In the context of Brans{Dicke theories, eternal ination is described in such a w a y that the evolution of the inaton eld is determined by the value of the Planck mass in dierent regions of the universe. The Planck mass is given by the values of the Brans{Dicke eld, which is coupled to the scalar curvature in the Lagrangian. We rst calculate the joint probability distributions of the inaton and Brans{Dicke elds, in order to compute the 3{volume ratios of homogeneous regions with arbitrary values of the elds still undergoing ination with respect to thermalized regions. From these volume ratios one is able to extract information on the values of the elds measured by a t ypical observer for a given potential and, in particular, the typical value of the Planck mass at the end of ination. In this paper, we i n v estigate volume ratios using a regularization procedure suggested by Vilenkin, and the results are applied to powerlaw and double{well potentials. The spectrum of density uctuations is calculated for generic potentials, and we discuss the likelihood of various scenarios that could tell us whether our region of the universe is typical or untypical depending on very general bounds on the evolution of the Brans{Dicke eld.

A scheme is developed which enables one to trace backwards in time the cosmic density and velocity elds, and to determine accurately the current-epoch velocity eld from the current-epoch density eld, or vice versa. The scheme implements the idea of Giavalisco et al. (1993) that the principle of least action should be used to formulate gravitational instability as a two-point boundary-value problem. We argue that the Eulerian formulation of the problem is to be preferred to the Lagrangian one, on grounds of computational simplicity, of ease of interfacing with observational data, and of internal consistency at early times. The scheme is successfully tested on an exact solution in one dimension, and on currently Gaussian elds in one and two dimensions. The application of the scheme to real observational data appears to be eminently feasible, though computationally costly.

A cosmological scenario is proposed where the dark matter (DM) and dark energy (DE) of the universe are two simultaneous manifestations of an inhomogeneous dilaton. The equation of state of the field is scale dependent and pressureless at galactic and larger scales and it has negative pressure as a DE at very large scales. The dilaton drives an initial inflationary phase followed by a kinetic energy-dominated one, as in the "quintessential inflation" model introduced by Peebles & Vilenkin, and soon after the end of inflation particle production seeds the first inhomogeneities that lead to galaxy formation. The dilaton is trapped near the minimum of the potential where it oscillates like a massive field, and the excess of kinetic energy is dissipated via the mechanism of "gravitational cooling" first introduced by Seidel & Suen. The inhomogeneities therefore behave like solitonic oscillations around the minimum of the potential, known as "oscillatons", that we propose account for most DM in galaxies. Those regions where the dilaton does not transform enough kinetic energy into reheating or carry an excess of it from regions that have cooled, evolve to the tail of the potential as DE, driving the acceleration of the universe.PACS numbers: 98.80.Bp, 98.80.Cq, 98.80.Ft, 95.35.+d, 98.62.Gq, 04.50.+h

In this paper we investigate extended inflation with an exponential potential V (σ) = V0 e −κσ , which provides a simple cosmological scenario where the distribution of the constants of Nature is mostly determined by κ. In particular, we show that this theory predicts a uniform distribution for the Planck mass at the end of inflation, for the entire ensemble of universes that undergo stochastic inflation. Eternal inflation takes place in this scenario for a broad family of initial conditions, all of which lead up to the same value of the Planck mass at the end of inflation. The predicted value of the Planck mass is consistent with the observed value within a comfortable range of values of the parameters involved. PACS: 98.80.Cq gr-qc/9804081

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