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It is common is cosmology to study density fluctuations in the early universe.

However, it is also common to assume that the background space is homogeneous and isotropic and use the FRW metric.

I do not see how density fluctuations can be possible in a homogeneous and isotropic space. Can you please explain?

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That's because the homogeneity and isotropy of the Universe (the "Cosmological Principle") is only assumed — and observed — to be valid on large scales.

The density fluctuations are assumed to have arosen during the epoch of inflation, and have their origin in primordial quantum mechanical uncertainties in positions and momenta of whatever field was around at that time. That is, a successful inflationary model should predict a homogeneous and isotropic Gaussian$^\dagger$ random fluctuation field, because this is what we observe in the cosmic microwave background, and because gravitational collapse of structures out of such a field is more or less consistent with observed structures. We can see that on small scales, the Universe is neither homogeneous nor isotropic (for instance, we're here), while on large scales (i.e. $\gtrsim1/2$ billion lightyears) it does seem to hold true.


$^\dagger$Some models consider non-Gaussian fields.

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  • $\begingroup$ Thanks for the answer. Would it be possible to explain how the density fluctuations arose during the inflationary epoch? $\endgroup$ – nightmarish Sep 18 '16 at 20:04
  • $\begingroup$ They were random quantum fluctuations. The uncertainty principle has it that particles (and fields and anything else) do not have exactly defined position and momentum (or other variables), and so they are fluctuating all the time. The sizes of those fluctuations are the Planck length, and with a random fluctuation with of those sizes you can calculate how much there can be later. The cosmic microwave background shows the fluctuations at the time of electron proton recombination, about 380000 years after the Big Bang, and the sizes of those are consistent with the now observed distributions $\endgroup$ – Bob Bee Sep 19 '16 at 5:38
  • $\begingroup$ @failexam: Bob Bee has it right (although I don't know about the length scales, but he probably knows what he's talking about). $\endgroup$ – pela Sep 19 '16 at 11:13

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