Noether's stars in f(R)f(\cal {R}) gravity

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in $f({\cal R})$ gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit $f({\cal R})\rightarrow {\cal R}$. We show that it is possible to construct the $M-R$ relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law $f({\cal R})$ gravity models.Comment: 7 pages, 4 figures, accepted for publication in Physics Letter

Topological invariant quintessence

The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.Comment: 8 page

Newtonian and relativistic theory of orbits and emission of gravitational waves

This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic corrections. Finally by a classification of orbits in accordance with the conditions of motion, we calculate the gravitational waves luminosity for different types of stellar encounters and orbits.Comment: 44 pages, 22 figures. arXiv admin note: substantial text overlap with arXiv:gr-qc/0501041 by other authors without attributio

Quadrupolar gravitational radiation as a test-bed for f(R)-gravity

The debate concerning the viability of f(R)-gravity as a natural extension of General Relativity could be realistically addressed by using results coming from binary pulsars like PSR 1913+16. To this end, we develop a quadrupolar approach to the gravitational radiation for a class of ana- lytic f(R)-models. We show that experimental results are compatible with a consistent range of f(R)-models. This means that f(R)-gravity is not ruled out by the observations and gravitational radiation (in strong field regime) could be a test-bed for such theories.Comment: 13 pages, 1 figur

Stochastic Background of Relic Scalar Gravitational Waves tuned by Extended Gravity

A stochastic background of relic gravitational waves is achieved by the so called adiabatically-amplified zero-point fluctuations process derived from early inflation. It provides a distinctive spectrum of relic gravitational waves. In the framework of scalar-tensor gravity, we discuss the scalar modes of gravitational waves and the primordial production of this scalar component which is generated beside tensorial one. Then we analyze different viable $f(R)$-gravities towards the Solar System tests and stochastic gravitational waves background. The aim is to achive experimental bounds for the theory at local and cosmological scales in order to select models capable of addressing the accelerating cosmological expansion without cosmological constant but evading the weak field constraints. It is demonstrated that viable $f(R)$-gravities under consideration not only satisfy the local tests, but additionally, pass the PPN-and stochastic gravitational waves bounds for large classes of parameters.Comment: 6 pages, 1 figure, Dark Energy, Florence 200

Gravitational waves from stellar encounters

The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave luminosity, the total energy output and gravitational radiation amplitude. A crude estimate of the expected number of events towards peculiar targets (i.e. globular clusters) is also given. In particular, the rate of events per year is obtained for the dense stellar cluster at the Galactic Center.Comment: 14 pages, 3 figure

Noether symmetries in extended gravity quantum cosmology

We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical behaviors in cosmic evolution according to the so called Hartle criterion. Such a criterion selects correlated regions in the configuration space of dynamical variables whose meaning is related to the emergence of classical observable universes. Some minisuperspace models are worked out starting from Extended Gravity, in particular coming from scalar tensor, f(R) and f(T) theories. Exact cosmological solutions are derived.Comment: 20 pages, Proceedings of "49th Winter School of Theoretical Physics Cosmology and non-equilibrium statistical mechanics", L{\ka}dek-Zdr\'oj, Poland, February 10-16, 201

On the universality of MOG weak field approximation at galaxy cluster scale

In its weak field limit, Scalar-tensor-vector gravity theory introduces a Yukawa-correction to the gravitational potential. Such a correction depends on the two parameters, $\alpha$ which accounts for the modification of the gravitational constant, and $\mu^{*-1}$ which represents the scale length on which the scalar field propagates. These parameters were found to be universal when the modified gravitational potential was used to fit the galaxy rotation curves and the mass profiles of galaxy clusters, both without Dark Matter. We test the universality of these parameters using the the temperature anisotropies due to the thermal Sunyaev-Zeldovich effect. In our model the intra-cluster gas is in hydrostatic equilibrium within the modified gravitational potential well and it is described by a polytropic equation of state. We predict the thermal Sunyaev-Zeldovich temperature anisotropies produced by Coma cluster, and we compare them with those obtained using the Planck 2013 Nominal maps. In our analysis, we find $\alpha$ and the scale length, respectively, to be consistent and to depart from their universal values. Our analysis points out that the assumption of the universality of the Yukawa-correction to the gravitational potential is ruled out at more than $3.5\sigma$ at galaxy clusters scale, while demonstrating that such a theory of gravity is capable to fit the cluster profile if the scale dependence of the gravitational potential is restored.Comment: 8 pages, 3 figures, 2 Tables. Accepted for publication on Physical Letter

Probing the physical and mathematical structure of f(R)f(R) gravity by PSR J0348+0432J0348+0432

There are several approaches to extend General Relativity in order to explain the phenomena related to the Dark Matter and Dark Energy. These theories, generally called Extended Theories of Gravity, can be tested using observations coming from relativistic binary systems as PSR $J0348+0432$. Using a class of analytical $f(R)$-theories, one can construct the first time derivative of orbital period of the binary systems starting from a quadrupolar gravitational emission. Our aim is to set boundaries on the parameters of the theory in order to understand if they are ruled out, or not, by the observations on PSR $J0348+0432$. Finally, we have computed an upper limit on the graviton mass showing that agree with constraint coming from other observations.Comment: 6 pages, 1 figure, accepted in International Journal of Geometric Methods in Modern Physic