Relaxation of vacuum energy in <Emphasis Type="Italic">q</Emphasis>-theory

The q-theory formalism aims to describe the thermodynamics and dynamics of the deep quantum vacuum. The thermodynamics leads to an exact cancellation of the quantum-field zero-point-energies in equilibrium, which partly solves the main cosmological constant problem. But, with reversible dynamics, the spatially flat Friedmann–Robertson–Walker universe asymptotically approaches the Minkowski vacuum only if the Big Bang already started out in an initial equilibrium state. Here, we extend q-theory by introducing dissipation from irreversible processes. Neglecting the possible instability of a de-Sitter vacuum, we obtain different scenarios with either a de-Sitter asymptote or collapse to a final singularity. The Minkowski asymptote still requires fine-tuning of the initial conditions. This suggests that, within the q-theory approach, the decay of the de-Sitter vacuum is a necessary condition for the dynamical solution of the cosmological constant problem.     

Dark Energy Models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Theory with Variable Deceleration Parameter

In this communication we have investigated Bianchi type-II dark energy (DE) cosmological models with and without presence of magnetic field in modified f(R, T) gravity theory as proposed by Harko et al. (Phys. Rev. D, 84, 024020, 2011). The exact solution of the field equations is obtained by setting the deceleration parameter q as a time function along with suitable assumption the scale factor \(a(t)= [sinh(\alpha t)]^{\frac {1}{n}}\), α and n are positive constant. We have obtained a class of accelerating and decelerating DE cosmological models for different values of n and α. The present study believes that the mysterious dark energy is the main responsible force for accelerating expansion of the universe. For our constructed models the DE candidates cosmological constant (Λ) and the EoS parameter (ω) both are found to be time varying quantities. The cosmological constant Λ is very large at early time and approaches to a small positive value at late time whereas the EoS parameters is found small negative at present time. Physical and kinematical properties of the models are discussed with the help of pictorial representations of the parameters. We have observed that our constructed models are compatible with recent cosmological observations.     

Dark matter from dark energy in <Emphasis Type="Italic">q</Emphasis>-theory

A constant (spacetime-independent) q-field may play a crucial role for the cancellation of Planck-scale contributions to the gravitating vacuum energy density. We now show that a small spacetime-dependent perturbation of the equilibrium q-field behaves gravitationally as a pressureless perfect fluid. This makes the fluctuating part of the q-field a candidate for the inferred dark-matter component of the present universe. For a Planck-scale oscillation frequency of the q-field perturbation, the implication would be that direct searches for dark-matter particles would remain unsuccessful in the foreseeable future.     

Geometro-thermodynamics of tidal charged black holes

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the five-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner–Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner–Nordströ m black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis show no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.     

Vacuum energy and the universe in special relativity

The problem of the cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, vacuum energy is important for the Universe even in the absence of gravity, i.e., in the case when Newton’s constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity and find that, as in general relativity, the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G and thus is valid in the limit G→0. However, the result obtained for the vacuum energy in a world without gravity, i.e., when G=0 exactly, is different.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Exploring plane-symmetric solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.     

Dark-energy cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G^5/6 support expansion of universe while those with f(G) = G^1/2 do not favor the current expansion.     

Statefinder—A new geometrical diagnostic of dark energy

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time derivative. The Statefinder pair is calculated for a number of existing models of dark energy having both constant and variable w. For the case of a cosmological constant, the Statefinder acquires a particularly simple form. We demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy. We also show that the mean Statefinder pair can be determined to very high accuracy from a SNAP-type experiment.     

Conformal transformation route to gravity’s rainbow

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we consider gravity’s rainbow, in which the metric can be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of a modified Newton’s constant and cosmological constant in gravity’s rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that Einstein gravity’s rainbow can be described by energy-dependent \(f(E,\tilde{R})\) gravity. At last, we study the f(R) gravity, when gravity’s rainbow is considered, which can also be described as energy-dependent \(\tilde{f}(E,\tilde{R})\) gravity.     

Strong energy condition and the repulsive character of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein’s equations, playing a central role for the understanding of the gravitational interaction in cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions—indeed the strong energy condition—must be assumed in order to guarantee the attractive character. In the context of f(R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f(R) models, we address the attractive/non-attractive character of f(R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters.     

An Analysis of Charged Anisotropic Star with de Sitter Spacetime

We propose a model for charged anisotropic star in de Sitter spacetime. We have taken Krori and Barua (J. Phys. A, Math. Gen. 8, 508, 1975) metric in de Sitter spacetime with non-zero cosmological constant. The model is free from singularity. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic charged star. To solve the Einstein-Maxwell field equations we assume the relation between the radial and transverse pressure as p _t ?p _r =g q(r)² r ² (where g is a non-zero positive constant). The physical conditions inside the stellar model are also discussed.     

Randall–Sundrum II model from small field inflation in light of planck data and reheating temperature

We focus on the behaviours of small field of an arctangent potential form, in Randall–Sundrum II braneworld. Within this framework, there is only one brane with positive tension while the second membrane is sent to infinity, and the configuration the model allows to localize the gravity on the curvature of the bulk. In that context, we found that inflationary observables (n _s, r, and dn _s/dlnk) depend only on the e-folding number N. From the power perturbation value P _R (k) given by the latest observational measurements, we evaluate the values of brane tension λ and the energy scale V ₀, and we have shown that the various inflationary perturbation parameters are widely consistent with the recent Planck data for a suitable choice of value of the number N. Concerning the reheating phase, we found a large value of the temperature T _re ～ 5 × 10¹⁴ GeV.     

Detection of spin excitation transfer in a two-dimensional electron system via photoluminescence of multiparticle exciton complexes

A modified-gravity theory with a four-form field strength F, a variable gravitational coupling parameter G(F), and a standard matter action are considered here. Maxwell and Einstein equations are now derived when including to action also derivates of F. The energy momentum tensor of the 4-form field contains both the part, which is typical for the fundamental (pseudo)scalar, and the part, which cancels the divergent contribution of the zero-point energies of quantum fields to the vacuum energy and thus leads to the natural nullification of the cosmological constant in Minkowski vacuum.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

On self-organizing during transition from a laminar to a turbulent flow for nonextensive systems

The evolution of parametric q-entropy and q-information divergence to the equilibrium state during spontaneous transitions and transitions from a laminar to a turbulent flow is considered as applied to nonextensive self-organizing systems. The S- and I-theorems on the variations of measures with constant mean energies are proved.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Non-Vacuum Plane Symmetric Solutions and their Energy Contents in f (R) Gravity

The exact vacuum solutions of static plane symmetric spacetimes in four, five, six and n-dimensions in metric approach of f (R) theory of gravity have already been found and are available in literature. In this paper, we extend the work done by Sharif and Farasat for the case of vacuum static plane symmetric solutions in f (R) theory of gravity to non-vacuum case. Two non-vacuum solutions have been determined by using constant Ricci scalar assumption. Moreover, for some specific choices of f (R) models, the energy distribution of these solutions has been explored by applying the generalized Landau-Lifshitz energy-momentum complex in the context of f (R) theory of gravity. In addition, we discuss the stability conditions for these solutions.     

The $$B\rightarrow \bar{K}\pi \ell \ell $$ distribution at low hadronic recoil

The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable Λ and G and bulk viscosity have been considered. We discuss three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity (ξ), cosmological constant (Λ), gravitational parameter (G) and deceleration parameter (q) for different equations of state. The model describes an accelerating Universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.     

Emergence and expansion of cosmic space as due to <Emphasis Type="Italic">M</Emphasis>0-branes

Recently, Padmanabhan (arXiv:1206.4916 [hep-th]) discussed that the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region causes the accelerated expansion of the universe. The main question arising is: what is the origin of this inequality between the surface degrees of freedom and the bulk degrees of freedom? We answer this question in M-theory. In our model, first M0-branes are compactified on one circle and N D0-branes are created. Then N D0-branes join each other, grow, and form one D5-branes. Next, the D5-brane is compactified on two circles and our universe’s D3-brane, two D1-branes and some extra energies are produced. After that, one of the D1-branes, which is closer to the universe’s brane, gives its energy into it, and this leads to an increase in the difference between the numbers of degrees of freedom and the occurring inflation era. With the disappearance of this D1-brane, the number of degrees of freedom of boundary surface and bulk region become equal and inflation ends. At this stage, extra energies that are produced due to the compactification cause an expansion of the universe and deceleration epoch. Finally, another D1-brane dissolves in our universe’s brane, leads to an inequality between degrees of freedom, and there occurs a new phase of acceleration.