Constraints on Non-Singular Cosmological Models with Quadratic Lagrangians

We consider the generalized set of theories of gravitation whose Lagrangians contain the term $R^{2}$ : $L=\sqrt{-g}(R+\beta R^{2})$. Inserting the RW metric with an imposed non-singular and inflationary behaviour of the scale factor $a(t)$, and using a arbitrary perfect fluid, we study the properties of $\rho$ and $p$ in this context. By requiring the positivity of the energy density, as well as real and finite velocity of sound, we can obtain the range of values of $\beta$ that ensure the inflationary behaviour and absence of singularity.Comment: 11 pages, RevTeX, 3 Postscript figure

Graceful exit from inflation using quantum cosmology

A massless scalar field without self interaction and string coupled to gravity is quantized in the framework of quantum cosmology using the Bohm-de Broglie interpretation. Gaussian superpositions of the quantum solutions of the corresponding Wheeler-DeWitt equation in minisuperspace are constructed. The bohmian trajectories obtained exhibit a graceful exit from the inflationary Pre-Big Bang epoch to the decelerated expansion phase.Comment: 8 pages, RevTeX, 4 Postscript figures, uses graficx.sty. Added more text and reference

Nonminimal Scalar-Tensor Theories and Quantum Gravity

Recentely, it is shown that the quantum effects of matter determine the conformal degree of freedom of the space-time metric. This was done in the framework of a scalar-tensor theory with one scalar field. A point with that theory is that the form of quantum potential is preassumed. Here we present a scalar-tensor theory with two scalar fields, and no assumption on the form of quantum potential. It is shown that using the equations of motion one gets the correct form of quantum potential plus some corrections.Comment: 15 page

On the consistency of a repulsive gravity phase in the early Universe

We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for the spatial section, is studied in detail. The background solutions display a bouncing, non-singular Universe. The model is well-behaved with respect to tensor perturbations. But, it exhibits growing models with respect to scalar perturbations whose maximum occurs in the bouncing. Hence, large inhomogeneties are produced. At least for this case, a repulsive phase may destroy homogeneity, and in this sense it may be unstable. A newtonian analogous model is worked out; it displays qualitatively the same behaviour. The generality of this result is discussed. In particular, it is shown that the addition of an attractive radiative fluid does not change essentially the results. We discuss also a quantum version of the classical repulsive phase, through the Wheeler-de Witt equation in mini-superspace, and we show that it displays essentially the same scenario as the corresponding attractive phase.Comment: Latex file, 15 pages, 7 figures. There is a new figure, a new section and some other minor correction

Bayesian Analysis of the (Generalized) Chaplygin Gas and Cosmological Constant Models using the 157 gold SNe Ia Data

The generalized Chaplygin gas model (GCGM) contains 5 free parameters, here, they are constrained through the type Ia supernovae data, i.e., the ``gold sample'' of 157 supernovae data. Negative and large positive values for $\alpha$ are taken into account. The analysis is made by employing the Bayesian statistics and the prediction for each parameter is obtained by marginalizing on the remained ones. This procedure leads to the following predictions: $\alpha = - 0.75^{+4.04}_{-0.24}$, $H_0=65.00^{+1.77}_{-1.75}$, $\Omega_{k0} = - 0.77^{+1.14}_{-5.94}$, $\Omega_{m0} = 0.00^{+1.95}_{-0.00}$, $\Omega_{c0} = 1.36^{+5.36}_{-0.85}$, $\bar A = 1.000^{+0.000}_{-0.534}$. Through the same analysis the specific case of the ordinary Chaplygin gas model (CGM), for which $\alpha = 1$, is studied. In this case, there are now four free parameters and the predictions for them are: $H_0 = 65.01^{+1.81}_{-1.71}$, $\Omega_{k0} = - 2.73^{+1.53}_{-0.97}$, $\Omega_{m0} = 0.00^{+1.22}_{-0.00}$, $\Omega_{c0} = 1.34^{+0.94}_{-0.70}$, $\bar A = 1.000^{+0.000}_{-0.270}$. To complete the analysis the $\Lambda$CDM, with its three free parameters, is considered. For all these models, particular cases are considered where one or two parameters are fixed. The age of the Universe, the deceleration parameter and the moment the Universe begins to accelerate are also evaluated. The quartessence scenario, is favoured. A closed (and in some cases a flat) and accelerating Universe is also preferred. The CGM case $\alpha = 1$ is far from been ruled out, and it is even preferred in some particular cases. In most of the cases the $\Lambda$CDM is disfavoured with respect to GCGM and CGM.Comment: 23 pages, LaTeX 2e, 6 tables, 38 EPS figures, uses graphic