A COVARIANT APPROACH TO THE GENERALIZED MULTI-INFLATON COSMOLOGICAL PERTURBATION

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3893-3916
Author(s):  
JOYDEV LAHIRI ◽  
GAUTAM BHATTACHARYA
Keyword(s):  
Arbitrary Field ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Covariant Approach ◽  
Slow Roll ◽  
Specific Choice ◽  
Basis System ◽  
Friedmann Robertson Walker ◽  
Scalar Part ◽  
Metric Perturbation

Following the formalism developed in Astrophys. J.375, 443 (1991), differential equations for the gauge invariant scalar part of the metric perturbation in the Friedmann–Robertson–Walker background with multiple inflatons with arbitrary field metric are obtained without any specific choice of gauge. Subsequently, an algorithm for the solution of these equations in the slow-roll approximation is given without any prior choice of the basis system in the field manifold. Vector and tensor perturbations are also briefly reviewed.

scholarly journals COSMOLOGICAL PERTURBATIONS IN RENORMALIZATION GROUP DERIVED COSMOLOGIES

2004 ◽  
Vol 13 (01) ◽  
pp. 107-121 ◽  
Author(s):  
A. BONANNO ◽  
M. REUTER
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matter Density ◽  
Explicit Solutions ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Covariant Approach ◽  
Cosmological Perturbation Theory ◽  
Spatial Gradients ◽  
Renormalization Group Equations

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant G and cosmological constant Λ is presented. A gauge invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, G, and Λ are thus obtained. Explicit solutions are discussed in cosmologies where both G and Λ vary according to renormalization group equations in the vicinity of a fixed point.

scholarly journals Application of the form invariance transformations of the scalar cosmological model in inflation theory

2021 ◽  
Vol 2090 (1) ◽  
pp. 012054
Author(s):  
O V Razina ◽  
P Yu Tsyba ◽  
N T Suikimbayeva
Keyword(s):  
Scalar Field ◽  
Equations Of Motion ◽  
Scale Factor ◽  
Transformation Model ◽  
Observation Data ◽  
Form Invariance ◽  
Slow Roll ◽  
Factor Α ◽  
Friedmann Robertson Walker ◽  
Invariance Transformation

Abstract In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.

scholarly journals xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 290 ◽  
Author(s):  
Ivan Agullo ◽  
Javier Olmedo ◽  
Vijayakumar Sreenath
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Computational Algorithm ◽  
Tensor Algebra ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Bianchi I ◽  
Space Formulation

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.

scholarly journals Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity

2009 ◽  
Vol 79 (4) ◽  
Author(s):  
Martin Bojowald ◽  
Golam Mortuza Hossain ◽  
Mikhail Kagan ◽  
S. Shankaranarayanan
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Perturbation Equations

scholarly journals ON THE DYNAMICS OF A QUADRATIC SCALAR FIELD POTENTIAL

2009 ◽  
Vol 18 (04) ◽  
pp. 621-634 ◽  
Author(s):  
L. ARTURO UREÑA-LÓPEZ ◽  
MAYRA J. REYES-IBARRA
Keyword(s):  
Scalar Field ◽  
Autonomous System ◽  
Equations Of Motion ◽  
Scalar Potential ◽  
Field Potential ◽  
System Of Equations ◽  
New Formalism ◽  
Slow Roll ◽  
Chaotic Model ◽  
Friedmann Robertson Walker

We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann–Robertson–Walker universe are written as an autonomous system of equations, and the solutions of physical interest appear as critical points. This new formalism is then applied to the study of inflation dynamics, in which we can go beyond the known slow-roll approximation.

scholarly journals Inflation in terms of a viscous van der Waals coupled fluid

2018 ◽  
Vol 15 (09) ◽  
pp. 1850150 ◽  
Author(s):  
I. Brevik ◽  
V. V. Obukhov ◽  
A. V. Timoshkin
Keyword(s):  
Van Der Waals ◽  
Accelerated Expansion ◽  
Frw Universe ◽  
Slow Roll ◽  
Analytic Expressions ◽  
Acceleration Of The Universe ◽  
The Universe ◽  
Gravitational Equations ◽  
Friedmann Robertson Walker ◽  
Planck Satellite

We propose to describe the acceleration of the universe by introducing a model of two coupled fluids. We focus on the accelerated expansion at the early stages. The inflationary expansion is described in terms of a van der Waals equation of state for the cosmic fluid, when account is taken of bulk viscosity. We assume that there is a weak interaction between the van der Waals fluid and the second component (matter). The gravitational equations for the energy densities of the two components are solved for a homogeneous and isotropic Friedmann–Robertson–Walker (FRW) universe, and analytic expressions for the Hubble parameter are obtained. The slow-roll parameters, the spectral index, and the tensor-to-scalar ratio are calculated and compared with the most recent astronomical data from the Planck satellite. Given reasonable restriction on the parameters, the agreement with observations is favorable.

scholarly journals Scalar perturbation potentials in a homogeneous and isotropic Weitzenböck geometry

2016 ◽  
Vol 25 (07) ◽  
pp. 1650087
Author(s):  
A. Behboodi ◽  
S. Akhshabi ◽  
K. Nozari
Keyword(s):  
Degrees Of Freedom ◽  
Teleparallel Gravity ◽  
Scalar Perturbation ◽  
Coordinate Frame ◽  
Field Equations ◽  
Tetrad Field ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Teleparallel Theory ◽  
Perturbation Parameters

We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory, perturbations are the result of small fluctuations in the tetrad field. The tetrad transforms as a vector in both its holonomic and anholonomic indices. As a result, in the gauge invariant formalism, physical degrees of freedom are those combinations of perturbation parameters which remain invariant under a diffeomorphism in the coordinate frame, followed by an arbitrary rotation of the local inertial (Lorentz) frame. We derive these gauge invariant perturbation potentials for scalar perturbations and present the gauge invariant field equations governing their evolution.

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