Linear growth of matter density perturbations in f(R,G) theories

Abstract

We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^ıtre-Robertson-Walker background for the general Lagrangian density $f(R,\GB)$ that is a function of a Ricci scalar $R$ and a Gauss-Bonnet term $\GB$. We find that the effective gravitational constant generically scales as distance squared at small distances. The effect of this diminishing of the gravitational constant might be important in the gravitational dynamics of cosmic objects such as galaxies, which can be in principle tested by observations. We also provide the general expressions for the effective anisotropic stress, which is useful to constrain modified gravity models from observations of large-scale structure and weak lensing. We also find that there is a special class of theories which evade this unusual behaviour and that the condition to belong to this special class is exactly the same as the one for not having super-luminal modes with propagation speed proportional to their wavenumber.

Accepted for publication in Progress of Theoretical Physics, references added and typos corrected, 13 pages

References in corpus (8)

• Dynamics of dark energy
• The Large Scale Structure of f(R) Gravity
• Solar System constraints to general f(R) gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• The Cosmology of Modified Gauss-Bonnet Gravity
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Stability of Cosmological Solution in f(R) Models of Gravity
• Newton's constant in f(R,R_{μν}R^{μν},\Box R) theories of gravity and constraints from BBN

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• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe
• Constructions of $f(R,G,\mathcal{T})$ Gravity from Some Expansions of the Universe
• The viable f(G) gravity models via reconstruction from the observations
• Purely metric Horndeski theories and spontaneous curvaturization of black holes
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models
• Generalized Noether Theorem for Gauss-Bonnet Cosmology