Second Order General Slow-Roll Power Spectrum

Recent combined results from the Wilkinson Microwave Anisotropy Probe (WMAP) and Sloan Digital Sky Survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.Comment: 11 pages, 1 figure ; A typo in Eq. (38) is fixed ; References expanded and a note adde

Completing Natural Inflation

If the inflaton is a pseudo-scalar axion, the axion shift symmetry can protect the flatness of its potential from too large radiative corrections. This possibility, known as natural inflation, requires an axion scale which is greater than the (reduced) Planck scale. It is unclear whether such a high value is compatible with an effective field theoretical description, and if the global axionic symmetry survives quantum gravity effects. We propose a mechanism which provides an effective large axion scale, although the original one is sub-Planckian. The mechanism is based on the presence of two axions, with a potential provided by two anomalous gauge groups. The effective large axion scale is due to an almost exact symmetry between the couplings of the axions to the anomalous groups. We also comment on a possible implementation in heterotic string theory.Comment: 9 pages, 1 figur

Evolution of Second-Order Cosmological Perturbations and Non-Gaussianity

We present a second-order gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann-Robertson-Walker universe filled by multiple interacting fluids. We apply such a general formalism to describe the evolution of the second-order curvature perturbations in the standard one-single field inflation, in the curvaton and in the inhomogeneous reheating scenarios for the generation of the cosmological perturbations. Moreover, we provide the exact expression for the second-order temperature anisotropies on large scales, including second-order gravitational effects and extend the well-known formula for the Sachs-Wolfe effect at linear order. Our findings clarify what is the exact non-linearity parameter f_NL entering in the determination of higher-order statistics such as the bispectrum of Cosmic Microwave Background temperature anisotropies. Finally, we compute the level of non-Gaussianity in each scenario for the creation of cosmological perturbations.Comment: 14 pages, LaTeX file. Further comments adde

The scalar bi-spectrum during preheating in single field inflationary models

In single field inflationary models, preheating refers to the phase that immediately follows inflation, but precedes the epoch of reheating. During this phase, the inflaton typically oscillates at the bottom of its potential and gradually transfers its energy to radiation. At the same time, the amplitude of the fields coupled to the inflaton may undergo parametric resonance and, as a consequence, explosive particle production can take place. A priori, these phenomena could lead to an amplification of the super-Hubble scale curvature perturbations which, in turn, would modify the standard inflationary predictions. However, remarkably, it has been shown that, although the Mukhanov-Sasaki variable does undergo narrow parametric instability during preheating, the amplitude of the corresponding super-Hubble curvature perturbations remain constant. Therefore, in single field models, metric preheating does not affect the power spectrum of the large scale perturbations. In this article, we investigate the corresponding effect on the scalar bi-spectrum. Using the Maldacena's formalism, we analytically show that, for modes of cosmological interest, the contributions to the scalar bi-spectrum as the curvature perturbations evolve on super-Hubble scales during preheating is completely negligible. Specifically, we illustrate that, certain terms in the third order action governing the curvature perturbations which may naively be expected to contribute significantly are exactly canceled by other contributions to the bi-spectrum. We corroborate selected analytical results by numerical investigations. We conclude with a brief discussion of the results we have obtained.Comment: v1: 15 pages, 4 figures; v2: 15 pages, 4 figures, discussion and references added, to appear in Phys. Rev.

The Price of WMAP Inflation in Supergravity

The three-year data from WMAP are in stunning agreement with the simplest possible quadratic potential for chaotic inflation, as well as with new or symmetry-breaking inflation. We investigate the possibilities for incorporating these potentials within supergravity, particularly of the no-scale type that is motivated by string theory. Models with inflation driven by the matter sector may be constructed in no-scale supergravity, if the moduli are assumed to be stabilised by some higher-scale dynamics and at the expense of some fine-tuning. We discuss specific scenarios for stabilising the moduli via either D- or F-terms in the effective potential, and survey possible inflationary models in the presence of D-term stabilisation.Comment: 15 pages, 6 figures, plain Late

The Lyth Bound and the End of Inflation

We derive an extended version of the well-known Lyth Bound on the total variation of the inflaton field, incorporating higher order corrections in slow roll. We connect the field variation $\Delta\phi$ to both the spectral index of scalar perturbations and the amplitude of tensor modes. We then investigate the implications of this bound for ``small field'' potentials, where the field rolls off a local maximum of the potential. The total field variation during inflation is {\em generically} of order $m_{\rm Pl}$, even for potentials with a suppressed tensor/scalar ratio. Much of the total field excursion arises in the last e-fold of inflation and in single field models this problem can only be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss the implications of this result for inflationary model building in string theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by JCAP

Naturally Large Cosmological Neutrino Asymmetries in the MSSM

A large neutrino asymmetry is an interesting possibility for cosmology, which can have significant observable consequences for nucleosynthesis and the cosmic microwave background. However, although it is a possibility, there is no obvious reason to expect the neutrino asymmetry to be observably large. Here we note that if the baryon asymmetry originates via the Affleck-Dine mechanism along a d=4 flat direction of the MSSM scalar potential and if the lepton asymmetry originates via Affleck-Dine leptogenesis along a d=6 direction, corresponding to the lowest dimension directions conserving R-parity, then the ratio n_{L}/n_{B} is naturally in the range 10^{8}-10^{9}. As a result, a potentially observable neutrino asymmetry is correlated with a baryon asymmetry of the order of 10^{-10}.Comment: 10 pages LaTeX. Final version to be published in Physical Review Letter

Primordial fluctuations and cosmological inflation after WMAP 1.0

The observational constraints on the primordial power spectrum have tightened considerably with the release of the first year analysis of the WMAP observations, especially when combined with the results from other CMB experiments and galaxy redshift surveys. These observations allow us to constrain the physics of cosmological inflation: (i) The data show that the Hubble distance is almost constant during inflation. While observable modes cross the Hubble scale, it changes by less than 3% during one e-folding: d(d_H)/dt < 0.032 at 2 sigma. The distance scale of inflation itself remains poorly constrained: 1.2 x 10^{-28} cm < d_H < 1 cm. (ii) We present a new classification of single-field inflationary scenarios (including scenarios beyond slow-roll inflation), based on physical criteria, namely the behaviour of the kinetic and total energy densities of the inflaton field. The current data show no preference for any of the scenarios. (iii) For the first time the slow-roll assumption could be dropped from the data analysis and replaced by the more general assumption that the Hubble scale is (almost) constant during the observable part of inflation. We present simple analytic expressions for the scalar and tensor power spectra for this very general class of inflation models and test their accuracy.Comment: 19 pages, 5 figures; section on the classification of models in the plane of tilt and tensor-to-scalar ratio added, references adde

Large-scale curvature perturbations with spatial and time variations of the inflaton decay rate

We present a gauge-invariant formalism to study the evolution of the curvature and entropy perturbations in the case in which spatial and time variations of the inflaton decay rate into ordinary matter are present. During the reheating stage after inflation curvature perturbations can vary with time on super-horizon scales sourced by a a gauge-invariant inflaton decay rate perturbation. We show that the latter is a function not only of the spatial variations of the decay rate generated during inflation, as envisaged in a recently proposed scenario, but also of the time variation of the inflaton decay rate during reheating. If only the second source is present, the final curvature perturbation at the end of the reheating stage is proportional to the curvature perturbation at the beginning of reheating with a coefficient of proportionality which can be either smaller or larger than unity depending upon the underlying physics governing the time variation of the inflaton decay rate. As a consequence, we show that the standard consistency relation between the amplitude of curvature perturbations, the amplitude of tensor perturbations and the tensor spectral index of one-single field models of inflation is violated and there is the possibility that the tensor-to-curvature amplitude ratio is larger than in the standard case.Comment: LaTeX file, 21 pages. A few typos correcte