Universe from vacuum in loop-string cosmology

TL;DR

This paper explores a loop-string cosmology model where the universe begins in a vacuum state with zero energy and coupling, avoiding singularities and evolving into a standard Big Bang and dark energy phase, with analytical and numerical solutions.

Contribution

It introduces a non-singular cosmological model combining loop quantum gravity and string theory effects, eliminating the need for T-duality for initial singularity avoidance.

Findings

Universe starts in vacuum with zero scale factor and energy density.

Model achieves a non-singular transition to a hot Big Bang phase.

Numerical solutions include a dilaton potential leading to dark energy dominance.

Abstract

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.