f(R)f(R) constant-roll inflation

The previously introduced class of two-parametric phenomenological inflationary models in General Relativity in which the slow-roll assumption is replaced by the more general, constant-roll condition is generalized to the case of $f(R)$ gravity. A simple constant-roll condition is defined in the original Jordan frame, and exact expressions for a scalaron potential in the Einstein frame, for a function $f(R)$ (in the parametric form) and for inflationary dynamics are obtained. The region of the model parameters permitted by the latest observational constraints on the scalar spectral index and the tensor-to-scalar ratio of primordial metric perturbations generated during inflation is determined.Comment: 8 pages, 3 figures; added Fig. 2 and Appendix, matches published versio

Constant-roll inflation: confrontation with recent observational data

The previously proposed class of phenomenological inflationary models in which the assumption of inflaton slow-roll is replaced by the more general, constant-roll condition is compared with the most recent cosmological observational data, mainly the Planck ones. Models in this two-parametric class which remain viable appear to be close to the slow-roll ones, and their inflaton potentials are close to (but still different from) that of the natural inflation model. Permitted regions for the two model parameters are presented.Comment: 4 pages, 1 figure; published versio

Correlation Functions in Stochastic Inflation

Combining the stochastic and $\delta N$ formalisms, we derive non perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and comment on the physical implications of this effect.Comment: 20 pages plus appendix, 4 figures, published in EPJC, typo corrected in Eq. (3.37

Stochastic dark energy from inflationary quantum fluctuations

We study the quantum backreaction from inflationary fluctuations of a very light, non-minimally coupled spectator scalar and show that it is a viable candiate for dark energy. The problem is solved by suitably adapting the formalism of stochastic inflation. This allows us to self-consistently account for the backreaction on the background expansion rate of the Universe where its effects are large. This framework is equivalent to that of semiclassical gravity in which matter vacuum fluctuations are included at the one loop level, but purely quantum gravitational fluctuations are neglected. Our results show that dark energy in our model can be characterized by a distinct effective equation of state parameter (as a function of redshift) which allows for testing of the model at the level of the background.Comment: 32 pages, 5 figures; published version, significant change

What do WMAP and SDSS really tell about inflation?

We derive new constraints on the Hubble function H(phi) and subsequently on the inflationary potential V(phi) from WMAP 3-year data combined with the Sloan Luminous Red Galaxy survey (SDSS-LRG), using a new methodology which appears to be more generic, conservative and model-independent than in most of the recent literature, since it depends neither on the slow-roll approximation, nor on any extrapolation scheme for the potential beyond the observable e-fold range, nor on additional assumptions about initial conditions for the inflaton velocity. This last feature represents the main improvement of this work, and is made possible by the reconstruction of H(phi) prior to V(phi). Our results only rely on the assumption that within the observable range, corresponding to ~ 10 e-folds, inflation is not interrupted and the function H(phi) is smooth enough for being Taylor-expanded at order one, two or three. We conclude that the variety of potentials allowed by the data is still large. However, it is clear that the first two slow-roll parameters are really small while the validity of the slow-roll expansion beyond them is not established.Comment: 5 pages, 3 figures. Numerical module available at http://wwwlapp.in2p3.fr/~valkenbu/inflationH/ . References added, discussion expande

Is cosmic acceleration slowing down?

We investigate the course of cosmic expansion in its `recent past' using the Constitution SN Ia sample (which includes CfA data at low redshifts), jointly with signatures of baryon acoustic oscillations (BAO) in the galaxy distribution and fluctuations in the cosmic microwave background (CMB). Earlier SN Ia data sets could not address this issue because of a paucity of data at low redshifts. Allowing the equation of state of dark energy (DE) to vary, we find that a coasting model of the universe (q_0=0) fits the data about as well as LCDM. This effect, which is most clearly seen using the recently introduced `Om' diagnostic, corresponds to an increase of Om(z) and q(z) at redshifts z \lleq 0.3. In geometrical terms, this suggests that cosmic acceleration may have already peaked and that we are currently witnessing its slowing down. The case for evolving DE strengthens if a subsample of the Constitution set consisting of SNLS+ESSENCE+CfA SN Ia data is analysed in combination with BAO+CMB using the same statistical methods. The effect we observe could correspond to DE decaying into dark matter (or something else). A toy model which mimics this process agrees well with the combined SN Ia+BAO+CMB data.Comment: 6 pages, 5 figures, presentation expanded, results for a new subsample of the Constitution set are added, new BAO data are accounted for, main results unchange