Classical and quantum cosmology of the little rip abrupt event

Abstract

We analyze from a classical and quantum point of view the behavior of the universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structure in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.

Cosmological perturbations in an effective and genuinely phantom dark energy Universe

“…For the three models at hand, we can solve (A5) analytically well inside the DE dominated regime, i.e., for t ≥ t * we have H 2 ≈ (κ 2 /3)ρ d , obtaining for each case the potential [40,41,[93][94][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. This applies even to the smoother version of these singular behaviours corresponding to a LSBR [41] (see also [43][44][45][46][47]). …”

“…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.…”

Cosmological Perturbations in Phantom Dark Energy Models

“…However, as energy density diverges in all the cases presented, one might expect that quantum effects become important at some point in the future evolution. In fact, a quantum analysis shows that in all cases, the classical abrupt event can be avoided from a quantum point of view [16][17][18][19].…”

The Avoidance of the Little Sibling of the Big Rip Abrupt Event by a Quantum Approach

“…The corresponding potential has a quadratic dependence with the scalar field, as given in Equation (15). We notice that the obtained potential show a lower dependence with respect to the scalar field, φ, when comparing with the resulting potentials of other DE models like those that induce the BR and LR events [46,47]. We could affirm that the stronger is the dependence of the potential V(φ) with respect to φ, the more relevant are the divergences of the cosmological variables.…”