Four-dimensional cosmology from dilaton coupled quantum matter in two dimensions

TL;DR

This paper investigates 2D cosmological models derived from 4D Einstein gravity with scalar fields, revealing various universe outcomes including singular, non-singular, and big crunch scenarios through numerical analysis.

Contribution

It introduces a detailed study of 2D cosmology from 4D gravity with dilaton coupling, incorporating large N quantum effects, and connects these models to 4D Kantowski-Sacks universes.

Findings

Most cases produce a 2D singular universe resembling a big bang.

Non-singular and big crunch universes are also observed in the models.

The 2D cosmology corresponds to 4D Kantowski-Sacks universes with diverse fates.

Abstract

The reduction of 4D Einstein gravity with $N$ minimal scalars leads to specific 2D dilaton gravity with dilaton coupled scalars. Applying s-wave and large $N$ approximation (where large $N$ quantum contribution due to dilaton itself is taken into account) we study 2D cosmology for CGHS model and for reduced Einstein gravity (in both cases with dilaton coupled scalars). Numerical study shows that in most cases we get 2D singular Universe which may correspond to big bang. Nevertheless, big crunch or non-singular Universes are also possible. For reduced 4D Einstein gravity one can regard the obtained 2D cosmology with time-dependent dilaton as 4D Kantowski-Sacks Universe of singular,non-singular or big crunch type.