expansion condition. Physically, it is motivated by an extension of Einstein’s Strong Equivalence Principle to cosmological averages at small scales (∼ 4 – 15 Mpc) where perturbations to average isotropic expansion and average isotropic motion cannot be observationally distinguished (Wiltshire 2008).
....
What I don't get here is the physical motivation, the hint to the Strong Equivalence Principle, which I understand as that feeling gravity is indistinguishable from feeling acceleration in a rocket. But where is the rocket? Everything is in free fall. Obviously the model is based on "expanding regions of the universe made up by voids".

That's not an update. It shares exactly one author, and the topic is not the same. Obviously, there is some relationship, but that's all. Here is how they refer to the paper I gave:

"Regardless of what model cosmology is to be the standard in
future, exploring more than one model is important. Indeed, the
timescape framework is consistent with new analysis of void statistics
in numerical relativity simulations using the full Einstein equations
(Williams et al. 2024). "

 

[PAllen]

What I don't get here is the physical motivation, the hint to the Strong Equivalence Principle, which I understand as that feeling gravity is indistinguishable from feeling acceleration in a rocket. But where is the rocket? Everything is in free fall. Obviously the model is based on "expanding regions of the universe made up by voids".

That is an exceedingly narrow statement of the equivalence principle. The most commonly accepted meaning of strong equivalence principle is given in (especially the end) of section 3.1.2 of the following:
https://link.springer.com/article/10.12942/lrr-2014-4

 

[Ibix]

Wasn't that the Timescape model?

I think Timescape is a model that says the inhomogeneity is strong enough to affect our observations, but you can model inhomogeneity as a perturbation to an arbitrary FLRW universe, so I don't think you need to worry about that to answer this question.