Modified Gravity and Cosmology

Abstract

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

Figures (15)

• Figure 1: A schematic representation of the late-time evolution of FLRW solutions as a function of $n$ and $\gamma$, for $n<1$.
• Figure 2: Likelihood plot in the parameter space of $-c_+$ and $-c_-$ from observations of the CMB and large-scale structure. The black lines are the $1$ and $2\sigma$ contours, for which we have marginalised over the values of the other parameters. The hatched region is excluded by Čerenkov constraints. The dashed line indicates the constraints available from binary pulsars.
• Figure 3: LEFT: The evolution in redshift of baryon density fluctuations in TeVeS (solid line), and in $\Lambda$CDM (dashed line) for a wavenumber $k=10^{-3}\textrm{Mpc}^{-1}$. In both cases, the baryon density fluctuates before recombination, and grows afterwards. In the case of $\Lambda$CDM, the baryon density eventually follows the CDM density fluctuation (dotted line), which starts growing before recombination. In the case of TeVeS, the baryons grow due to the potential wells formed by the growing mode in the vector field, $\alpha$ (dot-dashed line). RIGHT: The difference of the two gravitational potentials, $\Phi - \Psi$, for a wavenumber $k=10^{-3}\textrm{Mpc}^{-1}$ as a function of redshift for both TeVeS (solid line), and $\Lambda$CDM (dotted line).
• Figure 4: The potential given in Eq. (\ref{['frpot']}), normalised by its asymptotic value as $\phi \rightarrow \infty$.
• Figure 5: The potential for the scalar field in Starobinsky's theory, Eq. (\ref{['frstarobinsky']}), with $R_c=1$, $n=1$ and $\mu=2$.

Theorems & Definitions (2)

• Theorem 2.1
• Theorem 2.2