Could the Lyra manifold be the hidden source of the dark energy?

Abstract

In the course of investigation of our present universe by considering the five-dimensional locally rotationally symmetric (LRS) Bianchi type-I universe with timedependent deceleration parameters in Lyra manifold, it is excitingly found that the geometry itself of Lyra manifold behaves and consistent with present observational findings for accelerating universe. The behavior of the universes and their contribution to the process of evolution are examined. While studying their physical, dynamical and kinematical properties for different cases, it is found that this model is a new and viable form of model universe containing dark energy. It will be very helpful in explaining the present accelerated expansion behavior of the universe.

On causality violation in Lyra Geometry

“…Beesham [31] has studied FLRW cosmological models in Lyra manifold with time dependent displacement field. Recently, numerous studies have been done in the Lyra context, such as, an inhomogeneous Bianchi-I model in Lyra geometry has been studied [32], a thermodynamic analysis of gravitational field equations has been investigated [33], dark energy has been discussed [34], Bianchi type VI cosmological model in the presence of electromagnetic fields with variable magnetic permeability has been analyzed [35], bulk viscous with strange quark matter attached to the string cloud for higher dimensional Friedman-Robertson-Walker (FRW) universe has been studied [36], static traversable wormholes in Lyra manifold have been considered [37], among others. In this paper the main objective is studying the Gödel-type solutions in Lyra geometry looking for a new interpretation for the displacement vector and also solutions that avoid the causality violation.…”

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

“…(Note that x 0 is merely the symbol represents the gauge function following historical convention and has nothing to do with the time component of the spacetime coordinate.) Recently, many interesting theoretical topics in Lyra geometry have been widely discussed, like the singularity in a collapsing massive star [11], cosmology models in Lyra geometry [10,12,14,[18][19][20], gauge field as the source of gravity [7,13,16,17], so on and so forth. In this article, after we choose a series of smooth and spherically symmetric gauge functions, singularities emerge at r = 0.…”

“…will invoke eq. (19) to solve the λ(r). Since y = e ν(r) = −g 00 and y = C 2 · sin[ √ 2 2 ln(r)]/ √ r, we could calculate the derivative of ν(r) with respect to r:…”

“…Follow the ODE in eq. (19) and the expression of f (r) in eq. (A8), we could get the expression for λ ′ (r):…”