Massimo Pietroni

Scalar tensor gravity and quintessence

Scalar fields with inverse power-law effective potentials may provide a negative pressure component to the energy density of the universe today, as required by cosmological observations. In order to be cosmologically relevant today, the scalar field should have a mass

Flowing with time: a new approach to non-linear cosmological perturbations

m_\phi = O(10^{-33} {\mathrm eV})

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

, thus potentially inducing sizable violations of the equivalence principle and space-time variations of the coupling constants. Scalar-tensor theories of gravity provide a framework for accommodating phenomenologically acceptable ultra-light scalar fields. We discuss non-minimally coupled scalar-tensor theories in which the scalar-matter coupling is a dynamical quantity. Two attractor mechanisms are operative at the same time: one towards the tracker solution, which accounts for the accelerated expansion of the Universe, and one towards general relativity, which makes the ultra-light scalar field phenomenologically safe today. As in usual tracker-field models, the late-time behavior is largely independent on the initial conditions. Strong distortions in the cosmic microwave background anisotropy spectra as well as in the matter power spectrum are expected.

Dark matter relic abundance and scalar-tensor dark energy

Non-linear effects are crucial for computing the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order correlations are obtained—at any redshift and for any momentum scale—by integrating a system of differential equations. The method is similar to that of the familiar BBGKY (Bogoliubov–Born–Green–Kirkwood–Yvon) hierarchy. Truncating at the level of the trispectrum, the solution of the equations corresponds to the summation of an infinite class of perturbative corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than ΛCDM (CDM: cold dark matter), such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the baryonic acoustic oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density–velocity and velocity–velocity power spectra are also computed, revealing that they are much less contaminated by non-linearities than the density–density one. The approach can be seen as a particular formulation of the renormalization group, in which time is the flow parameter.

Non-linear dark energy clustering

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{sub NL}{sup 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.

Einstein and Jordan frames reconciled: A frame-invariant approach to scalar-tensor cosmology

Scalar-tensor theories of gravity provide a consistent framework to accommodate an ultralight quintessence scalar field. While the equivalence principle is respected by construction, deviations from general relativity and standard cosmology may show up at nucleosynthesis, cosmic microwave background, and solar system tests of gravity. After imposing all the bounds coming from these observations, we consider the expansion rate of the Universe at weakly interacting massive particle decoupling, showing that it can lead to an enhancement of the dark matter relic density up to few orders of magnitude with respect to the standard case. This effect can have an impact on supersymmetric candidates for dark matter.

Non-linear power spectrum including massive neutrinos: the time-RG flow approach

We consider a dark energy fluid with arbitrary sound speed and equation of state and discuss the effect of its clustering on the cold dark matter distribution at the non-linear level. We write the continuity, Euler and Poisson equations for the system in the Newtonian approximation. Then, using the time renormalization group method to resum perturbative corrections at all orders, we compute the total clustering power spectrum and matter power spectrum. At the linear level, a sound speed of dark energy different from that of light modifies the power spectrum on observationally interesting scales, such as those relevant for baryonic acoustic oscillations. We show that the effect of varying the sound speed of dark energy on the non-linear corrections to the matter power spectrum is below the per cent level, and therefore these corrections can be well modelled by their counterpart in cosmological scenarios with smooth dark energy. We also show that the non-linear effects on the matter growth index can be as large as 10–15 per cent for small scales.

Dark energy condensation

Scalar-tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame transformation in scalar-tensor theories amounts to a local redefinition of the metric, and then should not affect physical results. We analyze the issue in a cosmological context. In particular, we define all the relevant observables (redshift, distances, cross sections, ...) in terms of frame-independent quantities. Then, we give a frame-independent formulation of the Boltzmann equation, and outline its use in relevant examples such as particle freeze-out and the evolution of the cosmic microwave background photon distribution function. Finally, we derive the gravitational equations for the frame-independent quantities at first order in perturbation theory. From a practical point of view, the present approach allows the simultaneous implementation of the good aspects of the two frames in a clear and straightforward way.

Unified Dark Matter in Scalar Field Cosmologies

Future large scale structure observations are expected to be sensitive to small neutrino masses, of the order of 0.05 eV or more. However, forecasts are based on the assumption that by the time at which these datasets will be available, the non-linear spectrum in presence of neutrino mass will be predicted with an accuracy at least equal to the neutrino mass effect itself, i.e. about 3%. Motivated by these considerations, we present the computation of the non-linear power spectrum of ΛCDM models in the presence of massive neutrinos using the Renormalization Group (RG) time-flow approach, which amounts to a resummation of perturbative corrections to the matter power spectrum to all orders. We compare our results with those obtained with other methods, i.e. linear theory, one-loop perturbation theory and N-body simulations and show that the time-RG method improves the one-loop method in fitting the N-body data, especially in determining the suppression of the matter power spectrum when neutrino are massive with respect to the linear power spectrum.

On the physical significance of infra-red corrections to inflationary observables

The two most popular candidates for dark energy, i.e. a cosmological constant and quintessence, are very difficult to distinguish observationally, mostly because the quintessence field does not have sizable fluctuations. We study a scalar field model for dark energy in which the scalar field is invariant under reflection symmetry {phi}{yields}-{phi}. Under general assumptions, there is a phase transition at late times (z < or approx. 0.5). Before the phase transition, the field behaves as a cosmological constant. After the phase transition, a time-dependent {phi}-condensate forms, the field couples with dark matter and develops sizable perturbations tracking those of dark matter. The background cosmological evolution is in agreement with existing observations, but might be clearly distinguished from that of a cosmological constant by future Supernovae surveys. The growth of cosmological perturbations carries the imprint of the phase transition, however a nonlinear approach has to be developed in order to study it quantitatively.