Cosmological perturbations

Abstract

We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.

Anisotropy in solid inflation

“…One of the conditions for the conservation of ζ on super-horizon scales is that the anisotropic part of the stress-energy tensor vanishes in that regime [50]. This is the case for minimally coupled scalar fields with x−independent vev [53]. In the present model, however,…”

MSSM-inspired multifield inflation

“…Recent analyses [41][42][43][44][45][46][47][48] of multifield models showed that unlike the single-field models they generically provide density (entropy) perturbations which can induce the curvature perturbation to evolve beyond the cosmological horizon in the process of inflation [49]. Evolution of density perturbations in multifield models should be studied in order to analyze new features in the observables such as non-Gaussianities [50] which are absent in the single-field inflationary models.…”

“…Then the spectral index n s and tensor-to-scalar ratio r at the time when a characteristic scale (50-65 e-foldings before the end of inflation) is of the order of the Hubble radius in the course of inflation, can be calculated using the single-field equations valid to lowest order in slow-roll parameters [48,49] n s = 1 − 6 + 2η σσ , r = 16 . …”

Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

“…Let us first note that, once nonlinear effects are taken into account, the separation of scalar, vector and tensor become impossible. This is well-known in GR when we consider secondorder perturbations, where all the sectors of the firstorder perturbations become the sources of the secondorder ones [50]. Taking these into account, let us consider the non-perturbative solutions of the type,…”