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Abstract:

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.

Abstract:

Future ground-based cosmic microwave background (CMB) experiments will generate competitive large-scale structure data sets by precisely characterizing CMB secondary anisotropies over a large fraction of the sky. We describe a method for constraining the growth rate of structure to sub-1% precision out to z≈1, using a combination of galaxy cluster peculiar velocities measured using the kinetic Sunyaev-Zel'dovich (kSZ) effect, and the velocity field reconstructed from galaxy redshift surveys. We consider only thermal SZ-selected cluster samples, which will consist of O(104-105) sources for Stage 3 and 4 CMB experiments respectively. Three different methods for separating the kSZ effect from the primary CMB are compared, including a novel blind "constrained realization" method that improves signal-to-noise by a factor of ∼2 over a commonly-used aperture photometry technique. Assuming a correlation between the integrated tSZ y-parameter and the cluster optical depth, it should then be possible to break the kSZ velocity-optical depth degeneracy. The effects of including CMB polarization and SZ profile uncertainties are also considered. In the absence of systematics, a combination of future Stage 4 experiments should be able to measure the product of the growth and expansion rates, α≡fH, to better than 1% in bins of Δz=0.1 out to z≈1 - competitive with contemporary redshift-space distortion constraints from galaxy surveys. We conclude with a discussion of the likely impact of various systematics.

Abstract:

Euclid is a European Space Agency medium class mission selected for launch in 2020 within the Cosmic Vision 2015 2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and redshifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.