Slow-roll Inflationary Models Research Articles

The properties of the dark matter halo distribution in non-Gaussian scenarios

The description of halo abundance and clustering for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter | f NL | of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial | f NL | ≪ 1 , this signal sources extra contributions to the effective f NL of large-scale structures that are expected to be above the predicted detection threshold [C. Carbone, L. Verde, and S. Matarrese, ApJL 684 (2008) L1]. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. In particular, when we calibrate the analytic non-Gaussian mass function of [S. Matarrese, L. Verde, L. and R. Jimenez, ApJL 541 (2000) 10] and [M. LoVerde, A. Miller, S. Shandera and L. Verde, JCAP 04 (2008) 014] and the analytic description of halo clustering for non-Gaussian initial conditions on N-body simulations, we find excellent agreement between the simulations and the analytic predictions if we make the substitutions δ c → δ c × q and δ c → δ c × q where q ≃ 0.75 , in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of these corrections on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.

Erratum: Intuitive understanding of non-Gaussianity in ekpyrotic and cyclic models [Phys. Rev. D78, 023506 (2008)

It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-gaussianity. In this paper, we present a physically intuitive, semi-analytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-gaussianity parameter f_{NL} that is determined by the geometric mean of the equation of state w_{ek} during the ekpyrotic phase and w_{c} during the phase that curvature perturbations are generated and whose value is O(100) or more times the intrinsic value predicted by simple slow-roll inflationary models, f_{NL}^{intrinsic} = O(0.1). Other contributions to f_{NL}, which we also estimate, can increase |f_{NL}| but are unlikely to decrease it significantly, making non-gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-gaussianity and scalar spectral index that sharpens the test.

INFLATION AND SQUEEZED STATES: LATTICE SCHRÖDINGER PICTURE

In lattice Schrödinger picture, the wave functionals of the squeezed vacuum states of a free real scalar field in de Sitter space are constructed explicitly in momentum space by using the method of instantaneous Hamiltonian diagonalization. The modified power spectrum and particle production in the general mixed, squeezed initial states are also presented. For the massless minimally coupled scalar field which is relevant to slow roll inflationary models, we recover the power spectrum of scalar fluctuations for the squeezed vacuum states, and show that the evolution of the squeezed vacuum states exhibits an attractor behavior. The case of a massless conformally coupled scalar field is also discussed.

Inflationary trispectrum from graviton exchange

We compute the connected four-point correlation function of the primordial curvature perturbation generated during inflation with standard kinetic terms, where the correlation is established via exchange of a graviton between two pairs of scalar fluctuations. Any such correlation yields a contribution to the scalar trispectrum of the order of the tensor to scalar ratio r. This contribution is numerically one order of magnitude larger than the one previously calculated on the basis of scalar perturbations interacting at a point and satisfies a simple relation in the limit where the momentum of the graviton which is exchanged becomes much smaller than the external momenta. We conclude that the total non-linearity parameter generated by single-field models of slow-roll inflation is at maximum |τNL| ∼ r.

Non-canonical generalizations of slow-roll inflation models

We consider non-canonical generalizations of two classes of single-field inflation models. First, we study the non-canonical version of ''ultra-slow roll'' inflation, which is a class of inflation models for which quantum modes do not freeze at horizon crossing, but instead evolve rapidly on superhorizon scales. Second, we consider the non-canonical generalization of the simplest ''chaotic'' inflation scenario, with a potential dominated by a quadratic (mass) term for the inflaton. We find a class of related non-canonical solutions with polynomial potentials, but with varying speed of sound. These solutions are characterized by a constant field velocity, and we dub such models isokinetic inflation. As in the canonical limit, isokinetic inflation has a slightly red-tilted power spectrum, consistent with current data. Unlike the canonical case, however, these models can have an arbitrarily small tensor/scalar ratio. Of particular interest is that isokinetic inflation is marked by a correlation between the tensor/scalar ratio and the amplitude of non-Gaussianity such that parameter regimes with small tensor/scalar ratio have large associated non-Gaussianity, which is a distinct observational signature.

Non-Gaussian Halo Bias and Future Galaxy Surveys

We forecast constraints on primordial non-Gaussianity achievable from forthcoming surveys by exploiting the scale-dependent halo bias introduced on large scales by non-Gaussian initial conditions. We explore the performance of exploiting both the shape of the galaxy power-spectrum on large scales and the cross-correlation of galaxies with Cosmic Microwave Background maps through the Integrated Sachs Wolfe effect. We find that future surveys can detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter $|f_{\rm NL}|$ of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial $|f_{\rm NL}|\ll 1$, this signal sources extra contributions to the effective $f_{\rm NL}$ of large-scale structures that are expected to be above our predicted detection threshold.

Volume-weighted measure for eternal inflation

I propose a new volume-weighted probability measure for cosmological ``multiverse'' scenarios involving eternal inflation. The ``reheating-volume (RV) cutoff'' calculates the distribution of observable quantities on a portion of the reheating hypersurface that is conditioned to be finite. The RV measure is gauge-invariant, does not suffer from the ``youngness paradox,'' and is independent of initial conditions at the beginning of inflation. In slow-roll inflationary models with a scalar inflaton, the RV-regulated probability distributions can be obtained by solving nonlinear diffusion equations. I discuss possible applications of the new measure to ``landscape'' scenarios with bubble nucleation. As an illustration, I compute the predictions of the RV measure in a simple toy landscape.

On the issue of the ζ series convergence and loop corrections in the generation of observable primordialnon-Gaussianity in slow-roll inflation: I. The bispectrum

We show in this paper that it is possible to attain very high,including observable, values for the level of non-GaussianityfNL associated withthe bispectrum Bζ of the primordial curvature perturbationζ, in a subclass of small-field slow-roll models of inflation with canonical kinetic terms.Such a result is obtained by taking care of loop corrections both in the spectrumPζ and in thebispectrum Bζ.Sizable values for fNL arise even if ζ is generated during inflation. Five issues are considered when constraining the availableparameter space: (1) We must ensure that we are in a perturbative regime so that theζ series expansion, and its truncation, are valid. (2) We mustapply the correct condition for the (possible) loop dominance inBζ and/or Pζ. (3) We must satisfy the spectrum normalization condition. (4) We must satisfy thespectral tilt constraint. (5) We must have enough inflation to solve the horizonproblem.

Intuitive understanding of non-Gaussianity in ekpyrotic and cyclic models

It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-Gaussianity. In this paper, we present a physically intuitive, semianalytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-Gaussianity parameter ${f}_{NL}$ that is determined by the geometric mean of the equation of state ${w}_{ek}$ during the ekpyrotic phase and ${w}_{c}$ during the phase that curvature perturbations are generated, and whose value is $\mathcal{O}(100)$ or more times the intrinsic value predicted by simple slow-roll inflationary models, ${f}_{NL}^{\mathrm{intrinsic}}=\mathcal{O}(0.1)$. Other contributions to ${f}_{NL}$, which we also estimate, can increase $|{f}_{NL}|$ but are unlikely to decrease it significantly, making non-Gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-Gaussianity and scalar spectral index that sharpens the test.

Black hole formation and slow-roll inflation

Black hole formation may occur if the spectrum of the curvature perturbationζ increases strongly as the scale decreases. As no such increase is observed oncosmological scales, black hole formation requires strongly positive runningn′ of thespectral index n, though the running might only kick in below the ‘cosmological scales’ probed bythe cosmic microwave background anisotropy and galaxy surveys. A concreteand well-motivated way of producing this running is through the runningmass model of slow-roll inflation. We obtain a new observational boundn′<0.026 on the running provided by this model, improving an earlier result by a factor 2. We alsodiscuss black hole production in more general scenarios. We show that the usual conditions and are enough to derive the spectrum , the introduction of higher order parametersξ2 etc being optional.

Inflation without inflaton(s)

We propose a model for early universe cosmology without the need for fundamentalscalar fields. Cosmic acceleration and phenomenologically viable reheating of theuniverse result from a series of energy transitions, where during each transitionvacuum energy is converted to thermal radiation. We show that this ‘cascadinguniverse’ can lead to successful generation of adiabatic density fluctuations and anobservable gravity wave spectrum in some cases, where in the simplest case itreproduces a spectrum similar to slow-roll models of inflation. We also find the modelprovides a reasonable reheating temperature after inflation ends. This type ofmodel may also be relevant for addressing the smallness of the vacuum energytoday.

Constraints on the spectral index for the inflation models in the string landscape

We conjecture that the inflation models with trans-Planckian excursions in the field space should be in the swampland. We check this conjecture in a few examples and investigate the constraints on the spectral index for the slow-roll inflation model in the string landscape where the variation of the inflaton during the period of inflation is less than the Planck scale ${M}_{p}$. A red primordial power spectrum with a lower bound on the spectral index is preferred. Both the tensor-scalar ratio and the running can be ignored.

Slow-roll reconstruction for running spectral index

We reconstruct from the Wilkinson microwave anisotropy probe three-year data the slow-roll parameters in the standard slow-roll inflation model and the noncommutative inflation model. We also investigate the evolution of these slow-roll parameters. Requiring that slow-roll inflation lasts more than 20 e-folds after cosmic microwave background scales leave the horizon, we find that the potential at the last stage of inflation takes the form $V(\ensuremath{\phi})={V}_{0}(1+\frac{{\ensuremath{\eta}}_{c}}{2}\frac{(\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{c}{)}^{2}}{{M}_{p}^{2}})$, where ${\ensuremath{\eta}}_{c}$ is a constant. A natural mechanism to end inflation at $\ensuremath{\phi}={\ensuremath{\phi}}_{c}$ is the hybrid-type inflation.

Inflation in uplifted supergravities

We present a model of slow roll inflation in the context of effective supergravities arising from stringtheories. The uplifting of the potential (to generate de Sitter or Minkowski vacua) is provided by theD-term associatedwith an anomalous U(1), in a fully consistent and gauge invariant formulation. We develop a minimal workingmodel which incorporates eternal topological inflation and complies with observationalconstraints, avoiding the usual obstacles to implementing successful inflation (theη problem and the initial condition problem among others).

A note on nonlinear curvature perturbations in an exactly soluble model of multi-component slow-roll inflation

Using the nonlinear δN formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.

Slow roll reconstruction: constraints on inflation from the 3 year WMAP dataset

We study the constraints on the inflationary parameter space derived from the 3year WMAP data set using ‘slow roll reconstruction’, using the SDSS galaxypower spectrum to gain further leverage where appropriate. This approach insertsthe inflationary slow roll parameters directly into a Monte Carlo Markov chainestimate of the cosmological parameters, and uses the inflationary flow hierarchy tocompute the parameters’ scale dependence. We work with the first three parameters(ϵ,η and ξ) and pay close attention to the possibility that the 3 year WMAP data setcontains evidence for a ‘running’ spectral index, which is dominated by theξ term. Mirroring the WMAP team’s analysis we find that the permitted distribution ofξ is broad, and centred away from zero. However, when we require thatinflationary parameters yield at least 30 additional e-folds of inflationafter the largest observable scales leave the horizon, the bounds onξ tighten dramatically. We make use of the absence of an explicit pivot scale in theslow roll reconstruction formalism to determine the dependence of the computedparameter distributions on the pivot. We show that the choice of pivot has asignificant effect on the inferred constraints on the inflationary variables, and thespectral index and running derived from them. Finally, we argue that the nextround of cosmological data can be expected to place very stringent constraints onthe region of parameter space open to single field models of slow roll inflation.

Predictions of single field inflation for the tensor/scalar ratio and the running spectral index

We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn{sub s}/dlnk are studied in detail. We derive explicit formulas for n{sub s}, r and dn{sub s}/dlnk and provide relevant plots. In new inflation, and for the chosen central value n{sub s}=0.95, we predict 0.03 1 behavior. Hybrid inflation for {mu}{sub 0}{sup 2}>{lambda}{sub 0}M{sub Pl}{sup 2}/192 fulfills all the present CMB+LSS data for a large enough initial inflaton amplitude. Even if chaotic inflation predicts n{sub s} values compatible with the data, chaotic inflation is disfavored since it predicts a too high value r{approx_equal}0.27 for the ratio of tensor to scalar fluctuations. The model which best agrees with the current data and which best prepares the way to the expected data r(less-or-similar sign)0.1, is the trinomial potential with negative mass term: new inflation.« less

Bayesian model selection analysis of WMAP3

We present a Bayesian model selection analysis of WMAP3 data using our code CosmoNest. We focus on the density perturbation spectral index nS and the tensor-to-scalar ratio r, which define the plane of slow-roll inflationary models. We find that while the Bayesian evidence supports the conclusion that nS 6= 1, the data are not yet powerful enough to do so at a strong or decisive level. If tensors are assumed absent, the current odds are approximately 8 to 1 in favour of nS 6= 1 under our assumptions, when WMAP3 data is used together with external data sets. WMAP3 data on its own is unable to distinguish between the two models. Further, inclusion of r as a parameter weakens the conclusion against the Harrison–Zel’dovich case (nS = 1, r = 0), albeit in a prior-dependent way. In appendices we describe the CosmoNest code in detail, noting its ability to supply posterior samples as well as to accurately compute the Bayesian evidence. We make a first public release of CosmoNest, now available at www.cosmonest.org.

Approximate consistency condition from a running spectral index in slow-roll inflationary models

Density perturbations generated from inflation almost always have a spectral index ${n}_{s}$ which runs (varies with the wavelength). We explore a running spectral index scenario in which the scalar spectral index runs from blue (${n}_{s}g1$) on large length scales to red (${n}_{s}l1$) on short length scales. Specifically, we look for a correlation between the length scale at which ${n}_{s}\ensuremath{-}1=0$ and the length scale at which tensor to scalar ratio $\mathcal{T}/\mathcal{S}$ reaches a minimum for single field slow-roll inflationary models. By computing the distribution of length scale ratios, we conclude that there indeed is a new approximate consistency condition that is characteristic of running spectral index scenarios that run from blue to red. Specifically, with strong running, we expect 96% of the slow-roll models to have the two length scales to be within a factor of 2, with the length scale at which the tensor to scalar ratio reaching a minimum longer than the wavelength at which ${n}_{s}\ensuremath{-}1=0$.

Direct detection of the inflationary gravitational-wave background

Inflation generically predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO) or Japan's Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO), both currently under study. Here we investigate the detectability of the inflationary gravitational-wave background at BBO/DECIGO frequencies. To do so, we survey a range of slow-roll inflationary models consistent with constraints from the CMB and large-scale structure (LSS). We go beyond the usual assumption of power-law power spectra, which may break down given the 16 orders of magnitude in frequency between the CMB and direct detection, and solve instead the inflationary dynamics for four classes of inflaton potentials. Direct detection is possible in a variety of inflationary models, although probably not in any in which the gravitational-wave signal does not appear in the CMB polarization. However, direct detection by BBO/DECIGO can help discriminate between inflationary models that have the same slow-roll parameters at CMB/LSS scales.