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We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of $f(R)$, $f(G)$ or $f(R,G)$ gravity, model with non-linear gravitational coupling or string-inspired…
In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black…
Jeans instability is derived for the case of a low density self-gravitating gas beyond the Navier-Stokes equations. The Jeans instability criterium is shown to depend on a Burnett coefficient if the formalism is taken up to fourth order in…
We study possible spatial domains containing expanding extra dimensions. We show that they are predicted in the framework of $f(R)$ gravity and could appear due to quantum fluctuations during inflation. Their interior is characterized by…
Basic aspects of the background of gravitational waves and its mathematical characterization are reviewed. The spectral energy density parameter $\Omega(f)$, commonly used as a quantifier of the background, is derived for an ensemble of…
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…
Density perturbations in the cosmic microwave background within general $f(R,\phi)$ models of gravity are investigated. The general dynamical equations for the tensor and scalar modes in any $f(R,\phi)$ gravity model are derived. An…
We derive the equation of matter density perturbations on sub-horizon scales for a general Lagrangian density f(R, phi, X) that is a function of a Ricci scalar R, a scalar field phi and a kinetic term X=-(nabla phi)^2/2. This is useful to…
In this paper we investigate graviton-photon oscillation in the presence of an external magnetic field in alternative theories of gravity. Whereas the effect of an effective refractive index for the electromagnetic radiation was already…
We discuss the generation and evolution of density perturbations during the large curvature phase of string cosmology. We find that perturbations in the scalar components of the metric evolve with cosmic time as $\exp (\gamma H_st)$ where…
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations…
We derive a generalized equation for the evolution of tensor perturbations in a cosmological background, taking into account higher-curvature contributions and a tree-level coupling to the dilaton in the string frame. The equation is…
We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on…
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for…
The evolution of linear cosmological perturbations in modified theories of gravity is investigated assuming the Palatini formalism. It has been discussed about the stability problem in this model based on the equivalence between f(R)…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We use higher derivative classical gravity to study the nonlinear coupling between the cosmological expansion of the universe and metric oscillations of Planck frequency and very small amplitude. We derive field equations at high orders in…
A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability…
We present numerical calculation of the evolution of a background space-time metric and sub-horizon matter density perturbations in viable $f(R)$ gravity models of present dark energy and cosmic acceleration. We found that viable models…
We investigate the formation of the large scale structures in the present accelerated era in $f(R)$ gravity background. This is done by considering the linear growth of matter perturbations at low redshift $z<1$. The effect of $f(R)$ alters…