The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-t
ensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of $f(R)$ gravity is considered.
We present an extension of general relativity in which an $f(R)$ term `{a} la Palatini is added to the usual metric Einstein-Hilbert Lagrangian. Expressing the theory in a dynamically equivalent scalar-tensor form, we show that it can pass the Solar
System observational tests even if the scalar field is very light or massless. Applications to cosmology and astrophysics, and some exact solutions are discussed.
We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how relate th
em to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f(R) gravity.
We present the first analysis of extended stellar kinematics of elliptical galaxies where a Yukawa--like correction to the Newtonian gravitational potential derived from f(R)-gravity is considered as an alternative to dark matter. In this framework,
we model long-slit data and planetary nebulae data out to 7 Re of three galaxies with either decreasing or flat dispersion profiles. We use the corrected Newtonian potential in a dispersion-kurtosis Jeans analysis to account for the mass-anisotropy degeneracy. We find that these modified potentials are able to fit nicely all three elliptical galaxies and the anisotropy distribution is consistent with that estimated if a dark halo is considered. The parameter which measures the strength of the Yukawa-like correction is, on average, smaller than the one found previously in spiral galaxies and correlates both with the scale length of the Yukawa-like term and the orbital anisotropy.
Dynamics and collapse of collisionless self-gravitating systems is described by the coupled collisionless Boltzmann and Poisson equations derived from $f(R)$-gravity in the weak field approximation. Specifically, we describe a system at equilibrium b
y a time-independent distribution function $f_0(x,v)$ and two potentials $Phi_0(x)$ and $Psi_0(x)$ solutions of the modified Poisson and collisionless Boltzmann equations. Considering a small perturbation from the equilibrium and linearizing the field equations, it can be obtained a dispersion relation. A dispersion equation is achieved for neutral dust-particle systems where a generalized Jeans wave-number is obtained. This analysis gives rise to unstable modes not present in the standard Jeans analysis (derived assuming Newtonian gravity as weak filed limit of $f(R)=R$). In this perspective, we discuss several self-gravitating astrophysical systems whose dynamics could be fully addressed in the framework of $f(R)$-gravity.
Thanks to their enormous energy release, Gamma Rays Bursts (GRBs) have recently attracted a lot of interest to probe the Hubble diagram (HD) deep into the matter dominated era and hence complement Type Ia Supernovae (SNeIa). We consider here three di
fferent calibration methods based on the use of a fiducial LCDM model, on cosmographic parameters and on the local regression on SNeIa to calibrate the scaling relations proposed as an equivalent to the Phillips law to standardize GRBs finding any significant dependence. We then investigate the evolution of these parameters with the redshift to obtain any statistical improvement. Under this assumption, we then consider possible systematics effects on the HDs introduced by the calibration method, the averaging procedure and the homogeneity of the sample arguing against any significant bias.
We investigate whether there are any cosmological evidences for a scalar field with a mass and coupling to matter which change accordingly to the properties of the astrophysical system it lives in, without directly focusing on the underlying mechanis
m that drives the scalar field scale-dependent properties. We assume a Yukawa type of coupling between the field and matter and also that the scalar field mass grows with density, in order to overcome all gravity constraints within the solar system. We analyse three different gravitational systems assumed as cosmological indicators: supernovae type Ia, low surface brightness spiral galaxies and clusters of galaxies. Results show that: a) a quite good fit to the rotation curves of low surface brightness galaxies only using visible stellar and gas mass components is obtained; b) a scalar field can fairly well reproduce the matter profile in clusters of galaxies, estimated by X-ray observations and without the need of any additional dark matter; c) there is an intrinsic difficulty in extracting information about the possibility of a scale-dependent massive scalar field (or more generally about a varying gravitational constant) from supernovae type Ia.
We present the Hubble diagram (HD) of 66 Gamma Ray Bursts (GRBs) derived using only data from their X - ray afterglow lightcurve. To this end, we use the recently updated L_X - T_a correlation between the break time T_a and the X - ray luminosity L_X
measured at T_a calibrated from a sample of Swift GRBs with lightcurves well fitted by the Willingale et al. (2007) model. We then investigate the use of this HD to constrain cosmological parameters when used alone or in combination with other data showing that the use of GRBs leads to constraints in agreement with previous results in literature. We finally argue that a larger sample of high luminosity GRBs can provide a valuable information in the search for the correct cosmological model.
Coalescing binary systems, consisting of two collapsed objects, are among the most promising sources of high frequency gravitational waves signals detectable, in principle, by ground-based interferometers. Binary systems of Neutron Star or Black Hole
/Neutron Star mergers should also give rise to short Gamma Ray Bursts, a subclass of Gamma Ray Bursts. Short-hard-Gamma Ray Bursts might thus provide a powerful way to infer the merger rate of two-collapsed object binaries. Under the hypothesis that most short Gamma Ray Bursts originate from binaries of Neutron Star or Black Hole/Neutron Star mergers, we outline here the possibility to associate short Gamma Ray Bursts as electromagnetic counterpart of coalescing binary systems.
Gravitational waves detected from well-localized inspiraling binaries would allow to determine, directly and independently, both binary luminosity and redshift. In this case, such systems could behave as standard candles providing an excellent probe
of cosmic distances up to $z <0.1$ and thus complementing other indicators of cosmological distance ladder.
