Cosmological constraints on Brans-Dicke theory

We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using Cosmic Microwave Background data from Planck.We consider two types of models. First, the initial condition of the scalar field is fixed to give the same effective gravitational strength $G_{eff}$ today as the one measured on the Earth, $G_N$. In this case the BD parameter $\omega$ is constrained to $\omega > 692$ at the $99\%$ confidence level, an order of magnitude improvement over previous constraints.In the second type the initial condition for the scalar is a free parameter leading to a somewhat stronger constraint of $\omega > 890$ while $G_{eff}$ is constrained to $0.981 <\frac{G_{eff}}{G_N} <1.285$ at the same confidence level. We argue that these constraints have greater validity than for the BD theory and are valid for any Horndeski theory, the most general second-order scalar-tensor theory, which approximates BD on cosmological scales. In this sense, our constraints place strong limits on possible modifications of gravity that might explain cosmic acceleration.Comment: 4 pages, 2 figures. Accepted for publication at Physical Review Letter

A note on bigravity and dark matter

We show that a class of bi-gravity theories contain solutions describing dark matter. A particular member of this class is also shown to be equivalent to the Eddington-Born-Infeld gravity, recently proposed as a candidate for dark matter. Bigravity theories also have cosmological de Sitter backgrounds and we find solutions interpolating between matter and acceleration eras.Comment: 4 pages, 1 figure, minor corrections and reference additions, published in Phys. Rev.

Solving the Vlasov equation in two spatial dimensions with the Schr\"odinger method

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schr\"odinger method (ScM). With the ScM, one solves the Schr\"odinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2d-dimensional phase space density. The ScM also allows calculating the d-dimensional cumulants directly through quasi-local manipulations of the wave function, avoiding the complexity of 2d-dimensional phase space. We perform for the first time a quantitive comparison of the ScM and a conventional Vlasov solver in d=2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.Comment: 29 pages, 14 figures, corresponds to published versio