Non-gaussianity from the second-order cosmological perturbation

Several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-gaussianity in the primordial curvature perturbation \zeta, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter \zeta (and hence f_{NL}) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Non-adiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (`light non-inflaton fields'). During single-component inflation f_{NL} is constant, but multi-component inflation might generate |f_{NL}| \sim 1 or bigger. Preheating can affect f_{NL} only in atypical scenarios where it involves light non-inflaton fields. The curvaton scenario typically gives f_{NL} \ll -1 or f_{NL} = +5/4. The inhomogeneous reheating scenario can give a wide range of values for f_{NL}. Unless there is a detection, observation can eventually provide a limit |f_{NL}| \lsim 1, at which level it will be crucial to calculate the precise observational limit using second order theory.Comment: Latex file in Revtex style. 13 pages, 1 figure. v2: minor changes. Discussion in Subsection VI-A enlarged. References added. Conclusions unchanged. v3: minor typographic changes. Correlated and uncorrelated \chi^2 non-gaussianity concepts and consequences introduced. Section VI-A enlarged. Small change in Table I. References updated and added. Conclusions unchanged. Version to appear in Physical Review

Chaotic Inflation with Time-Variable Space Dimensions

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2\phi^2/2$. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.Comment: 19 pages, To be published in Int.J.Mod.Phys.D. Minor changes to match accepted versio

Contribution of the hybrid inflation waterfall to the primordial curvature perturbation

A contribution $\zeta_\chi$ to the curvature perturbation will be generated during the waterfall that ends hybrid inflation, that may be significant on small scales. In particular, it may lead to excessive black hole formation. We here consider standard hybrid inflation, where the tachyonic mass of the waterfall field is much bigger than the Hubble parameter. We calculate $\zeta_\chi$ in the simplest case, and see why earlier calculations of $\zeta_\chi$ are incorrect.Comment: Simpler and more complete results, especiallly for delta N approac

Non-Gaussianity in Axion N-flation Models

We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter fNL may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation

A new approach to the evolution of cosmological perturbations on large scales

We discuss the evolution of linear perturbations about a Friedmann-Robertson-Walker background metric, using only the local conservation of energy-momentum. We show that on sufficiently large scales the curvature perturbation on spatial hypersurfaces of uniform-density is conserved when the non-adiabatic pressure perturbation is negligible. This is the first time that this result has been demonstrated independently of the gravitational field equations. A physical picture of long-wavelength perturbations as being composed of separate Robertson-Walker universes gives a simple understanding of the possible evolution of the curvature perturbation, in particular clarifying the conditions under which super-horizon curvature perturbations may vary.Comment: 8 pages, revtex, 1 figure, version to appear in Phys Rev D. Sign errors in original version corrected plus other minor addition

The abundance of relativistic axions in a flaton model of Peccei-Quinn symmetry

Flaton models of Peccei-Quinn symmetry have good particle physics motivation, and are likely to cause thermal inflation leading to a well-defined cosmology. They can solve the $\mu$ problem, and generate viable neutrino masses. Canonical flaton models predict an axion decay constant F_a of order 10^{10} GeV and generic flaton models give F_a of order 10^9 GeV as required by observation. The axion is a good candidate for cold dark matter in all cases, because its density is diluted by flaton decay if F_a is bigger than 10^{12} GeV. In addition to the dark matter axions, a population of relativistic axions is produced by flaton decay, which at nucleosynthesis is equivalent to some number \delta N_\nu of extra neutrino species. Focussing on the canonical model, containing three flaton particles and two flatinos, we evaluate all of the flaton-flatino-axion interactions and the corresponding axionic decay rates. They are compared with the dominant hadronic decay rates, for both DFSZ and KSVZ models. These formulas provide the basis for a precise calculation of the equivalent \delta N_\nu in terms of the parameters (masses and couplings). The KSVZ case is probably already ruled out by the existing bound \delta N_\nu\lsim 1. The DFSZ case is allowed in a significant region of parameter space, and will provide a possible explanation for any future detection of nonzero $\delta N_\nu$

Generating the curvature perturbation at the end of inflation

The dominant contribution to the primordial curvature perturbation may be generated at the end of inflation. Taking the end of inflation to be sudden, formulas are presented for the spectrum, spectral tilt and non-gaussianity. They are evaluated for a minimal extension of the original hybrid inflation model.Comment: 5 pages. v3: as it will appear in JCA

Observational constraints on the spectral index of the cosmological curvature perturbation

We evaluate the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM hypothesis which represents the simplest viable cosmology. We first take $n$ to be practically scale-independent. Ignoring reionization, we find at a nominal 2-$\sigma$ level $n\simeq 1.0 \pm 0.1$. If we make the more realisitic assumption that reionization occurs when a fraction $f\sim 10^{-5}$ to 1 of the matter has collapsed, the 2-$\sigma$ lower bound is unchanged while the 1-$\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of $n$, which occurs in a physically reasonable regime of parameter space.Comment: ReVTeX, 15 pages, 5 figures and 3 tables, uses epsf.sty Improved treatment of reionization and small bug fixed in the constant n case; more convenient parameterization and better treatment of the n dependence in the CMB anisotropy for the running mass case; conclusions basically unchanged; references adde

Revisiting Cosmic No-Hair Theorem for Inflationary Settings

In this work we revisit Wald's cosmic no-hair theorem in the context of accelerating Bianchi cosmologies for a generic cosmic fluid with non-vanishing anisotropic stress tensor and when the fluid energy momentum tensor is of the form of a cosmological constant term plus a piece which does not respect strong or dominant energy conditions. Such a fluid is the one appearing in inflationary models. We show that for such a system anisotropy may grow, in contrast to the cosmic no-hair conjecture. In particular, for a generic inflationary model we show that there is an upper bound on the growth of anisotropy. For slow-roll inflationary models our analysis can be refined further and the upper bound is found to be of the order of slow-roll parameters. We examine our general discussions and our extension of Wald's theorem for three classes of slow-roll inflationary models, generic multi-scalar field driven models, anisotropic models involving U(1) gauge fields and the gauge-flation scenario.Comment: 21 pp, 4 .eps figure