Andrew Matas

Recently there has been interest in extending ghost-free massive gravity, bi-gravity, and multi-gravity by including non-standard kinetic terms and matter couplings. We first review recent proposals for this class of extensions, emphasizing how modifications of the kinetic and potential structure of the graviton and modifications of the coupling to matter are related. We then generalize existing no-go arguments in the metric language to the vielbein language in second-order form. We give an ADM argument to show that the most promising extensions to the kinetic term and matter coupling contain a Boulware-Deser ghost. However, as recently emphasized, we may still be able to view these extensions as effective field theories below some cutoff scale. To address this possibility, we show that there is a decoupling limit where a ghost appears for a wide class of matter couplings and kinetic terms. In particular, we show that there is a decoupling limit where the linear effective vielbein matter coupling contains a ghost. Using the insight we gain from this decoupling limit analysis, we place an upper bound on the cutoff for the linear effective vielbein coupling. This result can be generalized to new kinetic interactions in the vielbein language in second-order form. Combined with recent results, this provides a strong uniqueness argument on the form of ghost-free massive gravity, bi-gravity, and multi-gravity.

Stefano Anselmi, Diana López Nacir, Glenn D. Starkman

We reanalyze the behavior of Friedmann-Lema\^itre-Robertson-Walker cosmologies in the recently proposed quasidilaton massive-gravity model, and discover that the background dynamics present hitherto unreported features that require unexpected fine-tuning of the additional fundamental parameters of the theory for an observationally consistent background cosmology. We also identify new allowed regions in the parameters space and exclude some of the previously considered ones. The evolution of the mass of gravitational waves reveals non-trivial behavior, exhibiting a mass squared that may be negative in the past, and that presently, while positive, is larger than the square of the Hubble parameter. These properties of the gravity-wave mass have the potential to lead to observational tests of the theory. While quasidilaton massive gravity is known to have issues with stability at short distances, the current analysis is a first step toward the investigation of the more stable extended quasidilaton massive gravity theory, with some expectation that both the fine-tuning of parameters and the interesting behavior of the gravity-wave mass will persist.

Aaron M. Levy, Anna Ijjas, Paul J. Steinhardt

Ekpyrotic bouncing cosmologies have been proposed as alternatives to inflation. In these scenarios, the universe is smoothed and flattened during a period of slow contraction preceding the bounce while quantum fluctuations generate nearly scale-invariant super-horizon perturbations that seed structure in the post-bounce universe. An analysis by Tolley and Wesley (2007) showed that, for a wide range of ekpyrotic models, generating a scale-invariant spectrum of adiabatic or entropic fluctuations is only possible if the cosmological background is unstable, in which case the scenario is highly sensitive to initial conditions. In this paper, we analyze an important counterexample: a simple action that generates a Gaussian, scale-invariant spectrum of entropic perturbations during ekpyrotic contraction without requiring fine-tuned initial conditions. Based on this example, we discuss some generalizations.

Ophélia Fabre, Simon Prunet, Jean-Philippe Uzan

The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial topology on the properties of the cosmic microwave background anisotropies. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics, encodes a topological signature that can be used to distinguish a multi-connected space from an infinite space on sizes larger than the last scattering surface. The effect of the instrumental noise and of a galactic cut are estimated. We thus establish boundaries for the size of the biggest torus dintinguisable with temperature and polarization CMB data. We also describe the imprint of the spatial topology on the 3-point function and on non-Gaussianity.

Philippe Brax, Anne-Christine Davis

Modified gravity models with screening in local environments appear in three different guises: chameleon, K-mouflage and Vainshtein mechanisms. We propose to look for differences between these classes of models by considering cosmological observations at low redshift. In particular, we analyse the redshift dependence of the fine structure constant and the proton to electron mass ratio in each of these scenarios. When the absorption lines belong to unscreened regions of space such as dwarf galaxies, a time variation would be present for chameleons. For both K-mouflage and Vainshtein mechanisms, the cosmological time variation of the scalar field is not suppressed in both unscreened and screened environments, therefore enhancing the variation of constants and their detection prospect. We also consider the time variation of the redshift of distant objects using their spectrocopic velocities. We find that models of the K-mouflage and Vainshtein types have very different spectroscopic velocities as a function of redshift and that their differences with the $\Lambda$-CDM template should be within reach of the future ELT- HIRES observations.