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Title: Density perturbations in f(R) gravity theories in metric and Palatini formalisms

Abstract

We make a detailed study of matter density perturbations in both metric and Palatini formalisms. Considering general theories whose Lagrangian density is a general function, f(R), of the Ricci scalar R, we derive the equation of matter density perturbations in each case, in a number of gauges, including comoving, longitudinal and uniform density gauges. We show that for viable f(R) models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a subhorizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behavior of matter density perturbations as well as gravitational potentials for a number of classes of f(R) theories. In the metric formalism the quantity m=Rf{sub ,RR}/f{sub ,R} that characterizes the deviation from the {lambda}CDM model is constrained to be very small during a matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10{sup -1} around the present epoch can be allowed. These models also suffer from an additionalmore » fine-tuning due to the presence of scalaron oscillating modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than {approx}0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < or approx. 10{sup -5}-10{sup -4}. This is due to the peculiar evolution of matter perturbations in the Palatini case, which exhibits a rapid growth or a damped oscillation depending on the sign of m.« less

Authors:
; ;  [1];  [2]
  1. Department of Physics, Gunma National College of Technology, Gunma 371-8530 (Japan)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
21039086
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 77; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.77.043007; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; COSMOLOGICAL MODELS; COSMOLOGY; DENSITY; DISTURBANCES; GRAVITATION; LAGRANGIAN FUNCTION; OSCILLATIONS; PERTURBATION THEORY; POTENTIALS; SCALARS

Citation Formats

Tsujikawa, Shinji, Uddin, Kotub, Tavakol, Reza, and School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS. Density perturbations in f(R) gravity theories in metric and Palatini formalisms. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.77.043007.
Tsujikawa, Shinji, Uddin, Kotub, Tavakol, Reza, & School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS. Density perturbations in f(R) gravity theories in metric and Palatini formalisms. United States. doi:10.1103/PHYSREVD.77.043007.
Tsujikawa, Shinji, Uddin, Kotub, Tavakol, Reza, and School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS. Fri . "Density perturbations in f(R) gravity theories in metric and Palatini formalisms". United States. doi:10.1103/PHYSREVD.77.043007.
@article{osti_21039086,
title = {Density perturbations in f(R) gravity theories in metric and Palatini formalisms},
author = {Tsujikawa, Shinji and Uddin, Kotub and Tavakol, Reza and School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS},
abstractNote = {We make a detailed study of matter density perturbations in both metric and Palatini formalisms. Considering general theories whose Lagrangian density is a general function, f(R), of the Ricci scalar R, we derive the equation of matter density perturbations in each case, in a number of gauges, including comoving, longitudinal and uniform density gauges. We show that for viable f(R) models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a subhorizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behavior of matter density perturbations as well as gravitational potentials for a number of classes of f(R) theories. In the metric formalism the quantity m=Rf{sub ,RR}/f{sub ,R} that characterizes the deviation from the {lambda}CDM model is constrained to be very small during a matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10{sup -1} around the present epoch can be allowed. These models also suffer from an additional fine-tuning due to the presence of scalaron oscillating modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than {approx}0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < or approx. 10{sup -5}-10{sup -4}. This is due to the peculiar evolution of matter perturbations in the Palatini case, which exhibits a rapid growth or a damped oscillation depending on the sign of m.},
doi = {10.1103/PHYSREVD.77.043007},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 4,
volume = 77,
place = {United States},
year = {2008},
month = {2}
}