Unified description of screened modified gravity

Abstract

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of non-linearities in its interaction potential and/or its coupling to matter. Our approach covers chameleon, f (R) gravity, dilaton and symmetron models and allows a unified description of all these theories. We find that the dynamics of modified gravity are entirely captured by the time variation of the scalar field mass and its coupling to matter evaluated at the cosmological minimum of its effective potential, where the scalar field sits since an epoch prior to Big Bang Nucleosynthesis. This new parameterisation of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyse the full dynamics of the models, from the scale dependent growth of structures at the linear level to non-linear effects requiring N -body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, f (R) and symmetron models. I. INTRODUCTIONThe discovery of the acceleration of the expansion of the Universe [1] has led to a reappraisal of some of the tenets of modern cosmology. In particular, the possibility of modifying the laws of gravity on short or large scales is taken more and more seriously [2].In view of Weinberg's theorem stating that any Lorentz invariant field theory involving spin-2 fields must reduce to General Relativity (GR) at low energy [3], any attempt to modify GR must involve extra degree(s) of freedom. The majority of known models involve scalar fields and can be separated into two broad classes, the ones involving non-linearities in the kinetic terms and others with non-linear interaction potentials. All these models have a coupling of the scalar field to matter and there could be an environmental dependence which would manifest itself in the screening behaviour of the scalar field in high density regions [4,5]. Examples of such models abound: the dilatonic models [6,7] generalising the Damour-Polyakov mechanism [8] where the coupling to gravity turns off in dense environments, the chameleon models [9,10,[12][13][14] where a thin shell shielding the scalar field in dense bodies is present, the symmetron models [15][16][17][18][19][20][21] where the scalar field has a symmetry breaking potential where the field is decoupled at high density.Some models are essentially spin-offs of the previous ones like the f (R) theories [22][23][24][25][26][27][28][29][30][31][32] (for recent reviews of the f (R) gravity see [33,34]) which are only valid when they behave like chameleon theories with a thin shell mechanism in dense environments [32]. In all these *

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