TY - JOUR

T1 - Dispersion of growth of matter perturbations in f(R) gravity

AU - Tsujikawa, Shinji

AU - Gannouji, Radouane

AU - Moraes, Bruno

AU - Polarski, David

PY - 2009/10/29

Y1 - 2009/10/29

N2 - We study the growth of matter density perturbations δm for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m ≡ Rf,RR/f,R today is larger than the order of 10-6, linear perturbations relevant to the matter power spectrum evolve with a growth rate s ≡ d ln □ δm/d ln □ a (a is the scale factor) that is larger than in the ΛCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index γ0 ≡ γ(z=0) (z is the redshift) appears in the range of values 0.40 □ γ0 0.55, as well as the region in parameter space for which there is essentially no dispersion and γ0 converges to values around 0.40 □ γ □ 0.43. These latter values are much lower than in the ΛCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f(R) models with m(z=0) larger than the order of 10-6. These properties will be essential in the quest for f(R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the ΛCDM model.

AB - We study the growth of matter density perturbations δm for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m ≡ Rf,RR/f,R today is larger than the order of 10-6, linear perturbations relevant to the matter power spectrum evolve with a growth rate s ≡ d ln □ δm/d ln □ a (a is the scale factor) that is larger than in the ΛCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index γ0 ≡ γ(z=0) (z is the redshift) appears in the range of values 0.40 □ γ0 0.55, as well as the region in parameter space for which there is essentially no dispersion and γ0 converges to values around 0.40 □ γ □ 0.43. These latter values are much lower than in the ΛCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f(R) models with m(z=0) larger than the order of 10-6. These properties will be essential in the quest for f(R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the ΛCDM model.

UR - http://www.scopus.com/inward/record.url?scp=70449730233&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.80.084044

DO - 10.1103/PhysRevD.80.084044

M3 - Article

AN - SCOPUS:70449730233

SN - 1550-7998

VL - 80

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 8

M1 - 084044

ER -