scholarly journals Noether symmetry approach for teleparallel-curvature cosmology

2015 ◽  
Vol 12 (09) ◽  
pp. 1550095 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Ratbay Myrzakulov
Keyword(s):  
Dynamical System ◽  
Exact Solutions ◽  
Arbitrary Function ◽  
Lagrangian Density ◽  
Functional Form ◽  
Ricci Scalar ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Torsion Scalar ◽  
Symmetry Approach

We consider curvature-teleparallel F(R,T) gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar R and the torsion scalar T. Using the Noether Symmetry Approach, we show that the functional form of the F(R,T) function can be determined by the presence of symmetries. Furthermore, we obtain exact solutions through the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.

scholarly journals Noether symmetry approach in Gauss–Bonnet cosmology

2014 ◽  
Vol 29 (30) ◽  
pp. 1450164 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Sergei D. Odintsov
Keyword(s):  
Dynamical System ◽  
Exact Solutions ◽  
Functional Form ◽  
Topological Invariant ◽  
Cosmological Models ◽  
Ricci Scalar ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Symmetry Approach

We discuss the Noether Symmetry Approach in the framework of Gauss–Bonnet cosmology showing that the functional form of the F(R, 𝒢) function, where R is the Ricci scalar and 𝒢 is the Gauss–Bonnet topological invariant, can be determined by the presence of symmetries. Besides, the method allows to find out exact solutions due to the reduction of cosmological dynamical system and the presence of conserved quantities. Some specific cosmological models are worked out.

scholarly journals Some exact solutions in f(𝒢,T) gravity via Noether symmetries

2017 ◽  
Vol 32 (16) ◽  
pp. 1750086 ◽  
Author(s):  
M. Farasat Shamir ◽  
Mushtaq Ahmad
Keyword(s):  
Exact Solutions ◽  
Momentum Tensor ◽  
Gravity Models ◽  
Noether Symmetry ◽  
Type I ◽  
Conserved Quantities ◽  
Rotationally Symmetric ◽  
Bianchi Type I Universe ◽  
Modified Formula ◽  
Bonnet Term

This paper is devoted to investigate the recently proposed modified Gauss–Bonnet [Formula: see text] gravity, with [Formula: see text], the Gauss–Bonnet term, coupled with [Formula: see text], the trace of energy–momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important [Formula: see text] gravity models with anisotropic background. In particular, the Noether symmetry equations for modified [Formula: see text] gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss–Bonnet gravity may be used to reconstruct [Formula: see text]CDM cosmology without involving any cosmological constant.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

scholarly journals Noether symmetries as a geometric criterion to select theories of gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840007 ◽  
Author(s):  
Konstantinos F. Dialektopoulos ◽  
Salvatore Capozziello
Keyword(s):  
Exact Solutions ◽  
Cosmological Models ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Field Equations ◽  
Geometric Criterion ◽  
Symmetry Approach ◽  
Theories Of Gravity ◽  
Gravity Theories

We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.

Classical and quantum cosmology in f(T)-gravity theory: A Noether symmetry approach

2021 ◽  
Author(s):  
Roshni Bhaumik ◽  
Sourav Dutta ◽  
Subenoy Chakraborty
Keyword(s):  
Quantum Cosmology ◽  
Functional Form ◽  
Gravity Theory ◽  
Noether Symmetry ◽  
Field Equations ◽  
Time Model ◽  
Symmetry Approach ◽  
Walker Metric ◽  
Augmented Space ◽  
Space Time Model

In the framework of [Formula: see text]-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of [Formula: see text] is determined. A point transformation in the 2D augmented space restricts one of the variables to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly, for quantum cosmology, the WD equation is constructed and a possible solution has been evaluated.

Gödel universe in f(R,T) gravity

2019 ◽  
Vol 28 (07) ◽  
pp. 1950089 ◽  
Author(s):  
Değer Sofuoğlu
Keyword(s):  
Arbitrary Function ◽  
Functional Form ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Scalar ◽  
Modified Theory Of Gravity ◽  
Theory Of Gravity ◽  
Tensor Formula ◽  
Modified Theory ◽  
Gödel Universe

In this study, we have considered Gödel universe in the context of [Formula: see text] modified theory of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar [Formula: see text] and the trace of the energy–momentum tensor [Formula: see text]. We have shown that the Gödel solution exists in this modified theory for more general functional form of [Formula: see text] function than it appears in the literature.

Can Noether symmetry in modified f(G) gravity always yield cosmic evolution?

2017 ◽  
Vol 32 (11) ◽  
pp. 1750046
Author(s):  
Malay Krishna Dutta ◽  
B. Modak
Keyword(s):  
Ideal Fluid ◽  
Functional Form ◽  
Noether Symmetry ◽  
Late Time ◽  
Field Equations ◽  
Symmetry Approach ◽  
Cosmic Evolution ◽  
Accelerating Expansion ◽  
Modified Theory Of Gravity ◽  
Modified Theory

We discuss Noether symmetry approach in the modified theory of gravity with Gauss–Bonnet (GB) interaction-f(G) including an ideal fluid in Friedmann–Lemaître–Robertson–Walker (FLRW) background. It yields functional form of f(G) from the symmetry. The existence of Noether symmetry gives the scale factor in two cases, but these are not satisfied by field equations in general. In another case, the solution of field equations shows late-time transition to an accelerating expansion when matter is dust, however the solution including dust and radiation is always in accelerating era.

scholarly journals Noether symmetry approach for Dirac–Born–Infeld cosmology

2015 ◽  
Vol 12 (05) ◽  
pp. 1550065 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Ratbay Myrzakulov
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Interaction Potential ◽  
Noether Symmetry ◽  
Symmetry Approach ◽  
Canonical Scalar Field

We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field T with a Dirac–Born–Infeld Lagrangian and a potential V(T). Furthermore, we assume a coupled canonical scalar field ϕ with an arbitrary interaction potential B(T, ϕ). Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

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