Cosmological Results and Implications in Effective DGP

Abstract

We study a simple extension of the decoupling limit of boundary effctive actions for the Dvali-Gabadadze-Porrati model, by covariantizing the π lagrangian and coupling to gravity in the usual way. This extension agrees with DGP to leading order in Mpl^−1 , and simplifies the cosmological analysis. It is also shown to softly break the shift symmetry, while still being consistent with solar system observations. The generally covariant equations of motion for π and the metric are derived, then the cosmology is developed under the Cosmological Principle. Three analytic solutions are found and their stability is studied. Interesting DGP phenomenology is reproduced, and we consider one of the stable solutions. The cosmological analogue of the Vainshtein effect is reproduced and the effective equation of state, w_π, is shown to be bounded by −1 from above. This solution is additionally shown to be an attractor solution in an expanding universe. We evolve π numerically and reproduce these properties, and show that the universe will go through a contraction phase, due to this π field. We then place a constraint on r_c ≥ 10^29 cm, given recent WMAP5 data. This lower bound on r_c gives an upper bound on the anomalous perihelion precession of the moon ∼ 1 × 10^−13, 2 orders of magnitude below current experimental precision.