Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

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CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512005764 ◽

2012 ◽

Vol 10 ◽

pp. 63-68 ◽

Cited By ~ 1

Author(s):

JE-AN GU

Keyword(s):

General Relativity ◽

Differential Equations ◽

Early Time ◽

Einstein Equations ◽

Modified Theories Of Gravity ◽

Cosmological Perturbations ◽

Long Run ◽

Theories Of Gravity ◽

The Stability ◽

Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

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Big bounce with finite-time singularity: The F(R) gravity description

International Journal of Modern Physics D ◽

10.1142/s0218271817500857 ◽

2017 ◽

Vol 26 (08) ◽

pp. 1750085 ◽

Cited By ~ 29

Author(s):

S. D. Odintsov ◽

V. K. Oikonomou

Keyword(s):

Big Bang ◽

Einstein Frame ◽

Jordan Frame ◽

Cosmological Perturbations ◽

Scale Invariant ◽

Type Iv ◽

Big Rip ◽

Cosmological Scenario ◽

The Big Bang ◽

Big Bounce

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.

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Removing Ostrogradski’s ghost from cosmological perturbations in f(R,Rμν2,Cμνρσ2) gravity

Modern Physics Letters A ◽

10.1142/s021773231650067x ◽

2016 ◽

Vol 31 (11) ◽

pp. 1650067 ◽

Cited By ~ 1

Author(s):

Yuji Akita ◽

Tsutomu Kobayashi

Keyword(s):

General Formula ◽

Ricci Tensor ◽

Matter Density ◽

De Sitter ◽

Cosmological Perturbations ◽

Text Type ◽

Cosmological Background ◽

Density Perturbations ◽

Sitter Background ◽

Theories Of Gravity

Recently, it was argued that gravity with the square of the Ricci tensor can be stabilized by adding constraints to the theory in a Lorentz violating way. This was so far demonstrated for fluctuations on the Minkowski/de Sitter background. We show that the same scheme works equally well for removing Ostrogradski’s ghost from fluctuations on a cosmological background in generic [Formula: see text]-type theories of gravity. As an application, we derive the general formula for the spectrum of primordial tensor perturbations from the stabilized theory. The evolution of matter density perturbations is also discussed.

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f(R,∇μ1R,…,∇μ1…∇μnR) theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach

Physical Review D ◽

10.1103/physrevd.99.084053 ◽

2019 ◽

Vol 99 (8) ◽

Cited By ~ 1

Author(s):

R. R. Cuzinatto ◽

C. A. M. de Melo ◽

L. G. Medeiros ◽

P. J. Pompeia

Keyword(s):

Higher Order ◽

Einstein Frame ◽

Inflation Model ◽

Theories Of Gravity

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Scalar–tensor theories of gravity: validity of the cosmic no-hair conjecture

Canadian Journal of Physics ◽

10.1139/p11-074 ◽

2011 ◽

Vol 89 (9) ◽

pp. 937-940

Author(s):

Sudeshna Mukerji ◽

Nairwita Mazumder ◽

Ritabrata Biswas ◽

Subenoy Chakraborty

Keyword(s):

Coupling Parameter ◽

Matter Field ◽

Einstein Frame ◽

Energy Conditions ◽

Jordan Frame ◽

Scalar Tensor Theory ◽

Bianchi Models ◽

Tensor Theory ◽

Theories Of Gravity ◽

Theory Of Gravity

This paper deals with the cosmic no-hair conjecture for anisotropic Bianchi models in the scalar–tensor theory of gravity. Herein, we have considered both the Jordan frame and the Einstein frame to describe the scalar–tensor theory of gravity and examine the conjecture. In the Jordan frame, one should restrict both the coupling function of the scalar field and the coupling parameter, in addition to the usual energy conditions for the matter field, to maintain the validity of the cosmic no-hair conjecture, while in the Einstein frame, the restrictions are purely on the energy conditions.

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On the evolution and stability of cosmological perturbations in higher order scalar–tensor theories of gravity

Canadian Journal of Physics ◽

10.1139/cjp-2017-0495 ◽

2019 ◽

Vol 97 (4) ◽

pp. 360-373

Author(s):

Fateme Rajabi ◽

Kourosh Nozari

Keyword(s):

Scalar Field ◽

Higher Order ◽

De Sitter ◽

Cosmological Perturbations ◽

First Order ◽

Higher Order Terms ◽

General Scalar ◽

New Type ◽

Theories Of Gravity ◽

The Stability

We study a new type of extended theory of gravity in the framework of general scalar–tensor theories in which the higher order terms of curvature are coupled with a scalar field and its derivatives. We analyze the stability and evolution of cosmological perturbations in this setup. For this purpose, we perturb the Hubble parameter, matter density, and scalar field to check stability and evolution of perturbations to first order. In this framework, we investigate stability conditions for de Sitter and power law solutions and we examine viability of cosmological evolution of these perturbations. We consider some specific f(R) models and show that the stability analysis gives some constraints on the parameters of these models.

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F(R) GRAVITY IN PURELY AFFINE FORMULATION

International Journal of Modern Physics A ◽

10.1142/s0217751x08039773 ◽

2008 ◽

Vol 23 (12) ◽

pp. 1891-1901 ◽

Cited By ~ 5

Author(s):

NIKODEM J. POPŁAWSKI

Keyword(s):

General Relativity ◽

Hamiltonian Dynamics ◽

Einstein Frame ◽

Nonlinear Dependence ◽

Metric Tensor ◽

Theories Of Gravity ◽

Metric Variation ◽

Peculiar Behavior ◽

Theories Of Gravitation ◽

Affine Metric

The purely affine, metric-affine and purely metric formulation of general relativity are dynamically equivalent and the relation between them is analogous to the Legendre relation between the Lagrangian and Hamiltonian dynamics. We show that one cannot construct a dynamically equivalent, purely affine Lagrangian from a metric-affine or metric F(R) Lagrangian, nonlinear in the curvature scalar. Thus the equivalence between the purely affine picture and the two other formulations does not hold for metric-affine and metric theories of gravity with a nonlinear dependence on the curvature, i.e. F(R) gravity does not have a purely affine formulation. We also show that this equivalence is restored if the metric tensor is conformally transformed from the Jordan to the Einstein frame, in which F(R) gravity turns into general relativity with a scalar field. This peculiar behavior of general relativity, among relativistic theories of gravitation, with respect to purely affine, metric-affine and purely metric variation could indicate the physicality of the Einstein frame. On the other hand, it could explain why this theory cannot interpolate among phenomenological behaviors at different scales.

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Cosmological Perturbations in the Generalized Theories of Gravity

10.1063/1.3527197 ◽

2010 ◽

Author(s):

L. A. Popa ◽

Livius Trache ◽

Alexei Smirnov ◽

Sabin Stoica

Keyword(s):

Cosmological Perturbations ◽

Theories Of Gravity

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Invariant quantities in the multiscalar-tensor theories of gravitation

International Journal of Modern Physics A ◽

10.1142/s0217751x16410037 ◽

2016 ◽

Vol 31 (02n03) ◽

pp. 1641003 ◽

Cited By ~ 20

Author(s):

Piret Kuusk ◽

Laur Järv ◽

Ott Vilson

Keyword(s):

Scalar Fields ◽

Einstein Frame ◽

Current Paper ◽

Jordan Frame ◽

General Frame ◽

Newtonian Approximation ◽

Theories Of Gravity ◽

Theories Of Gravitation

The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the scalar fields are redefined. We introduce rules to construct further such objects and put forward a scheme that allows to express the results obtained either in the Einstein frame or in the Jordan frame as general ones. These so-called “translation” rules are used to show that the parametrized post-Newtonian approximation results obtained in the aforementioned two frames indeed are the same if expressed in a general frame.

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