Towards the Quantization of Eddington-inspired-Born-Infeld Theory

TL;DR

This paper investigates quantum effects near the big rip singularity in Eddington-inspired-Born-Infeld (EiBI) theory using quantum geometrodynamics, demonstrating that quantum approaches can potentially avoid the singularity.

Contribution

First application of quantum geometrodynamics to a modified gravity theory based on the Palatini formalism, providing new insights into singularity avoidance in EiBI theory.

Findings

DeWitt condition indicates singularity avoidance in all approaches

Quantum effects can potentially prevent the big rip singularity

Exact solutions of the Wheeler-DeWitt equation are obtained

Abstract

The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in Ref.[1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantom perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity can be avoided through the quantum approach within the EiBI theory.