Abstract
We revisit the question of viability of bigravity cosmology as a candidate for dark energy. In the context of the low energy limit model, where matter couples to a single metric, we study linear perturbations around homogeneous and isotropic backgrounds to derive the Poisson's equation for the Newtonian potential. Extending to second order perturbations, we identify the Vainshtein radius below which non-linear scalar self interactions conspire to reproduce GR on local scales. We combine all of these results to determine the parameter space that allows a late time de-Sitter attractor compatible with observations and a successful Vainsthein mechanism. We find that the requirement on having a successful Vainsthein mechanism is not compatible with the existence of cosmological solutions at early times.
Highlights
Einstein’s theory of general relativity (GR) [1] has been the widely accepted theory of gravity with the impeccable ability to match observations for over a century [2]
We considered a perfect fluid with equation of state P 1⁄4 0 coupled to the g metric and studied metric perturbations around Friedmann-LemaîtreRobertson-Walker, while adopting the healthy branch of solution with H 1⁄4 ξHf
We studied perturbations going beyond linear order and identified the Vainshtein radius, below which the derivative self-interactions of the scalar screen the effect of the fifth force and conspire to reproduce GR on local scales
Summary
Einstein’s theory of general relativity (GR) [1] has been the widely accepted theory of gravity with the impeccable ability to match observations for over a century [2]. The effect of endowing the graviton with a nonzero mass was first considered in 1939 by Fierz and Pauli in a linear construction [7] In this theory, the mass term is built by requiring the absence of negative energy states (ghosts) and breaks the linearized diffeomorphism invariance, resulting in a massive spin-2 field theory propagating 5 degrees of freedom (d.o.f.). The second way is the so-called “low energy limit” [31], where the bare mass parameter is allowed to be large m ≫ H0, while the late-time accelerated expansion can be achieved via a fine-tuning of coupling constants This tuning introduces a hierarchy between the interaction parameter m and the effective mass of the dynamical graviton modes.
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