Classical Analogous of Quantum Cosmological Perfect Fluid Models

Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state pQ = ρQ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase. PACS number(s): 04.20.Cv., 04.20.Me The existence of an initial singularity is one of the major drawbacks of the so-called standard cosmological model. It is a general belief that such problem can be solved through the employement of a quantum theory of gravity. Indeed, near the singularity sub-Planckian scales are reached and a classical description of the Universe under this situation is not appropriate. However, there is no consistent quantum theory of gravity untill now, and in this sense the problem of the initial singularity remains of actuality. On the other hand, it is possible to construct a quantum model for the Universe as a whole, through the Wheeler-de Witt equation, based in the ADM decomposition of the gravity sector, which leads to a hamiltonian formulation of general relativity, from which a canonical quantization procedure can be applied. This gives birth to quantum cosmology[1, 8]. Quantum cosmology is not free from problems. First, it can be applied only to geometries where a foliation is possible. Moreover, the hamiltonian formalism leads to a breakdown of general covariance, and the notion of time is lost [3]. There are some recent proposals by which this notion of time can be recovered. One of these proposals is based in the coupling of the gravity sector to a perfect fluid. Using the Schutz’s formulation of a perfect fluid [4], a quantization procedure is possible. The canonical momentum associated with the perfect fluid appears linearly in the Wheeler-de Witt equation, permiting e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]. Permanent Adress: IMSP Université Nationale du Bénin, Porto Novo, Bénin.