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The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop…
The discovery of apparent cosmological acceleration has spawned a huge number of dark energy and modified gravity theories. The f(R) models of gravity are obtained when one replaces the Ricci scalar in the Einstein-Hilbert action by an…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology, and then use it to calculate how…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
The decomposition of the linear-order metric perturbation is discussed in the context of the higher-order gauge-invariant perturbation theory. We show that the linear order metric perturbation is decomposed into gauge-invariant and…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
Perturbation of FRW spacetime is carried out in NP formalism. The equation governing the scalar, vector and tensor modes take on a very simple and transparent form. All of them can be combined in one master equation for all helicities. The…
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the…
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its…
In a recent paper (Phys. Rev. D78, 084031 (2008), arXiv:0808.0642, Ref. [1]) it was shown in examples that the covariant retarded Green's functions in particular gauges for electromagnetism and linearized gravity can be used to reproduce…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
Gauge bosons associated to new gauge symmetries under which the standard model particles are not charged are predicted in many extensions of the standard model of particles and interactions. We show that under very general conditions, the…
We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of…
Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In…
The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown…