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

Journal Article · Fri Feb 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.043007· OSTI ID:21039086

Tsujikawa, Shinji; Uddin, Kotub; Tavakol, Reza ^[1]

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1. Department of Physics, Gunma National College of Technology, Gunma 371-8530 (Japan)

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.

• OSTI ID: 21039086
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
COSMOLOGICAL MODELS
COSMOLOGY
DENSITY
DISTURBANCES
GRAVITATION
LAGRANGIAN FUNCTION
OSCILLATIONS
PERTURBATION THEORY
POTENTIALS
SCALARS