From the production of primordial perturbations to the end of inflation

In addition to generating the appropriate perturbation power spectrum, an inflationary scenario must take into account the need for inflation to end subsequently. In the context of single-field inflation models where inflation ends by breaking of the slow-roll condition, we constrain the first and second derivatives of the inflaton potential using this additional requirement. We compare this with current observational constraints from the primordial spectrum and discuss several issues relating to our results.Comment: RevTex4, 6 pages, 7 figures. To match version accepted by PR

K-essence and the coincidence problem

K-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behaviour of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.Comment: 5 pages RevTeX4 file with two figures incorporated. Minor changes to match PRD accepted versio

Perturbations in cosmologies with a scalar field and a perfect fluid

We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set of dynamical gauge-invariant equations in terms of the curvature and entropy perturbations, and display an efficient formulation of these equations as a first-order system linked by a fairly sparse matrix. Our formalism includes spatial gradients, extending previous formulations restricted to the large-scale limit, and fully accounts for the evolution of an isocurvature mode intrinsic to the scalar field. We then address the issue of the adiabatic condition, in particular demonstrating its preservation on large scales. Finally, we apply our formalism to the quintessence scenario and clearly underline the importance of initial conditions when considering late-time perturbations. In particular, we show that entropy perturbations can still be present when the quintessence field energy density becomes non-negligible.Comment: RevTex4, 9 pages, 3 figures. Significant additions on the quintessence scenario (new appendix and additional numerical example). Conclusions unchanged, but more robus

A new view of k-essence

K-essence models, relying on scalar fields with non-canonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behaviour of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine tuning arising in the models.Comment: 7 pages RevTeX4 file with four figures incorporate

Initial conditions for quintessence after inflation

We consider the behaviour of a quintessence field during an inflationary epoch, in order to learn how inflation influences the likely initial conditions for quintessence. We use the stochastic inflation formalism to study quantum fluctuations induced in the quintessence field during the early stages of inflation, and conclude that these drive its mean to large values (> 0.1 m_{Planck}). Consequently we find that tracker behaviour typically starts at low redshift, long after nucleosynthesis and most likely also after decoupling.Comment: 6 pages RevTeX4 file with five figures incorporated. Matches published versio