New Gravity Field Equation is derived by Einstein Field Equation in General Relativity Theory

We found the 4-order curvature term satisfied the co-variant derivative. Einstein gravity fieldequation is consist of 2-order curvature terms. Hence, the 4-order curvature term and 2-order curvature termsmake new gravity field equation. In this point, Einstein’s gravity field equation can be modified by new 4-order curvature term because gravity field equation’s term doesn’t have to be 2-order term. Indeed, Einsteinhimself was like that, 0-order term, the cosmological term. Therefore, our theory is based on legitimate facts.

On the cosmological solutions in Weyl geometry

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.

The massive supermembrane on a knot

We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generates a cosmological term in the Hamiltonian of the theory.The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in M9 × T2. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the (1, 1) − knots associated with the monodromies.

A probe of cosmological models in modified teleparallel gravity

In this paper, we have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function [Formula: see text] where [Formula: see text] and [Formula: see text] are model parameters and [Formula: see text] is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter [Formula: see text] in terms of equation of state (EoS) parameter [Formula: see text] and Hubble parameter [Formula: see text]. We have investigated the variation of [Formula: see text] over the observed values of Hubble constant in various observations within the range of redshift [Formula: see text]. Also, we have studied effective energy density [Formula: see text], effective pressure [Formula: see text] and effective EoS parameter [Formula: see text]. We have observed that the second term of [Formula: see text] function behaves just like variable cosmological term [Formula: see text] ([Formula: see text]) at late-time universe and causes the acceleration in expansion and works just like dark energy candidates. Also, we have evaluated the age of the present universe for various stages of matter [Formula: see text] and various [Formula: see text] functions.

FLRW Cosmological Models with Dynamic Cosmological Term in Modified Gravity

Although the standard lambda cold dark matter cosmological model is quite successful in describing the universe, there are still several issues that are still not resolved. Some of these are the cosmological constant problem, certain anomalies in the cosmic microwave background radiation and whether general relativity is valid on large scales. Therefore, it is interesting to examine modified theories in an attempt to solve these problems, and to examine the entire range of possibilities that are allowed. In this work, we examine one of these modified theories, viz., f(R,T) gravity. We study the homogeneous and isotropic models in this theory, which have some pleasing features, such as no initial singularity, a dynamic cosmological term, and a transition from early deceleration to late-time acceleration as intimated by observations. The physical parameters of the model, as well as the energy conditions, are discussed and a viable cosmological model can be constructed.

Almost-Pseudo-Ricci Symmetric FRW Universe with a Dynamic Cosmological Term and Equation of State

The objective of the present paper is to investigate an almost-pseudo-Ricci symmetric FRW spacetime with a constant Ricci scalar in a dynamic cosmological term Λ(t) and equation of state (EoS) ω(t) scenario. Several cosmological parameters are calculated in this setting and thoroughly studied, which shows that the model satisfies the late-time accelerating expansion of the universe. We also examine all of the energy conditions to check our model’s self-stability.

Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle–West-like model action for five-dimensional spacetime in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein’s field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell–Mansouri-like action that contains the Einstein–Hilbert term, the cosmological term as well as new terms coming from Maxwell extension in four-dimensional spacetime where the torsion-free condition is assumed. Finally, we have shown that both models are equivalent for an appropriately chosen gauge condition.

Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space Cl3,0 and anti-space Cl0,3 with a particular focus on the paravector representation, emphasizing the fact that both algebras have a center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3H0c. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl3,0 corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl0,3 leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

The paper briefly reviews the Clifford algebras of space Cl(3,0) and anti-space Cl(0,3) with a particular focus on the paravector representation, emphasizing the fact that both algebras have an isomorphic center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3Hc. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl(3,0) corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl(0,3) leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.