Noether symmetries of LRS Bianchi type-I spacetime in f(ℛ,φ,χ) gravity

2020 ◽  
Vol 17 (11) ◽  
pp. 2050163
Author(s):  
Adnan Malik ◽  
M. Farasat Shamir ◽  
Ibrar Hussain
Keyword(s):  
Bianchi Type ◽  
State Parameter ◽  
Noether Symmetry ◽  
Energy Conditions ◽  
Type I ◽  
Bianchi Type I ◽  
Symmetry Approach ◽  
Kinetic Energy Term ◽  
Theory Of Gravity ◽  
Modified Formula

This paper investigates the Noether symmetry approach in modified [Formula: see text] theory of gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is a scalar field and [Formula: see text] is the kinetic energy term. For this purpose, we consider Locally Rotationally Symmetric (LRS) Bianchi Type-I spacetimes. The cosmological solutions are developed through Noether symmetry approach. The determining equations are computed in the context of a point-like Lagrangian for [Formula: see text] gravity. In particular, three different cases are taken into account for the LRS Bianchi Type-I spacetimes. Some important conserved quantities for the Lagrangian in this modified theory of gravity are worked out through the determining equations. In this scenario, the graphical behavior of energy density, pressure component and equation of state parameter are reported and analyzed with the help of first integrals of motion. The negative trends of the strong energy conditions actually suggest that the said theory supports expanding Universe with dark energy.

scholarly journals Anisotropic solution in phantom cosmology via Noether symmetry approach

2018 ◽  
Vol 96 (7) ◽  
pp. 677-680 ◽  
Author(s):  
I. Basaran Oz ◽  
Y. Kucukakca ◽  
N. Unal
Keyword(s):  
Scalar Field ◽  
Bianchi Type ◽  
Space Time ◽  
Noether Symmetry ◽  
Type I ◽  
Field Equations ◽  
Anisotropic Solution ◽  
Bianchi Type I ◽  
Symmetry Approach ◽  
The Universe

In this study, we consider a phantom cosmology in which a scalar field is minimally coupled to gravity. For anisotropic locally rotational symmetric (LRS) Bianchi type I space–time, we use the Noether symmetry approach to determine the potential of such a theory. It is shown that the potential must be in the trigonometric form as a function of the scalar field. We solved the field equations of the theory using the result obtained from the Noether symmetry. Our solution shows that the universe has an accelerating expanding phase.

Noether symmetries of Bianchi type I spacetimes via Rif tree approach

2021 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Muhammad Farhan ◽  
Tahir Hussain
Keyword(s):  
Bianchi Type ◽  
Noether Symmetry ◽  
Type I ◽  
Noether Symmetries ◽  
Bianchi Type I ◽  
Tree Approach ◽  
Symmetry Algebras

In this paper, we have studied Noether symmetries of the general Bianchi type I spacetimes. The Lagrangian associated with the most general Bianchi type I metric is used to find the set of Noether symmetry equations. These equations are analyzed using an algorithm, developed in Maple, to get all possible Bianchi type I metrics admitting different Noether symmetries. The set of Noether symmetry equations is then solved for each metric to obtain the Noether symmetry algebras of dimensions 4, 5, 6 and 9.

The Mimetic Matter in LRS Bianchi Type-I Model

2021 ◽  
Author(s):  
Ertan Gudekli ◽  
E. Demir
Keyword(s):  
Bianchi Type ◽  
State Parameter ◽  
Relativity Theory ◽  
Type I ◽  
Field Equations ◽  
Bianchi Type I ◽  
Rotationally Symmetric ◽  
Bianchi Type I Universe ◽  
Expansion Of The Universe ◽  
The Universe

This paper deals with the Locally rotationally symmetric (LRS) Bianchi type-I universe model in Mimetic Gravity Theory assuming it an extended form of General Relativity Theory. It was proclaimed as a conformal transformation of the Einstein-Hilbert action from Einstein frame to Jordon frame. At the outset, we have proposed a potential function on account of clarifying the expansion of our universe by considering the general solutions of the field equations that originate from the action of the theory including the Lagrange multipliers. Lastly, after having been achieved the general equation of the state parameter ω, we discussed whether the result corresponds to some fluids illuminating the expansion of the Universe or not.

On a Bianchi type-I space-time with bulk viscosity in f(R,T) gravity

2021 ◽  
Author(s):  
M. Koussour ◽  
M. Bennai
Keyword(s):  
Deceleration Parameter ◽  
Bianchi Type ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Type I ◽  
Field Equations ◽  
Bulk Fluid ◽  
Bianchi Type I ◽  
Deceleration Phase ◽  
Spatially Homogeneous

In this paper, we present a spatially homogeneous and anisotropic Bianchi type-I cosmological model with a viscous bulk fluid in [Formula: see text] gravity where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy-momentum tensor, respectively. The field equations are solved explicitly using the hybrid law of the scale factor, which is related to the average Hubble parameter and gives a time-varying deceleration parameter (DP). We found the deceleration parameter describing two phases in the universe, the early deceleration phase [Formula: see text] and the current acceleration phase [Formula: see text]. We have calculated some physical and geometric properties and their graphs, whether in terms of time or redshift. Note that for our model, the bulk viscous pressure [Formula: see text] is negative and the energy density [Formula: see text] is positive. The energy conditions and the [Formula: see text] analysis for our spatially homogeneous and anisotropic Bianchi type-I model are also discussed.

Anisotropic universe and reconstructing f(R, T) theory from holographic Ricci dark energy

2017 ◽  
Vol 95 (5) ◽  
pp. 524-534 ◽  
Author(s):  
V. Fayaz ◽  
H. Hossienkhani ◽  
Z. Zarei ◽  
M. Ganji ◽  
N. Azimi
Keyword(s):  
Dark Energy ◽  
Bianchi Type ◽  
Equations Of State ◽  
State Parameter ◽  
Accelerated Expansion ◽  
Anisotropic Universe ◽  
Density Parameter ◽  
Type I ◽  
Ricci Dark Energy ◽  
Bianchi Type I

In this work, we regard f(R, T) gravity as an effective description of the acceleration of the universe and reconstruct the function f(R, T) from the holographic Ricci dark energy by considering a Bianchi type I universe. So the connection gives us an opportunity to redefine the Hubble parameter, the pressure, the equations of state parameter, and the energy density parameter representation by considering Bianchi type I models for holographic Ricci dark energy. We wrap up the evolution of the accelerated expansion of the anisotropic universe, which is faster than the evolution of the FRW and ΛCDM models.

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