Quantum cosmology of Eddington-Born–Infeld gravity fed by a scalar field: The big rip case

Abstract

We study the quantum avoidance of the big rip singularity in the Eddington-inspired-Born-Infeld (EiBI) phantom model. Instead of considering a simple phantom dark energy component, which is described by a perfect fluid, we consider a more fundamental degree of freedom corresponding to a phantom scalar field with its corresponding potential, which would lead the classical universe to a big rip singularity. We apply a quantum geometrodynamical approach by performing an appropriate Hamiltonian study including an analysis of the constraints of the system. We then derive the Wheeler-DeWitt (WDW) equation and see whether the solutions to the WDW equation satisfy the DeWitt boundary condition. We find that by using a suitable Born-Oppenheimer (BO) approximation, whose validity is proven, the DeWitt condition is satisfied. Therefore, the big rip singularity is expected to be avoided in the quantum realm. a imanol@ubi.pt b mariam.bouhmadi@ehu.eus c

Eddington-inspired-Born–Infeld tensorial instabilities neutralized in a quantum approach

“…It can be proven that the equations of motion derived from the original action (2.1) can be obtained unambiguously by varying the action (3.1) with respect to g µν and q µν . In our previous papers [40,42,43,45], we have used this alternative action (3.1) to deduce the classical Hamiltonian and the corresponding WDW equation in the EiBI gravity. It turns out that the construction of the WDW equation is much more straightforward because of the absence of the square root structure of the curvature present in the original action (2.1).…”

“…In Ref. [45], an improved investigation has been done in which the matter sector is assumed to be a scalar field rather than a perfect fluid. As expected, the Hamiltonian itself is a first class constraint and at the quantum level, it would be treated as a restriction on the Hilbert space, giving rise to the WDW equation.…”

“…(3.9) and (3.10) in Ref. [45]. Essentially, once we introduce the Dirac brackets to promote the phase space functions to quantum operators, the second class constraints can be regarded as zero operators [53].…”

“…Essentially, once we introduce the Dirac brackets to promote the phase space functions to quantum operators, the second class constraints can be regarded as zero operators [53]. As a result, the total Hamiltonian can be significantly simplified [45]…”

Classical and quantum fate of the little sibling of the big rip in f(R) cosmology

“…In the framework of quantum geometrodynamics several works have evaluated different kinds of cosmological singularities [44][45][46]. Furthermore, some works have also investigated this issue for alternative theories of gravity by formulating a modified quantum geometrodynamical framework [29,[47][48][49]. (See also reference [50] for a different approach to quantum f (R) gravity.)…”