The post-Minkowskian limit of f(R)-gravity

We formally discuss the post-Minkowskian limit of $f(R)$-gravity without adopting conformal transformations but developing all the calculations in the original Jordan frame. It is shown that such an approach gives rise, in general, together with the standard massless graviton, to massive scalar modes whose masses are directly related to the analytic parameters of the theory. In this sense, the presence of massless gravitons only is a peculiar feature of General Relativity. This fact is never stressed enough and could have dramatic consequences in detection of gravitational waves. Finally the role of curvature stress-energy tensor of $f(R)$-gravity is discussed showing that it generalizes the so called Landau-Lifshitz tensor of General Relativity. The further degrees of freedom, giving rise to the massive modes, are directly related to the structure of such a tensor.Comment: 9 page

Probing the dark matter issue in f(R)-gravity via gravitational lensing

For a general class of analytic f(R)-gravity theories, we discuss the weak field limit in view of gravitational lensing. Though an additional Yukawa term in the gravitational potential modifies dynamics with respect to the standard Newtonian limit of General Relativity, the motion of massless particles results unaffected thanks to suitable cancellations in the post-Newtonian limit. Thus, all the lensing observables are equal to the ones known from General Relativity. Since f(R)-gravity is claimed, among other things, to be a possible solution to overcome for the need of dark matter in virialized systems, we discuss the impact of our results on the dynamical and gravitational lensing analyses. In this framework, dynamics could, in principle, be able to reproduce the astrophysical observations without recurring to dark matter, but in the case of gravitational lensing we find that dark matter is an unavoidable ingredient. Another important implication is that gravitational lensing, in the post-Newtonian limit, is not able to constrain these extended theories, since their predictions do not differ from General Relativity.Comment: 7 pages, accepted for publication in EPJ

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 behaviors in cosmic evolution according to the so called Hartle criterion, that allows 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 of nonminimally coupled and higher-order models are discussed.Comment: 20 pages, Review paper to appear in EPJ

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

We analyze seven different viable $f(R)$-gravities towards the Solar System tests and stochastic gravitational waves background. The aim is to achieve 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. Beside large scale structure and galactic dynamics, these bounds can be considered complimentary in order to select self-consistent theories of gravity working at the infrared limit. It is demonstrated that seven viable $f(R)$-gravities under consideration not only satisfy the local tests, but additionally, pass the above PPN-and stochastic gravitational waves bounds for large classes of parameters.Comment: 23 pages, 8 figure

Oscillatory behavior of closed isotropic models in second order gravity theory

Homogeneous and isotropic models are studied in the Jordan frame of the second order gravity theory. The late time evolution of the models is analysed with the methods of the dynamical systems. The normal form of the dynamical system has periodic solutions for a large set of initial conditions. This implies that an initially expanding closed isotropic universe may exhibit oscillatory behaviour.Comment: 16 pages, 3 figures. With some minor improvements. To appear in General Relativity and Gravitatio

Reconstruction of some cosmological models in f(R,T) gravity

In this paper, we reconstruct cosmological models in the framework of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. We show that the dust fluid reproduces $\Lambda$CDM, phantom-non-phantom era and the phantom cosmology. Further, we reconstruct different cosmological models including, Chaplygin gas, scalar field with some specific forms of $f(R,T)$. Our numerical simulation for Hubble parameter shows good agreement with the BAO observational data for low redshifts $z<2$.Comment: 12 pages, 2 figure

Modified f(R) gravity from scalar-tensor theory and inhomogeneous EoS dark energy

The reconstruction of f(R)-gravity is showed by using an auxiliary scalar field in the context of cosmological evolution, this development provide a way of reconstruct the form of the function f (R) for a given evolution of the Hubble parameter. In analogy, f(R)-gravity may be expressed by a perfect fluid with an inhomogeneous equation of state that depends on the Hubble parameter and its derivatives. This mathematical equivalence that may confuse about the origin of the mechanism that produces the current acceleration, and possibly the whole evolution of the Hubble parameter, is shown here.Comment: 8 page

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure $F(R)$ gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-$\Lambda$-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-$\Lambda$ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure $F(R)$ gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at $r=0$. We should note that the Kreschmann scalar of charged solutions goes to infinity as $r \rightarrow 0$, but with a rate slower than that of uncharged solutions.Comment: 21 pages, 4 figures, generalization to higher dimensions, references adde

Some Adventures in the Search for a Modified Gravity Explanation for Cosmic Acceleration

The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a theoretically consistent and observationally viable modification of gravity that is capable of describing the accelerating universe. I will discuss f(R) models, and their obvious extensions, and the DGP model as an example of extra-dimensional implementations. I will then briefly describe the Galileon models and their very recent multifield and curved space extensions - a class of four-dimensional effective field theories encoding extra dimensional modifications to gravity. This article is dedicated to the career of my friend and former colleague, Joshua Goldberg, and is written to appear in his festschrift.Comment: 17 pages, to appear in a festschrift for Joshua Goldber