Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors

Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and the nonperturbative sectors. Then, we show that the dynamics in the deep multistreaming regime is governed by attractors. In the case of simple initial conditions, these attractors coincide with the asymptotic configurations of the adhesion model, but in general they may differ. These results are applied to a cosmological setting, and an algorithm to build the attractor solution starting from the Zel'dovich approximation is developed. Finally, this algorithm is applied to the search of `haloes' and the results are compared with those obtained from the exact dynamical equations.Comment: 30 page

Ward identities and consistency relations for the large scale structure with multiple species

We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in Peloso, Pietroni '13 and Kehagias, Riotto '13 in the single species case. The multi-species relations apply to the standard dark matter + baryons scenario, as well as to the case in which some of the fields are auxiliary quantities describing a particular population, such as dark matter halos or a specific galaxy class. If a large scale velocity bias exists between the different populations new terms appear in the consistency relations with respect to the single species case. As an illustration, we discuss two physical cases in which such a velocity bias can exist: (1) a new long range scalar force in the dark matter sector (resulting in a violation of the equivalence principle in the dark matter-baryon system), and (2) the distribution of dark matter halos relative to that of the underlying dark matter field.Comment: Published versio

Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure

We discuss the constraints imposed on the nonlinear evolution of the Large Scale Structure (LSS) of the universe by galilean invariance, the symmetry relevant on subhorizon scales. Using Ward identities associated to the invariance, we derive fully nonlinear consistency relations between statistical correlators of the density and velocity perturbations, such as the power spectrum and the bispectrum. These relations are valid up to O (f_{NL}^2) corrections. We then show that most of the semi-analytic methods proposed so far to resum the perturbative expansion of the LSS dynamics fail to fulfill the constraints imposed by galilean invariance, and are therefore susceptible to non-physical infrared effects. Finally, we identify and discuss a nonperturbative semi-analytical scheme which is manifestly galilean invariant at any order of its expansion.Comment: 29 pages, 7 figure

Galilean invariant resummation schemes of cosmological perturbations

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.Comment: 21 pages, 5 figure

Spherical collapse and halo mass function in the symmetron model

We study the gravitational clustering of spherically symmetric overdensities and the statistics of the resulting dark matter halos in the "symmetron model", in which a new long range force is mediated by a $Z_2$ symmetric scalar field. Depending on the initial radius of the overdensity, we identify two distinct regimes: for small initial radii the symmetron mediated force affects the spherical collapse at all redshifts; for initial radii larger than some critical size this force vanishes before collapse because of the symmetron screening mechanism. In both cases overdensities collapse earlier than in the $\Lambda$CDM and statistically tend to form more massive dark matter halos. Regarding the halo-mass function of these objects, we observe order one departures from standard $\Lambda$CDM predictions. The formalism developed here can be easily applied to other models where fifth-forces participate to the dynamics of the gravitational collapse.Comment: 17 pages, 5 figures. Minor revisions to match published versio

Local transformations of units in Scalar-Tensor Cosmology

The physical equivalence of Einstein and Jordan frame in Scalar Tensor theories has been explained by Dicke in 1962: they are related by a local transformation of units. We discuss this point in a cosmological framework. Our main result is the construction of a formalism in which all the physical observables are frame-invariant. The application of this approach to CMB codes is at present under analysis.Comment: To appear in the proceedings of IRGAC 2006, 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15 200