We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up to third order in perturbations, for the dark matter density contrast (and for the dark matter velocity) only three coefficients are not fixed by symmetries and depend on the particular cosmology. For generic biased tracers, where number/mass and momentum conservation cannot be imposed in general, this number rises to seven in agreement with other bias expansions discussed in the literature. A crucial role in our analysis is provided by extended Galilean invariance, which follows from diffeomorphism invariance in the non-relativistic limit. We identify a full hierarchy of extended Galilean invariance constraints, which fix the analytic structure of the perturbation theory kernels as the sums of an increasing number of external momenta vanish. Our approach is especially relevant for non-standard models that respect the same symmetries as ΛCDM and where perturbation theory at higher orders has not been exhaustively explored, such as dark energy and modified gravity scenarios. In this context, our results can be used to systematically extend the bias expansion to higher orders and set up model independent analyses.

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a ΛCDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter Ωrc and the primordial amplitude of fluctuations As . Fixing the latter to the Planck central value, we obtain a posterior distribution with Ωrc ≲ 0.65 at 95% C.L., under the assumption of a flat prior on log10 Ωrc. This upper bound, however, depends strongly on the prior on Ωrc. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and ΛCDM model, which gives Ωrc ≲ 0.2 at 95% C.L..

Consistency Relations (CR) for the Large Scale Structure are exact equalities between correlation functions of different order. These relations descend from the equivalence principle and hold for primordial perturbations generated by single-field models of inflation. They are not affected by nonlinearities and hold also for biased tracers and in redshift space. We show that Baryonic Acoustic Oscillations (BAO) in the bispectrum (BS) in the squeezed limit are suppressed with respect to those in the power spectrum (PS) by a coefficient that depends on the BS configuration and on the bias parameter (and, in redshift space, also on the growth rate). We test these relations using large volume N-body simulations and show that they provide a novel way to measure large scale halo bias and, potentially, the growth rate. Since bias is obtained by comparing two directly observable quantities, the method is free from theoretical uncertainties both on the computational scheme and on the underlying cosmological model. I. CONSISTENCY RELATIONS AND BAO'SThe Large Scale Structure of the Universe (LSS) is governed by nonlinear effects of different nature: the evolution of the dark matter (DM) field, redshift space distortions (RSD), and the bias of the field for the considered tracers (galaxies, halos...) with respect to the DM one. All these effects limit the application of analytical techniques to rather large scales, thus excluding large part of the data from actual analyses. It is therefore remarkable that fully nonlinear statements can be made, in the form of "consistency relations" (CR) [1,2]. These are statements about the effect of perturbations at large scales on small scales ones, expressed in terms of relations between correlation functions of different order.The CR's are based on two ingredients. At the dynamical level, the Equivalence Principle (EP), which states that a change in the phase space comoving coordinates from (x, p) to (x , p ), with x = x + d(τ ) and p = p + amḋ(τ ), can always be absorbed by a change in the gravitational force from ∇φ(x, τ ) towhere τ is conformal time, d(τ ) is an arbitrary uniform but time-dependent displacement, dots denote derivatives wrt τ , and H =ȧ/a. We stress that this is an invariance of the Vlasov equation, which describes the phase space evolution beyond the fluid approximation commonly advocated in analytical approaches, such as Perturbation Theory (PT). Therefore, the resulting CR's hold not only at all PT orders but also beyond that, including all possible non-perturbative effects such as shellcrossing and multistreaming [3]. The second ingredient leading to CR's comes from relating the displacement d(τ ) with actual long wavelength velocity modes of the Universe we live in. The connection is done, in Fourier space, by considering a wavenumber dependent displacement,where δ m (q, τ ) is the DM overdensity field, and we have used linear PT, assuming it holds small q limit. We will focus on the BSwhere k ± = k ± q 2 , q = |q|, k ± = |k ± |, and the prime indicates that the e...

The consistency relations for the large scale structure provide a link between the amplitude of baryonic acoustic oscillations in the squeezed bispectrum (BS) and in the power spectrum (PS). This relation depends on the large scale bias of the considered tracer, bα, and on the growth rate of structures, f. Remarkably, originating from basic symmetry principles, this relation is exact and independent on the underlying cosmological model. By analysing data from large volume simulations, both for dark matter and for haloes, we illustrate how BS and PS measurements can be used to extract bα and f without the need of any theoretical approximation scheme for the computation of the BS and the PS. We show that, combining measurements of the squeezed BS with the quadrupole to monopole ratios for the PS at large scales can successfully break the bα −f degeneracy. We forecast that this method, applied to a Euclid-like survey, will be able to measure bias, and then the growth rate, at better than 10% level, with no extra assumption.

We produce z = 1 galaxy catalogues with the semi-analytic code Galacticus to study the dependence on the assembly history of the host halos of the non-Gaussian bias parameter bφ for galaxies selected by color magnitude and emission line luminosities. Galaxies selected by g − r color shows a large assembly bias consistent with previous analyses: a larger value of the normalization amplitude σ8 implies a faster mass assembly and, therefore, older and redder galaxies. For galaxies selected by Hα luminosity, we do not detect a significant assembly bias for the redshift and the halo masses considered here. This indicates that the non-Gaussian assembly bias should be less of a concern for future emission line galaxy surveys. We investigate, for the first time, the sensitivity of the non-Gaussian assembly bias to a change in the parameters of the galaxy formation model: these induce variations up to order unity in the measured Δbφ, but the overall trends with color or luminosity remain the same. Since these results may be sensitive to the specific galaxy formation model, it will be prudent to extend this analysis to other semi-analytic models in addition to halo mass and redshift.