Narrow Results

We investigate the spacetime of a local gauge string with a phenomenological energy momentum tensor, as prescribed by Vilenkin, in the presence of the cosmological term Λ. A set of solutions of full nonlinear Einstein's equations for interior region of such a string is presented.

We investigate the spacetime of a global monopole in a five-dimensional spacetime in the presence of the cosmological term. Also the gravitational properties of the monopole solution are discussed.

Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical Λ-term. Exact solutions of the model equations are obtained for the different equations of state of the matter, that fills the universe, and for the certain assumptions on the decaying law for Λ.

In this research, we have investigated tachyon and $k$-essence dark energy (DE) candidates with varying $G$ and $\mathrm{\Lambda }$ for Marder universe in $f(R,T)$ gravitation theory [Harko et al., Phys. Rev. D84, 024020 (2011)]. Here, $f(R,T)$ is the arbitrary function of Ricci scalar ($R$) and the trace of $T_{ik}$. To solve $f(R,T)$ gravity field equations, three different approximations have been used such as cosmological term, equation of state (EoS) parameter and the anisotropy feature of Marder universe. Also, we have discussed some physical results with various graphics.

The cosmological term is formulated in the framework of the extended loop representation and its particularization from the extended loop to the loop representations is given. The properties of the Gauss self-linking number are investigated. It is shown that the phase factor of the Kauffman bracket satisfies the Mandelstam identities, the diffeomorphism constraint and the Hamiltonian constraint with the cosmological constant in the extended loop calculus.

Quantum fluctuation of unstable modes about gravitational instantons causes the instability of flat space at finite temperature, leading to the spontaneous process of nucleating quantum black holes. The energy-density of quantum black holes, depending on the initial temperature, gives the cosmological term, which naturally accounts for the inflationary phase of the early universe. The reheating phase is attributed to the Hawking radiation and annihilation of these quantum black holes. Then, the radiation energy-density dominates over the energy-density of quantum black holes, the universe started the standard cosmology phase. In this phase the energy-density of quantum black holes depends on the reheating temperature. It asymptotically approaches to the cosmological constant in matter domination phase, consistently with current observations.

Motivated by Aoki et al.’s recent research on conserved charges and entropy current, we reinvestigated the conservation of relativistic Ertel’s current, which has received little attention outside the field of geophysical fluid dynamics. Ertel’s charge is an important indicator of the correlation between vortex vectors and entropy gradient fields in Earth’s meridional heat transport. We first show that in the generalized Hamiltonian structure of baroclinic fluids, the duality between the total energy and the Casimir as a function of Ertel’s charge plays an important role in the nonrelativistic case. Then, by extending the result to relativistic cases, we show that this finding has far-reaching implications not only for space–time issues in cosmology but also for the foundation of quantum field theory. An especially important finding is that, as an unreported dual form of the Einstein field equation, we identify a special equation satisfied not only by the vortex tensor field generated by the conserved charge but also by the Weyl tensor in interpreting the physical nature of the metric tensor $g^{\mu \nu }$, which appears in the cosmological term $\mathrm{\Lambda }{g}^{\mu \nu }$.

We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center. The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure associated with an r-dependent cosmological term , whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λg_μν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space–time symmetry. In the case of the flat asymptotic, space–time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ m_crit, the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < m_crit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild–de Sitter at large r. Λ_μν geometry describes, dependently on parameters m and and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λg_μν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.

Here we study an anisotropic model of the universe with constant energy per particle. A decaying cosmological constant and particle production in an adiabatic process are considered as the sources for the entropy. The statefinder parameters {r, s} are defined and their behavior are analyzed graphically in some cases.

Nonmetricity derived from a scalar field is shown to exist as a cosmic field, without direct coupling to matter. It leads to a variable cosmological term, a term that dominates the expansion in the early universe but dies away at later times.

A study is made of the LRS Bianchi type-I cosmological model in $f(R,T)$ modified gravity theory. Einstein’s field equations in $f(R,T)$ gravity are solved by taking $f(R,T)=R+2f(T)$ and the deceleration parameter $(q)$ to be a linear function of the Hubble parameter $(H)$. The universe begins with an initial singular state and changes with time from an early deceleration phase to a late time acceleration phase. We have found that the jerk parameter $(j)$ in the model approaches that of the $\mathrm{\Lambda }CDM$ model at late times. We also discuss the physical and geometrical properties of the model.

We consider a $(4+2k)$-dimensional Einstein–Gauss–Bonnet model with the cosmological $\mathrm{\Lambda }$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional “our” world and internal subspaces with dimensions $k_1=k$ and $k_2=k$.

In this study, we have investigated homogeneous and anisotropic Marder and Bianchi type I universe models filled with normal and phantom scalar field matter distributions with $\mathrm{\Lambda }$ in $f(R,T)$ gravitation theory (T. Harko et al., Phys. Rev. D84 (2011) 024020). In this model, $R$ is the Ricci scalar and $T$ is the trace of energy–momentum tensor. To obtain exact solutions of modified field equations, we have used anisotropy feature of the universe and different scalar potential models with $f(R,T)=R+2f(T)$ function. Also, we have obtained general relativity (GR) solutions for normal and phantom scalar field matter distributions in Marder and Bianchi type I universes. Additionally, we obtained the same scalar function values by using different scalar field potentials for Marder and Bianchi type I universe models with constant difference in $f(R,T)$ gravity and GR theory. From obtained solutions, we get negative cosmological term value for $V(\varphi )=V_0$ constant scalar potential model with Marder and Bianchi type I universes in GR theory. These results agree with the studies of Maeda and Ohta, Aktaş et al. also Biswas and Mazumdar. Finally, we have discussed and compared our results in gravitation theories.

What can the exact solutions of the 5D STM Universe imply when they are compared to the field equations of a Corrected Metric Tensor Universe? The comparison implies the possibility of clarifying the meaning of the cosmological term.