Cosmological perturbations in the early universe

Classical and Quantum Gravity, 2011

Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously complicated. Our goal in this paper is to formulate the governing equations for linear perturbation theory in a particularly simple and concise form in order to facilitate the extension to nonlinear perturbations. Our approach has several novel features. We show that the use of so-called intrinsic gauge invariants has two advantages. It naturally leads to: (i) a physically motivated choice of a gauge invariant associated with the matter density, and (ii) two distinct and complementary ways of formulating the evolution equations for scalar perturbations, associated with the work of Bardeen and of Kodama and Sasaki. In the first case the perturbed Einstein tensor gives rise to a second order (in time) linear differential operator, and in the second case to a pair of coupled first order (in time) linear differential operators. These operators are of fundamental importance in cosmological perturbation theory, since they provide the leading order terms in the governing equations for nonlinear perturbations.

Classical and Quantum Gravity, 2012

Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress-energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage.

Physical Review D, 2009

Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K. Nakamura, Prog. Theor. Phys. 117 (2007), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.

Progress of Theoretical Physics Supplement, 1984

The linear perturbation theory of spatially homogeneous and isotropic universes is reviewed and reformulated extensively. In the first half of the article, a gauge-invariant formulation of the theory is carried out with special attention paid to the geometrical meaning of the perturbation. In the second half of the article, the application of the theory to some important cosmological models is

Physical Review D, 2000

Physical Review D, 1997

Previously defined covariant and gauge-invariant perturbation variables, representing, e.g., the fractional spatial energy density gradient on hypersurfaces of constant expansion, are used to simplify the linear perturbation analysis of a classical scalar field. With the help of conserved quantities on large scales we establish an exact first-order relation between comoving fluid energy density perturbations at 'reentry' into the horizon and corresponding scalar field energy density perturbations at the first Hubble scale crossing during an early de Sitter phase of a standard inflationary scenario.

Physical Review D, 2012

We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small scale limit, and for the open FRW solution we repeat the analysis around the full background. We find that the perturbations display similar properties: the longitudinal modes of the massive graviton are instantaneous at quadratic level, but they acquire a kinetic term at cubic order.

Physical Review D, 2006

Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.

Physics Letters B, 2006

Using the Ponce de Leon background metric, which describes a 5D universe in an apparent vacuum:Ḡ AB = 0, we study the effective 4D evolution of both, the inflaton and gauge-invariant scalar metric fluctuations, in the recently introduced model of space time matter inflation.

Classical and Quantum Gravity, 1996

We further clarify how scalar metric perturbations are ampli ed in an in ationary cosmology. We rst construct a simple, analytic model of an inationary cosmology in which the expansion scale factor evolves continuously from an in ationary era to a radiation-dominated era. From this model, it is clear to see how scalar perturbations are ampli ed. Second, we examine the recent claims of Grishchuk, and the reply by Deruelle and Mukhanov, regarding the evolution of scalar perturbations through an abrupt transition in the equation of state of the cosmological uid. We demonstrate that the \standard results" regarding the ampli cation of scalar, density perturbations from in ation are valid.