Unified description of screened modified gravity

Philippe Brax, Anne-Christine Davis, Baojiu Li, and Hans A. Winther

Phys. Rev. D 86, 044015 – Published 8 August 2012

Abstract

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of nonlinearities 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 has sat since an epoch prior to big bang nucleosynthesis. This new parametrization of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyze the full dynamics of the models, from the scale dependent growth of structures at the linear level to nonlinear effects requiring $N$ -body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, $f (R)$ and symmetron models.

Received 2 April 2012

DOI:https://doi.org/10.1103/PhysRevD.86.044015

Authors & Affiliations

Philippe Brax^1,*, Anne-Christine Davis^2,†, Baojiu Li^3,‡, and Hans A. Winther^4,§

¹Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex, France
²DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
³ICC, Physics Department, University of Durham, South Road, Durham DH1 3LE, United Kingdom
⁴Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway

^*philippe.brax@cea.fr
^†a.c.davis@damtp.cam.ac.uk
^‡baojiu.li@durham.ac.uk
^§h.a.winther@astro.uio.no

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Issue

Vol. 86, Iss. 4 — 15 August 2012

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Images

Figure 1
The constraints on $m_{0} / H_{0}$ as a function of $r$ for $β_{0} = 1 / \sqrt{6}$ and $s = 0$ . Valid models must be above the (listed from top to bottom at $r = 2$ ) mauve (cavity), green ( $m > H$ ), red (solar system), brown (galaxy), light red ( $\dot{μ}$ ), and cyan ( $m L ≳ 1$ ) lines. The blue line (bottom line at $r = 2$ ) gives the detectability of effects on the CMB by the Planck satellite. The strongest constraints are the cavity and galactic bounds for small and large $r$ respectively. Models with $r ≳ 3$ satisfy the constraints and can lead to a modified gravity regime on large scales.Reuse & Permissions
Figure 2
The relative difference of the matter power spectrum $P (k)$ in the chameleon model from that in the $Λ CDM$ model with exactly the same background expansion history, initial conditions and physical parameters. Upper left panel: The dependence of the result on the modified gravity parameter $β_{0}$ . Upper right panel: The dependence of the result on the parameter $r$ . Lower left panel: The dependence of the result on the parameter $s$ . Lower right panel: The dependence of the result on the parameter $ξ \equiv H_{0} / m_{0}$ .Reuse & Permissions
Figure 3
The relative difference of the matter power spectrum $P (k)$ in generalized symmetron models from that in the $Λ CDM$ model with exactly the same background expansion history, initial conditions and physical parameters. Upper left panel: The dependence of the result on the parameter $a_{⋆}$ (the scale factor value at which the symmetry breaking of the effective potential happens). Upper right panel: The dependence of the result on the modified gravity parameter $β_{⋆}$ . Lower left panel: The dependence of the result on the parameter $q$ . Lower right panel: The dependence of the result on the parameter $ξ \equiv H_{0} / m_{⋆}$ . As an example we have chosen $p = 2$ .Reuse & Permissions
Figure 4
An illustration of the time evolution of the scalar field perturbation $δ ϕ$ . The black solid curve is the numerical solution while the green dashed curve is the analytical approximation given in Eq. (184). The results here are for $k = 1 h {Mpc}^{- 1}$ but the qualitative feature remains for other values of $k$ . The modified gravity parameters are shown beside the curves.Reuse & Permissions
Figure 5
The time evolution of $γ (k, a)$ for a chosen value of $k = 0.1 h {Mpc}^{- 1}$ as an illustration. The black solid is the full numerical solution, the red dashed curve is obtained using the numerical value of $Φ_{N}$ using the analytical solution of $δ ϕ$ given in Eq. (184), while the blue solid curve is Eq. (196). The modified gravity parameters are shown beside the curves.Reuse & Permissions

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