Large-scale cosmological perturbations on the brane

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.

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".

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.

We study adiabatic ~curvature! and entropy ~isocurvature! perturbations produced during a period of cosmological inflation that is driven by multiple scalar fields with an arbitrary interaction potential. A local rotation in field space is performed to separate out the adiabatic and entropy modes. The resulting field equations show explicitly how on large scales entropy perturbations can source adiabatic perturbations if the background solution follows a curved trajectory in field space, and how adiabatic perturbations cannot source entropy perturbations in the long-wavelength limit. It is the effective mass of the entropy field that determines the amplitude of entropy perturbations during inflation. We present two applications of the equations. First, we show why one in general expects the adiabatic and entropy perturbations to be correlated at the end of inflation, and calculate the cross correlation in the context of a double inflation model with two non-interacting fields. Second, we consider two-field preheating after inflation, examining conditions under which entropy perturbations can alter the large-scale curvature perturbation and showing how our new formalism has advantages in numerical stability when the background solution follows a non-trivial trajectory in field space.

Suppressing the large scale curvature perturbation by interacting fluids

We propose a new variant model of the modulated reheating. If particles have\nlarge scale fluctuations on their velocities, or equivalently their Lorentz\nfactors, the decay rate also fluctuates and the curvature perturbation is\ninduced via their decay processes in analogy with modulated reheating. For\nexample, if they are produced nonthermally by the decay of another field with\nits mass fluctuating on large scales, such a situation is realized. We\nexplicitly calculate the resulting curvature perturbation and non-linearity\nparameters and show that the effect of velocity-modulation is not negligible if\nthe particles are semi-relativistic at the decay.\n

We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform density curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform density and comoving curvature perturbations at second order, in a scalar field dominated universe, are conserved. Finally, in the light of this result, we comment on the variables recently used in the literature to compute non-Gaussianities.

Since a positive future detection of non-linearity in the cosmic microwave background anisotropy pattern might allow to descriminate among different mechanisms giving rise to cosmological adiabatic perturbations, we study the evolution of the second-order cosmological curvature perturbation on super-horizon scales in the curvaton scenario. We provide the exact expression for the non-Gaussianity in the primordial perturbations including gravitational second-order corrections which are particularly relevant in the case in which the curvaton dominates the energy density before it decays. As a byproduct, we show that in the standard scenario where cosmological curvature perturbations are induced by the inflaton field, the second-order curvature perturbation is conserved even during the reheating stage after inflation.

We study the imprints of an effective dark energy fluid in the large scale structure of the universe through the observed angular power spectrum of galaxies in the relativistic regime. We adopt the phenomenological approach that introduces two parameters {Q,η} at the level of linear perturbations and allow to take into account the modified clustering (or effective gravitational constant) and anisotropic stress appearing in models beyond ΛCDM . We characterize the effective dark energy fluid by an equation of state parameter w=−0.95 and various sound speed cases in the range 10−6⩽ cs2⩽ 1, thus covering K-essence and quintessence cosmologies. We calculate the angular power spectra of standard and relativistic effects for these scenarios under the {Q,η} parametrization, and we compare these relative to a fiducial ΛCDM cosmology. We find that, overall, deviations relative to ΛCDM are stronger at low redshift since the behavior of the dark energy fluid can mimic the cosmological constant during matter domination era but departs during dark energy domination. In particular, at z=0.1 the matter density fluctuations are suppressed by up to ∼3% for the quintessence-like case, while redshift-space distortions and Doppler effect can be enhanced by ∼15% at large scales for the lowest sound speed scenario. On the other hand, at z=2 we find deviations of up to ∼5% in gravitational lensing, whereas the Integrated Sachs-Wolfe effect can deviate up to ∼17%. Furthermore, when considering an imperfect dark energy fluid scenario, we find that all effects are insensitive to the presence of anisotropic stress at low redshift, and only the Integrated Sachs-Wolfe effect can detect this feature at z=2 and very large scales.

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.

Non-singular matter bouncing cosmological setups are of particular interest since apart from adressing the initial singularity problem they can give rise as well to a nearly scale-invariant curvature power spectrum on scales $k<10^{4}\mathrm{Mpc}^{-1}$, favored by Cosmic Microwave Background (CMB) experiments. Interestingly enough, one can find that within such non-singular bouncing cosmological setups, curvature perturbations grow on super-horizon scales during the matter contracting phase. In this work, we account for the evolution of cosmological perturbations during the transition to the Hot Big Bang expanding Universe, finding at the end naturally enhanced curvature perturbations on very small scales at horizon-crossing time during the expanding phase. These enhanced cosmological perturbations can induce gravitational waves (GWs) due to second order gravitational interactions and collapse as well to form primordial black holes (PBHs), with the latter acting as one of the most viable dark matter candidates. Remarkably, we find an induced GW background with a universal infrared (IR) frequency scaling of $f^2$, in excellent agreement with the recently released $\mathrm{nHz}$ GW data by the NANOGrav collaboration, being potentially detectable as well by other GW observatories such as LISA and ET, depending on the values of the bouncing cosmological parameters at hand.

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for generic single-field inflation. Our inflaton is described by the Lagrangian of the form $W(X,\phi)-G(X,\phi)\Box\phi$ with $X=-\partial^{\mu}\phi\partial_{\mu}\phi/2$, which is no longer equivalent to a perfect fluid. This model is more general than k-inflation, and is called G-inflation. A general nonlinear solution for the metric and the scalar field is obtained at second order in gradient expansion. We derive a simple master equation governing the large-scale evolution of the nonlinear curvature perturbation. It turns out that the nonlinear evolution equation is deduced as a straightforward extension of the corresponding linear equation for the curvature perturbation on uniform $\phi$ hypersurfaces.

In this paper, we continue our study of the curvaton model with nonminimal derivative coupling (NDC) to Einstein gravity proposed in our previous work (Feng in Phys Lett B 729:99, 2014; Feng and Qiu in Phys Rev D 90(12):123508, 2014), focusing on the reheating mechanism. We found that according to whether the curvaton has or has not dominated the background after the end of inflation, it will have two different behaviors of evolution, which should be the general property of the curvaton with nonminimal couplings. This will cause two different parts of reheating, which goes on via the parametric resonance process. The reheating temperature is estimated for both cases in which reheating completes before and after curvaton domination, and the constraints are quite loose compared to that of overproduction of gravitinos. Finally we investigated the evolution of curvature perturbation during reheating. We have shown both analytically and numerically that the curvature perturbation will not blow up during the resonance process.

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 the asymmetric primordial fluctuations in a model of inflation in which translational invariance is broken by a domain wall. We calculate the corrections to the power spectrum of curvature perturbations; they are anisotropic and contain dipole, quadrupole, and higher multipoles with non-trivial scale-dependent amplitudes. Inspired by observations of these multipole asymmetries in terms of two-point correlations and variance in real space, we demonstrate that this model can explain the observed anomalous power asymmetry of the cosmic microwave background (CMB) sky, including its characteristic feature that the dipole dominates over higher multipoles. We test the viability of the model and place approximate constraints on its parameters by using observational values of dipole, quadrupole, and octopole amplitudes of the asymmetry measured by a local-variance estimator. We find that a configuration of the model in which the CMB sphere does not intersect the domain wall during inflation provides a good fit to the data. We further derive analytic expressions for the corrections to the CMB temperature covariance matrix, or angular power spectra, which can be used in future statistical analysis of the model in spherical harmonic space.