Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

Abstract

Listen

Translate article

It is stated that holonomy corrections inloop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation isobtained in an inconsistent way, whatmeans that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem isthat holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, toa non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the bigrip singularity avoidance isto disregard modification in the gravitational part of the Hamiltonian, andonly consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, thebig rip singularity survives in loop quantum cosmology.Another way to deal with the big rip avoidance is to take into account geometric quantum effectsgiven by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, theexpectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, onecan conclude that the big rip singularity survives when one takes into account these quantum effects.However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude thatthe classicalevolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external timesthat allows us to define the classical andquantum evolution of the universe up to the big rip singularity.