ar X iv : g r - qc / 0 41 01 12 v 2 2 5 O ct 2 00 4 Quantum cosmology and the accelerated Universe ∗

In order to explain the present accelerated expansion of the Universe, suggested by the measurements of high redshifts supernovae[2] [3], we consider that presently, at cosmological scales, classical General Relativity (GR) is not valid. Instead of changing the right hand side of Einstein’s equations by introducing some new negative pressure fluid, we modify its left hand side according to physical considerations. We study a quantum universe and, keeping in mind that a macroscopic universe behaves classicaly or quantically depending on its initial quantum state, we investigate if is it possible that quantum cosmological effects at large scales can mimic a negative pressure fluid yielding a positive acceleration. The aim of this talk is to show with a simple model that it is indeed possible for some suitable initial quantum states of the universe. We consider a quantum minisuperspace model containing a free massless scalar field φminimally coupled to gravity in a Friedmann geometry. We interpret this model in the framework of the Bohm-de Broglie (BdB) interpretation of quantum theories [4] [5], in order to extract predictions from the wave functional of the Universe. After quantize the model according to Dirac’s procedure, we obtain the Wheeler-DeWitt (WDW) equation. We only concentrate in the flat model and we consider the following solution of WDW equation Ψ =| σ | √π{exp [− (α+φ) σ 4 ] exp(id(α + φ)) + exp [− (α−φ) σ 4 ] exp(id(α − φ))}, where α ≡ ln(a) being a the (dimensionless) scale factor and σ and d are parameters of the quantum model[1]. The quantum trajectories, can be obtained by integrating the Bohm’s guidance equations, given by: α̇ = φσ 2 sin(2dφ)−2d cos(2dφ)−2d cosh(σαφ) e2[cos(2dφ)+cosh(σαφ)] and φ̇ = − 2 sin(2dφ)+2d sinh(σαφ) e2[cos(2dφ)+cosh(σαφ)] . They are shown in Fig. 1. We can see two differThis talk is based on a work in collaboration with N. Pinto-Neto, see Ref. [1] [email protected] Please see Ref. [6] for a previous work on BdB interpretation of quantum minisuperspace models and Ref.[7][8][9] for the full quantum superspace.