Perturbative instability of inflationary cosmology from quantum potentials

TL;DR

This paper investigates the stability of inflationary cosmology under quantum corrections, finding that both stable and unstable perturbation modes can occur, with implications for the early Universe's evolution.

Contribution

It provides a detailed analysis of perturbative stability in quantum-corrected inflationary models, highlighting conditions for instability and stability in different cosmic eras.

Findings

Unstable and stable modes are incompatible with standard FLRW universe.

Unstable modes exist at small anisotropic perturbations and various equations of state.

Both instability and stability are likely in flat FLRW universe depending on conditions.

Abstract

It was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature [MPLA31(2016)1650044]. In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obtained for radiation- and matter-dominated eras, merely, instability modes exist in case of a finite cosmological constant and also if the vacuum energy dominates the cosmic background geometry.