Kasner solutions, climbing scalars and big-bang singularity

TL;DR

This paper investigates the climbing scalar phenomenon near the big-bang singularity, analyzing conditions for its occurrence with multiple scalars and higher-derivative corrections, and exploring implications for initial conditions in inflation.

Contribution

It generalizes the climbing scalar phenomenon to multiple scalars and higher-derivative corrections, and discusses its implications for cosmological initial conditions.

Findings

Climbing behavior occurs for steep potentials above a critical steepness.

Steep potentials induce oscillations in scalars near the big-bang.

Potential applications to initial conditions in inflation are proposed.

Abstract

We elaborate on a recently discovered phenomenon where a scalar field close to big-bang is forced to climb a steep potential by its dynamics. We analyze the phenomenon in more general terms by writing the leading order equations of motion near the singularity. We formulate the conditions for climbing to exist in the case of several scalars and after inclusion of higher-derivative corrections and we apply our results to some models of moduli stabilization. We analyze an example with steep stabilizing potential and notice again a related critical behavior: for a potential steepness above a critical value, going backwards towards big-bang, the scalar undergoes wilder oscillations, with the steep potential pushing it back at every passage and not allowing the scalar to escape to infinity. Whereas it was pointed out earlier that there are possible implications of the climbing phase to CMB, we point out here another potential application, to the issue of initial conditions in inflation.