Physical Foundations of Cosmology

354 Inflation II: origin of the primordial inhomogeneities

1

t

m−1/2

φ

Fig. 8.8.

self-reproduction scale,φrep∼m−^1 /^2 , quantum fluctuations are no longer relevant.

The size of these regions grows exponentially and eventually they produce very

large homogeneous domains where the universe is hot.

Problem 8.16Determine the self-reproduction scale for the power-law potential

V=(λ/n)φn.

To conclude, we have found that inflation generically leads to a self-reproducing

universe and induces complicated global structure on very large scales. This global

structure may become relevant for an observer but only inmany manybillions of

years. However, for a better understanding of the initial condition problem, the self-

reproduction regime is very important. There is no complete and reliable description

of the self-reproducing universe at present and much more work has to be done to

clarify the question of the global structure of the universe.

8.6 Inflation as a theory with predictive power

Assuming a stage of cosmic acceleration – inflation – we are able to make ro-

bust predictions even in the absence of the actual inflationary scenario. The most

important among them are:

(i) the flatness of the universe;

(ii)Gaussian scalar metric perturbations with a slightly red-tilted spectrum;

(iii)long-wavelength gravitational waves.