Bouncing universe for deformed non-minimally coupled inflation model

TL;DR

This paper explores a non-minimally coupled gravity model with non-commutative geometry to realize a bouncing universe, analyzing stability and the crossing of the equation of state parameter below -1.

Contribution

It introduces a new Hamiltonian and Lagrangian formulation with harmonic oscillator form for a non-minimally coupled gravity model incorporating non-commutative geometry, applied to bouncing universe scenarios.

Findings

The equation of state crosses -1 during evolution.

Stability conditions depend on parameters θ and β.

The model supports a stable bouncing universe solution.

Abstract

In this paper, we consider a non-minimally coupled gravity model to study the bouncing universe. The holographic principle has various effects on the bouncing universe. We choose some suitable new variables and achieve the new Hamiltonian and Lagrangian which have harmonic oscillator form. The corresponding Lagrangian is deformed by non-commutative geometry. In order to have a solution for the bouncing universe we specify the potential in the equation state. In that case, we draw the equation of state in terms of time and show that the equation of state crosses $-1$. Such bouncing behavior leads us to apply some conditions on $\theta$ and $\beta$ from non-commutative geometry. Here, we can also check the system's stability due to the deformation of the non-minimally coupled gravity model. In order to examine the stability of the system we obtain the variation of pressure with respect to density energy. Also, we draw the variation of pressure with respect to energy density and show the stability condition.