Inflationary Trajectory Research Articles

Global stability analysis for scalar‐tensor models

AbstractThe phase space of a cosmological model with a scalar field coupled to curvature is discussed in detail for any value of the coupling constant ξ and any power law (ϕ2n) potential. The results obtained generalize previous studies with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). In many cases one finds global attractors and inflationary trajectories, with or without the correct Friedmannian limit. If the coupling constant is positive, a forbidden region cuts out a large part of the phase space, while, if it is negative, escaping regions may occur. Semi‐classical instability of vacuum states and singularity‐free trajectories are also discussed.

Initial conditions for R+ epsilon R2 cosmology.

A pure gravity cosmology based on the R+\ensuremath{\epsilon}${R}^{2}$ Lagrangian is known to exhibit inflation for a wide range of initial conditions. In this paper we use the wave function from quantum cosmology to describe this inflation as a chaotic inflationary phase immediately following the quantum creation of the Universe. We evaluate, compare, and discuss the distributions over initial conditions that are fixed by the two boundary-condition proposals of Hartle and Hawking (``no boundary'') and Vilenkin (``tunneling from nothing''). We find that among all classical inflationary trajectories that begin on the classical-quantum boundary, those that lead to an inflation of at least 70 e-foldings make up a fraction of \ensuremath{\sim}exp${(\mathrm{\ensuremath{-}}10}^{12}$) in the former case and \ensuremath{\sim}1-exp(-8\ifmmode\times\else\texttimes\fi{}${10}^{10}$) in the latter. Thus, in the simplest interpretation, the observable Universe would be the outcome of a rare event for the first boundary-condition proposal and a typical event for the second.

Initial conditions for perturbations in R+ epsilon R2 cosmology.

In a classical inflationary cosmology based on the R+\ensuremath{\epsilon}${R}^{2}$ Lagrangian the parameters of the model (such as \ensuremath{\epsilon} and the initial conditions for inflationary trajectories) are constrained by the observational requirement that any perturbations be delivered small to the present horizon volume. Previous calculations of the evolution of these perturbations (and, hence, of the parameter constraints enforced by their evolution) have assumed that the modes begin in their ground state. In this paper, following the procedure of Halliwell and Hawking, the Wheeler-DeWitt equation is derived for this model's inhomogeneous modes in perturbative superspace. Then, the two boundary-condition proposals of Hartle and Hawking (``no boundary'') and Vilenkin (``tunneling from nothing'') are implemented, verifying that both boundary conditions require the inhomogeneous modes to begin in their ground states.