M. De Laurentis

Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behavior in cosmic evolution according to the so-called Hartle criterion, which allows one to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples for non-minimally coupled and higher-order models are discussed.

Hydrostatic equilibrium and stellar structure in f ( R ) gravity

Dipartimento di Ingegneria, Universita’ del Sannio,Palazzo Dell’Aquila Bosco Lucarelli, Corso Garibaldi, 107 - 82100, Benevento, Italy.(Dated: January 4, 2011)We investigate the hydrostatic equilibrium of stellar structure by taking into account the modi-fied Lan´e-Emden equation coming out from f(R)-gravity. Such an equation is obtained in metricapproach by considering the Newtonian limit of f(R)-gravity, which gives rise to a modified Poissonequation, and then introducing a relation between pressure and density with polytropic index n. Themodified equation results an integro-differential equation, which, in the limit f(R) → R, becomesthe standard Lan´e-Emden equation. We find the radial profiles of gravitational potential by solvingfor some values of n. The comparison of solutions with those coming from General Relativity showsthat they are compatible and physically relevant.

Classifying and avoiding singularities in the alternative gravity dark energy models

The future finite-time singularities emerging in alternative gravity dark energy models are classified and studied in Jordan and Einstein frames. It is shown that such singularity may occur even in flat spacetime for the specific choice of the effective potential. The conditions for the avoidance of finite-time singularities are presented and discussed. The problem is reduced to the study of a scalar field evolving on an effective potential by using the conformal transformations. Some viable modified gravity models are analyzed in detail and the way to cure singularity is considered by introducing the higher order curvature corrections. These results may be relevant for the resolution of the conjectured problem in the relativistic star formation in such modified gravity where finite-time singularity is also manifested.

Jeans analysis of self-gravitating systems in f(R) gravity

Dynamics and collapse of collisionless self-gravitating systems is described by the coupled collisionless Boltzmann and Poisson equations derived from

Noether symmetries and analytical solutions in f(T)-cosmology: A complete study

f(R)

f (R) gravity constrained by PPN parameters and stochastic background of gravitational waves

-gravity in the weak field approximation. Specifically, we describe a system at equilibrium by a time-independent distribution function

From Dark Energy & Dark Matter to Dark Metric

f_0(x,v)

Numerical solutions of the modified Lane–Emden equation in f(R)-gravity

and two potentials

Constraining

\Phi_0(x)

f(R)

and