Cosmological perturbations in homogeneous and isotropic spac

[spaghetti3451]

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?

 

[bapowell]

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?

They are treated as small perturbations about the homogeneous FRW solution.

 

[spaghetti3451]

Why (during the inflationary epoch) are these perturbations believed to have formed?

 

[bapowell]

Why (during the inflationary epoch) are these perturbations believed to have formed?

Perturbations were generated continuously during inflation. Those relevant to the CMB and large scale structure were generated between 60 and 40 or so e-folds before the end of inflation.

EDIT: Sorry, I initially read your question as "when". Why? Quantum fluctuations cause the classical evolution of the inflaton field as it rolls down to its minimum to have a bit of a jerky ride. Sometimes a quantum fluctuation drives the field closer to the minimum in some parts of the universe than others. Since a particular region of the universe stops inflating when the inflaton field dominating the energy density there drops to zero potential energy, these quantum jumps forward cause different parts of the universe to stop inflating before others. Those parts of the universe that stopped inflating earlier reheated sooner, expanding along with the universe. Since these regions expanded more than those that stopped inflating later, they have redshifted relative to later regions and so are less dense. Since the quantum fluctuations are stochastic, you get a pockmarked universe with Gaussian random density fluctuations across a range of length scales.

I hope that made some sense...