Why do we think that the FRW metric should be valid throughout the entire history of the universe?
Answer
The F(L)RW metric comes with very few assumptions, though these are fairly strong:
- Spacetime is homogeneous.
- Spacetime 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.
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