How Robust Are the Inflationary Predictions?

Abstract

Matter is distributed very homogeneously and isotropically on scales larger than a few hundred Mpc. The measurements of the microwave background temperature fluctuations show that at recombination the universe was extremely homogeneous and isotropic (with accuracy ∼ 10−4) on all scales up to the present horizon.1),2) Given that the universe evolves according to the Hubble law, it is natural to ask which initial conditions could lead to such homogeneity and isotropy. Because we are nearly certain that nonperturbative quantum gravity becomes very important at the Planckian curvature and the notion of classical spacetime breaks down we address the initial conditions at the Planckian time ti = tPl ∼ 10−43 s. There are two independent sets of initial conditions characterizing matter: a) its spatial distribution, described by the energy density e (x) and b) the initial field of velocities. Let us determine them given the current state of the universe and assuming that gravity was always decelerating the expansion of the universe. Homogeneity, isotropy (horizon) problem. The present homogeneous, isotropic domain of the universe is at least as large as the present horizon scale, ct0 ∼ 1028 cm. Initially the size of this domain was smaller by the ratio of the corresponding scale factors, ai/a0 and therefore we may safely conclude that the size of the homogeneous, isotropic region from which our universe originated at t = ti was larger than li ∼ ct0 ai a0 . (1.1) It is natural to compare this scale to the size of a causal region lc ∼ cti : li lc ∼ t0 ti ai a0 ∼ ȧi ȧ0 , (1.2)