Cosmological Perturbations Through the Big Bang

We study the background dynamics and primordial perturbation in $\alpha$-attractor-type double inflation. The model is composed of two minimally coupled scalar fields, where each of the fields has a potential of the $\alpha$-attractor type. We find that the background trajectory in this double inflation model is given by two almost straight lines connected with a turn in the field space. With this simple background, we can classify the property of the perturbations generated in this double inflation model just depending on whether the turn occurs before the horizon exit for the mode corresponding to the scale of interest or not. In the former case, the resultant primordial curvature perturbation coincides with the one obtained by the single-field $\alpha$-attractor. On the other hand, in the latter case, it is affected by the multifield effects, like the mixing with the isocurvature perturbation and the change of the Hubble expansion rate at the horizon exit. We obtain the approximated analytic solutions for the background, with which we can calculate the primordial curvature perturbation by the $\delta N$ formalism analytically, even when the multifield effects are significant. We also impose observational constraints on the model parameters and initial values of the fields in this double inflation model based on the Planck result.

The idea of the universe having a mirror sector in which all particles and forces are identical to those in the familiar sector has been proposed recently in the context of neutrino physics as well as superstring theories some time ago. Assuming that all the quark and charged lepton masses in the mirror universe are scaled by a common factor, ζ, as is required in one interpretation of the neutrino data, we investigate domains of the parameter ζ where physical conditions are favorable for the formation of compact structures given the initial condition ΩB Ω ( denoting the mirror baryon). We consider both isocurvature and curvature perturbations; we address primordial mirror molecule formation, mirror Compton cooling, mirror Silk and collisionless damping, and various mirror cooling mechanisms that can lead to compact mirror structures for various regions of ζ space, so that the mirror model can be confronted with astrophysical observations. For isocurvature perturbations, we find a variety of possible structural final states. For curvature (or adiabatic) perturbations, we find a likelihood that part of ζ space would result in detectable effects that are not observed, while a part would not.

A simple extension of the minimal supersymmetric standard model which naturally and simultaneously solves the strong CP and mu problems via a Peccei-Quinn and a continuous R symmetry is considered. This model is supplemented with hybrid inflation and leptogenesis, but without taking the specific details of these scenarios. It is shown that the Peccei-Quinn field can successfully act as a curvaton generating the total curvature perturbation in the universe in accord with the cosmic background explorer measurements. A crucial phenomenon, which assists us to achieve this, is the "tachyonic amplification" of the perturbation acquired by this field during inflation if the field, in its subsequent evolution, happens to be stabilized for a while near a maximum of the potential. In this case, the contribution of the field to the total energy density is also enhanced ("tachyonic effect"), which helps too. The cold dark matter in the universe consists, in this model, mainly of axions which carry an isocurvature perturbation uncorrelated with the total curvature perturbation. There are also lightest sparticles (neutralinos) which, like the baryons, originate from the inflationary reheating and, thus, acquire an isocurvature perturbation fully correlated with the curvature perturbation. So, the overall isocurvature perturbation has a mixed correlation with the adiabatic one. It is shown that the presently available bound on such an isocurvature perturbation from cosmic microwave background radiation and other data is satisfied. Also, the constraint on the non-Gaussianity of the curvature perturbation obtained from the recent Wilkinson microwave anisotropy probe data is fulfilled thanks to the "tachyonic effect".

Non-linear CMB temperature anisotropies up to the third-order on large scales are calculated. On large scales and in the Sachs-Wolfe limit, we give the explicit expression for the observed temperature anisotropy in terms of the primordial curvature perturbation up to the third-order. We derived the final bispectrum and trispectrum of anisotropies and the corresponding non-linear parameters, in which the contributions to the observed non-Gaussianity from primordial perturbations and from the non-linear mapping from primordial curvature perturbation to the temperature anisotropy are transparently separated.

In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The total curvature perturbation is not necessarily constant for adiabatic matter perturbations, but can change due to the Weyl entropy perturbation. To relate this curvature perturbation to the longitudinal gauge metric potentials requires knowledge of the Weyl anisotropic stress which is not determined by the equations on the brane. We discuss the implications for large-angle anisotropies on the cosmic microwave background sky.

The non-adiabatic pressure in general scalar field systems

We analytically compute the power spectrum of primordial curvature perturbations in Type III hilltop inflation models under the slow-roll approximation. The model parameters are constrained using current Cosmic Microwave Background (CMB) data. The curvature perturbations that exit the horizon at small scales show sufficiently large amplitudes to produce primordial black holes (PBHs). We then consider the quantum one-loop corrections in these models from both the self-interaction of the inflaton and its interaction with the waterfall field. We show the loop corrections in both cases for 60 e-folds of inflation are negligible, ensuring the tree-level results are reliable within the chosen parameter regime.

We study the CMB constraints on non-Gaussianity in CDM isocurvature perturbations.Non-Gaussian isocurvature perturbations can be produced in various models at the very early stage of the Universe. Since the isocurvature perturbations little affect thestructure formation at late times, CMB is the best probe of isocurvature non-Gaussianity at least in the near future. In this paper, we focus on non-Gaussian curvature and isocurvature perturbations of the local-type, which are uncorrelated and in the formζ = ζG+(3/5)fNL(ζG2−⟨ζG2⟩)and S = SG+fNL(ISO)(SG−⟨SG2⟩), and constrain the non-linearity parameter of isocurvature perturbations, fNL(ISO), as well as the curvature one fNL.For this purpose, we employ several state-of-art techniques for the analysis of CMB data and simulation. Assuming that isocurvature perturbations are subdominant, we apply our method to the WMAP 7-year data of temperature anisotropy and obtain constraints on a combination α2fNL(ISO),where α is the ratio of the power spectrum of isocurvature perturbationsto that of the adiabatic ones.When the adiabatic perturbations are assumed to be Gaussian, we obtained a constraint α2fNL(ISO) = 40±66assuming the power spectrum of isocurvature perturbations is scale-invariant.When we assume that the adiabatic perturbations can also be non-Gaussian, we obtain fNL = 38±24 and α2fNL(ISO) = −8±72. We also discuss implications of our results for the axion CDM isocurvature model.

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.

We discuss the residual isocurvature perturbations, fully correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally uncorrelated ``intrinsic'' isocurvature perturbation generated by an additional field such as the axion. We present a general formula for the residual isocurvature perturbations, referring only to the generation of the relevant quantity [cold dark matter (CDM), baryon number or lepton number] in an unperturbed universe. Specific formulas for the residual isocurvature CDM perturbation are given for most of the commonly considered CDM candidates.

A contracting universe driven by two scalar fields

We study the effect of the nonlinear relation between density and curvature perturbations on the formation of PBHs. By calculating the variance and skewness of the density perturbation we derive the non-Gaussian property. As a criterion for PBH formation, the compaction function is used and it is found that larger curvature perturbations are required due to the nonlinear effect. We estimate the PBH abundance based on the Press-Schechter formalism with non-Gaussian probability density function during Radiation dominated era. It is found that the nonlinear effect slightly suppresses the PBH formation and the suppression is comparable to that expected if the primordial curvature perturbation would have the local form of non-Gaussianity with nonlinear parameter $f_\text{NL} \sim -1$.

We propose an alternative implementation of the curvaton mechanism for generating the curvature perturbations which does not rely on a late decaying scalar decoupled from inflation dynamics. In our mechanism the supersymmetric Higgs scalars are coupled to the inflaton in a hybrid inflation model, and this allows the conversion of the isocurvature perturbations of the Higgs fields to the observed curvature perturbations responsible for large scale structure to take place during reheating. We discuss an explicit model which realises this mechanism in which the $\mu$ term in the Higgs superpotential is generated after inflation by the vacuum expectation value of a singlet field. The main prediction of the model is that the spectral index should deviate significantly from unity, $|n-1|\sim 0.1$. We also expect relic isocurvature perturbations in neutralinos and baryons, but no significant departures from gaussianity and no observable effects of gravity waves in the CMB spectrum.

An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point in the context of [Formula: see text] modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce do not produce a scale-invariant spectrum and also the short wavelength modes after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result indicating that the singular bounce theory is unstable at the singularity point for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.

Whether or not the primordial gravitational wave (GW) produced during inflation is sufficiently strong to be observable, GWs are necessarily produced from the primordial curvature perturbations in the second order of perturbation. The induced GWs can be enhanced by curvature perturbations enhanced at small scales or by the presence of matter-dominated stages of the cosmological history. We analytically calculate the integral in the expression of the power spectrum of the induced GWs which is a universal part independent of the spectrum of the primordial curvature perturbations. This makes the subsequent numerical integrals significantly easy. In simple cases, we derive fully analytic formulas for the induced GW spectrum.