Lattice simulations of inflation

We investigate the dynamics of inflation models driven by multiple, decoupled scalar fields and calculate the Hubble parameter and the amplitude of the lightest field at the end of inflation. The results are very simple and similar to those of the single field inflation, mainly depending on the underlying spectrum of the masses. The mass distribution is heavily constrained by the power spectrum of density perturbations P and the spectral index ns. The overall mass scale gives the amplitude of P and ns is affected by the number of fields and the spacing between masses in the distribution. The drop‐out effect of the massive fields makes the perturbation spectrum typically redder than the single field inflation spectrum. We illustrate this using two different mass distributions.

We revisit the idea of generating primordial anisotropies at the end of inflation in models of inflation with gauge fields. To be specific we consider the charged hybrid inflation model where the waterfall field is charged under a U(1) gauge field so the surface of end of inflation is controlled both by inflaton and the gauge fields. Using δN formalism properly we find that the anisotropies generated at the end of inflation from the gauge field fluctuations are exponentially suppressed on cosmological scales. This is because the gauge field evolves exponentially during inflation while in order to generate appreciable anisotropies at the end of inflation the spectator gauge field has to be frozen. We argue that this is a generic feature, that is, one can not generate observable anisotropies at the end of inflation within an FRW background.

We investigate the production of dark matter from metric perturbations produced during inflation or in standard cosmology. Perturbations break Weyl flatness of the Friedmann-Lemaître-Robertson-Walker metric, allowing conformally coupled fields-in particular, fermions studied here-to be produced even when their mass is negligible. Particle production can be computed by studying the Bogoliubov transformation induced by the stochastic background. For perturbations generated during inflation, we present a closed formula for the resulting abundance of particles that depends solely on the power spectrum of curvature perturbations at the end of inflation. This production mechanism can be dominant especially if the amplitude of curvature perturbations is enhanced for modes that exit the horizon toward the end of inflation. In the simplest scenario, the critical dark matter abundance is reproduced for M≳10^{6} GeV.

The advent of explicit Dirac-Born-Infeld inflationary models within string theory has drawn renewed interest to the cosmological role of unusual scalar field dynamics, usually referred to as $k$-inflation. In this situation, the standard method used to determine the behavior of cosmological perturbations breaks down. We present a generic method, based on the uniform approximation, to analytically derive the power spectra of scalar and tensor perturbations. For this purpose, a simple hierarchy of parameters, related to the sound speed of the cosmological fluctuations and its successive derivatives, is introduced in a $k$-inflation analogue of the Hubble flow functions. The scalar spectral index and its running are obtained up to next-to-next-to-leading order for all $k$-inflationary models. This result relies on the existence of a well-motivated initial state, which is not trivial in the present context: having the wavelength of the Fourier mode smaller than the sonic horizon is indeed not enough and some conditions on the dynamics of the sound speed are also required. Our method is then applied to various models encountered in the literature. After deriving a generic slow-roll trajectory valid for any Dirac-Born-Infeld model, simple formulae for the cosmological observables are obtained. In particular, the running, as the spectral index, for the so-called UV and IR brane inflationary models is found to be uniquely determined by the 't Hooft coupling. Finally, the accuracy of these cosmological predictions is assessed by comparing the analytical approximations with exact numerical integrations.

The effect of the length of inflation on the power spectra of scalar and tensor perturbations is estimated using the power-law inflation model with a scale factor of a(η) = (−η)p = tq. Considering various pre-inflation models with radiation-dominated or scalar matter-dominated periods before inflation in combination with two matching conditions, the temperature angular power spectrum (TT) and temperature–polarization cross-power spectrum (TE) are calculated and a likelihood analysis is performed. It is shown that the discrepancies between the Wilkinson microwave anisotropy probe (WMAP) data and the ΛCDM model, such as suppression of the spectrum at l = 2, 3 and oscillatory behaviour, may be explained by the finite length of inflation model if the length of inflation is near 60 e-folds and q ⩾ 300. The proposed models retain similar values of χ2 to that achieved by the ΛCDM model with respect to fit to the WMAP data, but display different characteristics of the angular TE power spectra at l ⩽ 20.

We investigate in the context of brane inflation the possibility of additional light scalar fields generating significant power spectrum and non-Gaussianities at the end of inflation affecting the CMB scale observations. We consider the specific mechanism outlined by Lyth and describe the necessary criteria for it to be potentially important in a warped throat. We also discuss different mechanisms for uplifting the vacuum energy which can lead to different dominant contributions of the inflaton potential near the end of inflation. We then apply such criteria to one of the most detailed brane inflation models to date, and show that inflation can persist towards the tip of the throat, however for the specific stable inflationary trajectory, the light residual isometry direction becomes degenerate. We also estimate the effects for other inflationary trajectories with non-degenerate residual isometries.

The production of GWs during preheating in the Starobinsky model with a nonminimally coupled auxiliary scalar field is studied through the lattice simulation in this paper. We find that the GW spectrum Omega _{mathrm{gw}} grows fast with the increase of the absolute value of coupling parameter xi . This is because the resonant bands become broad with the increase of |xi |. When xi <0, Omega _{mathrm{gw}} begins to grow once the inflation ends and grows faster than the case of xi >0. Omega _{mathrm{gw}} reaches the maximum at xi =-20 (xi =42 for the case xi >0) and then decreases with slight oscillation. Furthermore we find that the GWs produced in the era of preheating satisfy the limits from the Planck and next-generation CMB experiments.

We update the constraints on the power spectra of primordial curvature perturbation and tensor perturbation including Planck data 2015 (P15) and recently released BICEP2/Keck data (BK15), Baryon Acoustic Oscillation data and the Type Ia supernovae data. We find that the upper limits of tensor-to-scalar ratio are $0.061$, $0.064$ and $0.072$ at $95\%$ confidence level (CL) in the $\Lambda$CDM+$r$, $\Lambda$CDM+$r$+$\alpha_s$ and $\Lambda$CDM+$r$+$\alpha_s$+$\beta_s$ models respectively, where $\alpha_s$ and $\beta_s$ are the running of scalar spectral index and running of running. The inflation model with a concave potential is favored at more than $95\%$ CL. In addition, parametrizing the slow-roll parameter $\epsilon\sim 1/N^p$, where $N$ is the e-folding number before the end of inflation and taken in the range of $[50,60]$ and $[14,75]$ respectively, we conclude that the inflation model with a monomial potential $V(\phi)\sim \phi^n$ is disfavored at more than $95\%$ CL, and both the Starobinsky inflation model and brane inflation model are still consistent with the data.

Inflationary cosmology and the scale-invariant spectrum

We study the development of entropy fluctuations in brane inflation in a warped throat, including the brane–antibrane tachyon as the waterfall field. We find that there is a period at the end of inflation during which the entropy mode associated with the tachyon field increases exponentially. In turn, the induced entropy seeds a contribution to the curvature fluctuation on cosmological scales which grows rapidly and could exceed the primordial curvature perturbation. We identify parameter values for which in the absence of backreaction the induced curvature fluctuations are larger than the primordial adiabatic ones. In the specific model we study, however, backreaction limits the growth of the entropy fluctuations. We discuss situations in which backreaction effects are less constraining. The lesson of our investigation is that the study of the development of entropy fluctuations at the end of the period of inflation can lead to constraints on models of brane inflation and suggests that the curvaton mechanism may contribute significantly to the spectrum of cosmological perturbations.

Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. We find that the model can be completely described in terms of a single parameter, viz. the ratio of the scale associated with the bounce to the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.

We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to local symmetry restoration and faster thermalization. We believe this explains why tachyonic preheating is so effective in transferring energy away from the inflaton zero mode.

The matter bounce scenario is an alternative to inflation where scale-invariant perturbations are generated in a dust-dominated contracting space-time.In the context of loop quantum cosmology, the cosmological singularity is generically resolved and replaced by a bounce; furthermore, it is possible to deterministically evolve the perturbations from the contracting branch through the quantum bounce and calculate the form of the perturbations at the onset of the expanding branch.For the matter bounce scenario in loop quantum cosmology, scale-invariant perturbations and a small tensor-to-scalar ratio are predicted [1], in agreement with the latest observations of Planck and BICEP2 [2].

The effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational data. In this paper we study the observational predictions of the EFT of inflation by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble flow parameters and the flow of four new slow-roll parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. The flow of the four new slow-roll parameters, which arise from the four new operators introduced in the action of the EFT of inflation, can affect the primordial perturbation spectra at the leading-order and the corresponding spectral indices at the next-to-leading order.

Well-known causality arguments show that events occurring during or at the end of inflation, associated with reheating or preheating, could contribute a blue component to the spectrum of primordial curvature perturbations, with the dependence k3. We explore the possibility that they could be observably large in CMB, LSS, and Lyman-α data. We find that a k3 component with a cutoff at some maximum k can modestly improve the fits (Δχ2 = 2.0, 5.4) of the low multipoles (ℓ ~ 10–50) or the second peak (ℓ ~ 540) of the CMB angular spectrum when the three-year WMAP data are used. Moreover, the results from WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are included in the analysis. Including the SDSS galaxy clustering power spectrum, we find weak positive evidence for the k3 component at the level of Δχ2′ = 2.4, with the caveat that the nonlinear evolution of the power spectrum may not be properly treated in the presence of the k3 distortion. To investigate the high-k regime, we use the Lyman-α forest data (LUQAS, Croft et al., and SDSS Lyman-α); here we find evidence at the level Δχ2′ = 3.8. Considering that there are two additional free parameters in the model, the above results do not give a strong evidence for features; however, they show that surprisingly large bumps are not ruled out. We give constraints on the ratio between the k3 component and the nearly scale-invariant component, r3 &lt; 1.5, over the range of wave numbers 2.3 × 10-3 Mpc -1 &lt; k &lt; 8.2 Mpc -1. We also discuss theoretical models which could lead to the k3 effect, including ordinary hybrid inflation and double D-term inflation models. We show that the well-motivated k3 component is also a good representative of the generic spikelike feature in the primordial perturbation power spectrum.