Towards the quantization of Eddington-inspired-Born-Infeld theory

Abstract

Abstract. The quantum effects close to the classical big rip singularity within the Eddingtoninspired-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 WentzelKramers-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 is expected to be avoided through the quantum approach within the EiBI theory.

Cosmological perturbations in an effective and genuinely phantom dark energy Universe

“…The classical singular asymptotic behaviour of these dark energy models has led to a quantum cosmological analysis of these setups [39][40][41][42]95]. In these works, it was concluded that once the Universe enters in a genuinely quantum phase; i.e., where coherence and entanglement effects are important, the Universe would evade a doomsdayà la rip.…”

Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity

“…As shown in [29], this can be reached by considering an alternative action which is dynamically equivalent to the action (10):…”

“…Classically, these actions are dynamically equivalent. Starting from the action (13) and inserting the FLRW ansatz, we can obtain the Lagrangian of this model in which the matter field is described by a perfect fluid (see Reference [29])…”

“…We will focus on one particular alternative theory of gravity, dubbed Eddington-inspired-Born-Infeld (EiBI) theory. It was recently proposed in [26], pioneered in [27], and has attracted much attention [28][29][30][31][32][33][34]. The EiBI theory has been shown to be able to remove the big bang singularity for a radiation-dominated universe through a loitering effect or a bounce in the past [26].…”

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

“…An attractive candidate is the EiBI theory [3]. This theory has been widely investigated both from the cosmological and astrophysical points of view [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The EiBI theory is able to cure the big bang singularity at the cosmological level [19].…”