On the Consistency of the Wheeler-DeWitt Equation in the Quantized Eddington-inspired Born-Infeld Gravity

TL;DR

This paper investigates the quantum consistency of the Wheeler-DeWitt equation in Eddington-inspired Born-Infeld gravity, showing that quantum effects may resolve classical big rip singularities.

Contribution

It provides a thorough analysis of the classical Hamiltonian constraints and derives a self-consistent modified Wheeler-DeWitt equation using Dirac brackets.

Findings

The modified Wheeler-DeWitt equation is consistent and corroborates previous results.

Quantum effects potentially prevent the big rip singularity caused by phantom energy.

The approach confirms the viability of quantum geometrodynamics in this gravity theory.

Abstract

We re-examine the quantum geometrodynamical approach within the Eddington-inspired-Born-Infeld theory of gravity, which was first proposed in our previous work [1]. A thorough analysis of the classical Hamiltonian with constraints is carried and the correctness and self-consistency of the modified Wheeler-DeWitt equation (WDW) is studied. We find that based on the newly obtained WDW equation derived with the use of the Dirac brackets, the conclusion reached in Ref.[1] can be corroborated. The big rip singularity present in the classical theory, and induced by a phantom perfect fluid, is expected to be avoided when quantum effects encoded on the modified WDW equation are taken into account.