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Cosmological models with Galileon gravity are an alternative to the standard $\Lambda {\rm CDM}$ paradigm with testable predictions at the level of its self-accelerating solutions for the expansion history, as well as large-scale structure formation. Here, we place constraints on the full parameter space of these models using data from the cosmic microwave background (CMB) (including lensing), baryonic acoustic oscillations (BAO) and the Integrated Sachs-Wolfe (ISW) effect. We pay special attention to the ISW effect for which we use the cross-spectra, $C_\ell^{\rm T g}$, of CMB temperature maps and foreground galaxies from the WISE survey. The sign of $C_\ell^{\rm T g}$ is set by the time evolution of the lensing potential in the redshift range of the galaxy sample: it is positive if the potential decays (like in $\Lambda {\rm CDM}$), negative if it deepens. We constrain three subsets of Galileon gravity separately known as the Cubic, Quartic and Quintic Galileons. The cubic Galileon model predicts a negative $C_\ell^{\rm T g}$ and exhibits a $7.8\sigma$ tension with the data, which effectively rules it out. For the quartic and quintic models the ISW data also rule out a significant region of the parameter space but permit regions where the goodness-of-fit is comparable to $\Lambda {\rm CDM}$. The data prefers a non zero sum of the neutrino masses ($\sum m_\nu\approx 0.5$eV) with $ \sim \! 5\sigma$ significance in these models. The best-fitting models have values of $H_0$ consistent with local determinations, thereby avoiding the tension that exists in $\Lambda {\rm CDM}$. We also identify and discuss a $\sim \! 2\sigma$ tension that Galileon gravity exhibits with recent BAO measurements. Our analysis shows overall that Galileon cosmologies cannot be ruled out by current data but future lensing, BAO and ISW data hold strong potential to do so., Comment: 26 pages, 7 Figures; published version

We introduce a rigorous definition of general power-spectrum responses as resummed vertices with two hard and $n$ soft momenta in cosmological perturbation theory. These responses measure the impact of long-wavelength perturbations on the local small-scale power spectrum. The kinematic structure of the responses (i.e., their angular dependence) can be decomposed unambiguously through a "bias" expansion of the local power spectrum, with a fixed number of physical response coefficients, which are only a function of the hard wavenumber $k$. Further, the responses up to $n$-th order completely describe the $(n+2)$-point function in the squeezed limit, i.e. with two hard and $n$ soft modes, which one can use to derive the response coefficients. This generalizes previous results, which relate the angle-averaged squeezed limit to isotropic response coefficients. We derive the complete expression of first- and second-order responses at leading order in perturbation theory, and present extrapolations to nonlinear scales based on simulation measurements of the isotropic response coefficients. As an application, we use these results to predict the non-Gaussian part of the angle-averaged matter power spectrum covariance ${\rm Cov}^{\rm NG}_{\ell = 0}(k_1,k_2)$, in the limit where one of the modes, say $k_2$, is much smaller than the other. Without any free parameters, our model results are in very good agreement with simulations for $k_2 \lesssim 0.06\ h/{\rm Mpc}$, and for any $k_1 \gtrsim 2 k_2$. The well-defined kinematic structure of the power spectrum response also permits a quick evaluation of the angular dependence of the covariance matrix. While we focus on the matter density field, the formalism presented here can be generalized to generic tracers such as galaxies., Comment: 28 pages + appendices and references. 5 figures. Comments welcomed

We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, massless and massive neutrinos, in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the CMB, lensing potential and matter power spectra are affected by the fifth force, and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology, or those who are interested in the cosmological behaviour of the K-mouflage model., Comment: 22 pages, 4 figures