Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Higher Dimensional Cosmology with Normal Scalar Field and Tachyonic Field

We have considered N-dimensional Einstein field equations in which four-dimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have supposed that the higher dimensional anisotropic universe is filled with only normal scalar field or tachyonic field. Here we have found the nature of potential of normal scalar field or tachyonic field. From graphical representations, we have seen that the potential is always decreases with field φ increases.     

Oscillatory Phase of Inflaton and Power-Law Expansion in Bianchi Type-I Universe

A homogeneous massive scalar field, minimally coupled to the spatially homogeneous and anisotropic background metric, in the semiclassical theory of gravity is examined. In the oscillatory phase of inflaton, the approximate leading solution to the semiclassical Einstein equation for the Bianchi type-I universe shows, each scale factor in each direction obeys t ^2/3 power-law expansion. Further noted that the evolution of scale factors are mutually correlated.     

New developments in the theory of gravity interacting with quantized fields

Renormalization in the theory of a quantized scalar field interacting with the classical Einstein gravitational field is discussed. The scalar field obeys the generalization of the Klein-Gordon equation which is conformally invariant in the limit of vanishing mass. A generalized Kasner metric corresponding to an anisotropic expansion of the universe is considered. Results obtained in collaboration with S.A. Fulling and B.L. Hu are described, which show explicitly how the infinities appearing in the expectation value of the energy-momentum tensor can be absorbed through renormalization of the cosmological constant and the coefficients of a quadratic tensor appearing in a slightly generalized form of the Einstein equation. There is also a finite renormalization of the gravitational constant.     

Tachyon field in cosmology

We study cosmological effects of homogeneous tachyon field as dark energy. We concentrate on two different scalar field potentials, the inverse square potential and the exponential potential. These models have a unique feature that the matter density parameter and the density parameter for tachyons remain comparable for a large range in red-shift. It is shown that there exists a range of parameters for which the universe undergoes an accelerated expansion and the evolution is consistent with structure formation requirements. For a viable model we require fine tuning of parameters comparable to that in ACDM or in quintessence models. For the exponential potential, the accelerated phase is followed by a phase witha(t) α t ^2/3 thus eliminating a future horizon.     

De Sitter solutions in higher order gravity

We consider de Sitter solutions, relevant for instance in studies of inflation, in cosmologies where the gravitational Lagrangian is a functionf(R),R being the scalar curvature. Previous investigations have mostly concentrated onf(R) = R+R² which always has a solution matching the conventional de Sitter one. We show that this circumstance is rather exceptional, and that one must go to higher terms to see signs of the generic behaviour, In general the de Sitter solutions are different from those of Einstein gravity. We present complete solutions for the general cubic Lagrangian. We also address the question of when the solutions to equations from truncated actions can be expected to well represent solutions of some full (and possibly unknown) theory. Such theories provide the possibility of weakening the bounds on the energy density of the inflaton, allowing an easier reconciliation of the inflationary universe with structure-forming topological defects.     

Bianchi Type-III Magnetized Wet Dark Fluid Cosmological Model in General Relativity

Bianchi type-III cosmological model of universe filled with dark energy from a wet dark fluid (WDF) in presence and absence of magnetic field is investigated in general theory of relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar i.e. (B=C ⁿ ). The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model do not approach isotropy through the evolution of the universe.     

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have considered Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with Variable Modified Chaplygin Gas (VMCG). Here we find normal scalar field ? and the self interacting potential V(?) to describe the VMCG Cosmology. We have also graphically analyzed the geometrical parameters named Statefinder Parameters in anisotropic Kaluza-Klein model. Next, we have considered a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter interacts between themselves and for that we also choose the interaction term. We convert that interaction term to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.     

General models of Einstein gravity with a non-Newtonian weak-field limit

We investigate Einstein theories of gravity, coupled to a scalar field j{\varphi} and point-like matter, which are characterized by a scalar field-dependent matter coupling function e^H(j){e^{H(\varphi)}} . We show that under mild constraints on the form of the potential for the scalar field, there are a broad class of Einstein-like gravity models—characterized by the asymptotic behavior of H—which allow for a non-Newtonian weak-field limit with the gravitational potential behaving for large distances as ln r. The Newtonian term GM/r appears only as sub-leading. We point out that this behavior is also shared by gravity models described by f (R) Lagrangians. The relevance of our results for the building of infrared modified theories of gravity and for modified Newtonian dynamics is also discussed.     

On the stability of scalar-vacuum space-times

We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with arbitrary potentials V(ϕ), and in particular space-times with throats (including wormholes), which are possible if the scalar is phantom. At such a throat, the effective potential for perturbations V _eff has a positive pole (a potential wall) that prevents a complete perturbation analysis. We show that, generically, (i) V _eff has precisely the form required for regularization by the known S-deformation method, and (ii) a solution with the regularized potential leads to regular scalar field and metric perturbations of the initial configuration. The well-known conformal mappings make these results also applicable to scalar-tensor and f(R) theories of gravity. As a particular example, we prove the instability of all static solutions with both normal and phantom scalars and V(ϕ)≡0 under spherical perturbations. We thus confirm the previous results on the unstable nature of anti-Fisher wormholes and Fisher’s singular solution and prove the instability of other branches of these solutions including the anti-Fisher “cold black holes.”     

New mechanism to cross the phantom divide

Recently, type Ia supernova data appear to support a dark energy whose equation of state w crosses −1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in gravity with an additional inverse power-law term of the Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with w<−1 or w>−1 are obtained. A minimally coupled scalar with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are investigated via numerical methods, respectively. All these potentials lead to the crossing behavior. We show that it is a robust result which is hardly dependent on the concrete form of the potential of the scalar.     

Spectral asymmetry of Dirac Hamiltonian in a five-dimensional Kaluza-Klein theory

It is shown that the fermion number in a five-dimensional Kaluza-Klein theory (M⁴×S¹) in which the fermion is interacting with a monopole field, is quantized in units of (ϕR)² where the scalar ϕ is asymptotically constant andR is the radius of S¹.     

Axially Symmetric Inflationary Universe in General Relativity

We have investigated a simple axially symmetric inflationary universe in the presence of mass less scalar field with a flat potential. To get an inflationary universe, we have considered a flat region in which potential V is constant. Some physical properties of the universe are also discussed.     

Dark energy,induced gravity and broken scale invariance

We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ   coupling to the Ricci curvature γσ²R$\gamma {\sigma }^{2}R$.     

Interacting Ricci Logarithmic Entropy-Corrected Holographic Dark Energy in Brans-Dicke Cosmology

In the derivation of Holographic Dark Energy (HDE), the area law of the black hole entropy assumes a crucial role. However, the entropy-area relation can be modified including some quantum effects, motivated from the Loop Quantum Gravity (LQG), string theory and black hole physics. In this paper, we study the cosmological implications of the interacting logarithmic entropy-corrected HDE (LECHDE) model in the framework of Brans-Dicke (BD) cosmology. As system’s infrared (IR) cut-off, we choose the average radius of Ricci scalar curvature, i.e. R ^?1/2. We obtain the Equation of State (EoS) parameter ω _D , the deceleration parameter q and the evolution of energy density parameter $\varOmega'_{D}$ of our model in a non-flat universe. Moreover, we study the limiting cases corresponding to our model without corrections and to the Einstein’s gravity.     

Do observations favour Galileon over quintessence?

We study the Galileon scalar field model arising as a decoupling limit of the Dvali–Gababdaze–Porrati (DGP) construction for the late time acceleration of the universe. The model has one extra Galileon correction term over and above the standard kinetic and potential energy terms for a canonical quintessence field. We aim to study whether the current observational data can distinguish between the Galileon and the quintessence field. Our study shows the remarkable result that for linear and ?²${?}^2$ potentials, the data prefers the Galileon model over quintessence with significant Bayesian evidence. It confirms that the observable universe indeed prefers the inclusion of higher derivative Galileon correction in the standard scalar field Lagrangian.     

Emergent Universe in Einstein-Gauss-Bonnet Theory

In this work, Emergent Universe scenario has been developed in Einstein-Gauss-Bonnet (EGB) theory. The universe is chosen as homogeneous and isotropic FRW model and the matter in the universe has two components—the first one is a perfect fluid with barotropic equation of state p=ω ρ (ω, a constant) and the other component is a real or phantom (or tachyonic) scalar field. Various possibilities for the existence of emergent scenario has been discussed and the results are compared with those in Einstein gravity.     

Spherically Symmetric Solutions and Dark Matter on the Brane

It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane embedded in a five dimensional spacetime. The field equations involve a term depending on the five dimensional Weyl tensor, so that the solutions will not be Schwarzschild in general. This Weyl term is traceless so that any solution of ⁽⁴⁾ R = 0 is a possible four dimensional spacetime. Different solutions correspond to different five dimensional spacetimes and to different induced energy-momentum tensors on the brane. One interesting possibility is that the Weyl term could be responsible for the observed dark matter in the universe. It is shown that there are solutions of the equation ⁽⁴⁾ R = 0 that can account for the observed rotation curves of spiral galaxies.     

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ⁴ in a curved spacetime that, along with the term–ξR|φ|² quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ₀(φ + φ⁺) linear in φ, where φ₀ is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R _c < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.     

A Higher Dimensional Inflationary Universe in General Relativity

A five dimensional Kaluza-Klein inflationary universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary universe a flat region in which potential V is constant is considered. Some physical and kinematical properties of the universe are also discussed.