The Effect of Modified Gravity on the Odds of the Bound Violations of the Turn-around Radii

We present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra. The Planck spectra at high multipoles are extremely well described by the standard spatially-flat six-parameter LCDM cosmology. In this model Planck data determine the cosmological parameters to high precision. We find a low value of the Hubble constant, H0=67.3+/-1.2 km/s/Mpc and a high value of the matter density parameter, Omega_m=0.315+/-0.017 (+/-1 sigma errors) in excellent agreement with constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent-level precision using Planck CMB data alone. We present results from an analysis of extensions to the standard cosmology, using astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured significantly over standard LCDM. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find a 95% upper limit of r<0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles. Using BAO and CMB data, we find N_eff=3.30+/-0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the summed neutrino mass. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N_eff=3.046. We find no evidence for dynamical dark energy. Despite the success of the standard LCDM model, this cosmology does not provide a good fit to the CMB power spectrum at low multipoles, as noted previously by the WMAP team. While not of decisive significance, this is an anomaly in an otherwise self-consistent analysis of the Planck temperature data.

We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at large distances the potential is that of a 5D theory. We discuss some phenomenological issues in this framework.

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.