The horizon problem as a clue: a smooth big bang?

TL;DR

This paper identifies the conditions under which a big bang universe can be causally connected immediately after the initial singularity, providing insights into the homogeneity of the universe and supporting inflationary scenarios.

Contribution

It establishes the necessary and sufficient condition for the absence of particle horizons in a big bang universe based on initial conditions of the scale factor's behavior.

Findings

Absence of particle horizons requires a finite derivative of the scale factor at the big bang.

Immediate causal connection between distant regions is possible shortly after the big bang.

Homogeneity of the cosmic microwave background can be explained by initial conditions rather than inflation alone.

Abstract

The necessary and sufficient condition for the absence of particle horizons in a big bang Friedmann-Robertson-Walker universe is provided. It happens to be a "smooth big bang" initial condition: the proper time derivative of the expansion factor $a(t)$ must be finite at the big bang. Equivalently, the energy density must not diverge faster than $a^{-2}$ at the big bang. This is just an initial condition: only the scale factor asymptotic behavior at the very moment of the big bang matters. The causal connection between remote space regions could then take place immediately after the big bang. Even $10^{-36}$ seconds of proper time, would allow for an infinite number of light crossing times between any two space regions, no matter how far apart. This justifies inflationary scenarios starting from a quasi-homogeneous scalar field close to equilibrium. The high degree of homogeneity of the Cosmological Background Radiation can be seen then not as a problem, but rather as a clue to the equation of state in the big bang limit.