Phase space analysis of the bouncing universe with stringy effects

TL;DR

This paper explores how string theory-inspired modifications to Friedmann equations can resolve the initial singularity and allow for accelerated expansion in a bouncing universe through phase space analysis.

Contribution

It introduces a phase space analysis of a bouncing universe using string T-duality effects that modify Friedmann equations, highlighting the role of zero-point length and the equation of state.

Findings

Stringy effects can avoid the initial singularity.

The universe can undergo accelerated expansion in certain conditions.

Equilibrium points depend on the equation of state parameter.

Abstract

We use the recently modified Friedmann equations obtained from string T-duality effects that encode the zero-point length (Phys. Lett. B 836 (2023), 137621) to study the phase space analyses of a bouncing early universe. An important implication of such stringy effects is that they can alleviate the initial singularity since the Raychaudhuri equation is modified. We investigate if the Universe can undergo an accelerated expansion phase for a specific domain of the equation of state parameter. The stringy effects are encoded in the parameter $\Gamma$, which depends not only on the zero-point length but also on the state parameter $\omega$. We construct two dynamical systems depending on whether $-1 < \omega \leq -1/3$ and $\omega \geq -1/3$, and we classify the equilibrium points of each system. Exact solutions and cosmological implications are discussed.