FRW metric and its validity througout the age of the universe

Question

Why do we think that the FRW metric should be valid throughout the entire history of the universe?

Answer 1

The F(L)RW metric comes with very few assumptions, though these are fairly strong:

• Space is homogeneous.
• Space is isotropic.

Or, in other words, the cosmological principle is assumed. Philosophically this is very desirable, as the notion that there are preferred locations or directions in the Universe is, from a modern point of view, somewhat repulsive. Furthermore, our ability to understand the physics of the Universe hinges rather strongly on the cosmological principle holding, so we very much want it to hold. Fortunately, observations seem to point to homogeneity and isotropy on "large enough" scales. And it's not like we ignore any departures from perfect homogeneity and isotropy; we know how to evolve linear perturbations (analytically) and non-linear perturbations (numerically) on top of a background F(L)RW metric. Using this perturbative machinery, we can work through different models of the Universe.

In any F(L)RW model we consider realistic, departures from homogeneity and isotropy tend to grow with time, so if we claim the cosmological principle holds now (well enough that we can use F(L)RW + perturbations to get a working model), we implicitly claim it holds back in time at least as far as inflation. And if we're correct and we're entering a dark energy dominated epoch, the cosmological principle will continue to hold for the (rather long) foreseeable future.

Answer 2

We don't think the FLRW metric is valid throughout the entire history of the universe.

If we take a metric of the form:

$$ ds^2 = -dt^2 + a^2(t) d\Sigma^2 $$

then we expect this to be valid throughout the history of the universe as long as the universe is isotropic and homogenous. However we need to find the equation for the function $a(t)$, and this is what the FLRW metric does. It relates $a(t)$ to the matter/energy content of the universe and allows us to calculate the form of $a(t)$. If you're interested I've calculated $a(t)$ for our universe in my answer to How does the Hubble parameter change with the age of the universe?.

However the calculation makes assumptions about the matter/energy content. In particular it assumes only three types of energy/matter need to be considered:

1. relativistic matter and radiation

2. normal everyday matter

3. the cosmological constant

The way the densities of these three components scale with the size of the universe determines the form of $a(t)$. Relativistic matter and radiation dominate at early times, normal matter dominates at intermediate times and the cosmological constant dominates at long times. Our universe made the switch from matter dominated to dark energy dominated around 6 - 8 billion years after the Big Bang.

But ...

We expect there to be other factors affecting the overall energy density. For example most cosmologists believe there was an inflationary period starting about $10^{-36}$ seconds after the Big Bang. This was driven by an as yet unidentified source called the inflaton field. The inflaton field is not included in the FLRW metric, so the FLRW metric misses out inflation.

Another more controversial possibility is that dark energy is time dependant, in which case it's normally referred to as quintessence. In that case the assumption of a constant dark energy density is invalid, an the FLRW metric will fail to describe the universe during the dark energy dominated phase.

But I'm possibly being a bit hard on messers Friedmann, Lemaître, Robertson and Walker because the general form of their metric will still be valid. It's just that you need to include extra components in the matter/energy density that were unknown in their time. The Friedmann, Lemaître, Robertson, Walker, Rennie metric $^1$ that does include all the components that will ever affect the matter/energy density will be valid throughout the entire history of the universe.

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$^1$ a work in progress