On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page

Cardy-Verlinde formula of Kehagias-Sfetsos black hole

In this paper, we have shown that the entropy of the Kehagias-Sfetsos black hole in Ho$\check{\textbf{r}}$ava-Lifshitz (HL) gravity can be expressed by the Cardy-Verlinde formula. The later is supposed to be an entropy formula of conformal field theory in any dimension.Comment: 10 pages, accepted by IJT

Detailed balance condition and ultraviolet stability of scalar field in Horava-Lifshitz gravity

Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relativistic general covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant $\lambda$, generalized lately by da Silva, it is also true in other versions of the HL theory. With the detailed balance condition softly breaking, the number of independent coupling constants can be still significantly reduced. It is remarkable to note that, unlike other setups, in this da Silva generalization, there exists a master equation for the linear perturbations of the scalar field in the flat Friedmann-Robertson-Walker background.Comment: Some typos are corrected. To appear in JCA

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against sensitivities of VIRGO, LIGO and LISA interferometers.Comment: 12 pages, 4 figure

T-Duality For String in Horava-Lifshitz Gravity

We continue our study of the Lorentz breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz breaking string theories and show that they are the same as that of Buscher's T-duality for the relativistic strings.Comment: 17 pages, references adde

Gravitational Lensing and f(R) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f(R) extended theories of gravity. Starting from an exact solution of the f(R) field equations, which corresponds to the Schwarzschild-de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the non linearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.Comment: 7 Pages, RevTex, 1 eps figure; references added; revised to match the version accepted for publication in General Relativity and Gravitatio

Phenomenological covariant approach to gravity

We covariantly modify the Einstein-Hilbert action such that the modified action perturbatively resolves the flat rotational velocity curve of the spiral galaxies and gives rise to the Tully-Fisher relation, and dynamically generates the cosmological constant. This modification requires introducing just a single new universal parameter.Comment: v6: a mistake in deriving the equation of the cosmological constant corrected, refs adde

Filtering out the cosmological constant in the Palatini formalism of modified gravity

According to theoretical physics the cosmological constant (CC) is expected to be much larger in magnitude than other energy densities in the universe, which is in stark contrast to the observed Big Bang evolution. We address this old CC problem not by introducing an extremely fine-tuned counterterm, but in the context of modified gravity in the Palatini formalism. In our model the large CC term is filtered out, and it does not prevent a standard cosmological evolution. We discuss the filter effect in the epochs of radiation and matter domination as well as in the asymptotic de Sitter future. The final expansion rate can be much lower than inferred from the large CC without using a fine-tuned counterterm. Finally, we show that the CC filter works also in the Kottler (Schwarzschild-de Sitter) metric describing a black hole environment with a CC compatible to the future de Sitter cosmos.Comment: 22 pages, 1 figure, discussion extended, references added, accepted by Gen.Rel.Gra

Dark energy from conformal symmetry breaking

The breakdown of conformal symmetry in a conformally invariant scalar-tensor gravitational model is revisited in the cosmological context. Although the old scenario of conformal symmetry breaking in cosmology containing scalar field has already been used in many earlier works, it seems that no special attention has been paid for the investigation on the possible connection between the breakdown of conformal symmetry and the existence of dark energy. In this paper, it is shown that the old scenario of conformal symmetry breaking in cosmology, if properly interpreted, not only has a potential ability to describe the origin of dark energy as a symmetry breaking effect, but also may resolve the coincidence problem.Comment: 11 pages, minor revision, published online in EPJ

Neutron stars in generalized f(R) gravity

Quartic gravity theory is considered with the Einstein-Hilbert Lagrangean $R+aR^{2}+bR_{\mu \nu}R^{\mu \nu},$ $R_{\mu \nu}$ being Ricci\'s tensor and R the curvature scalar. The parameters $a$ and $b$ are taken of order 1 km$^{2}.$ Arguments are given which suggest that the effective theory so obtained may be a plausible approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. As in the standard Oppenheimer-Volkoff calculation the star mass increases with increasing central density until about 1 solar mass and then decreases. However a dramatic difference exists in the behaviour of the baryon number, which increases monotonically. The calculation suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.Comment: Keywords: stars, neutron stars; gravity; modified gravity Accepted in Astrophysics and Space Scienc