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.

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 FLRW-cosmology in generic gravity theories

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade
Keyword(s):  
Perfect Fluid ◽  
Gravity Theory ◽  
Fluid Type ◽  
Field Equations ◽  
Walker Metric ◽  
Flrw Cosmology ◽  
Arbitrary Dimensions ◽  
Gravity Theories

AbstractWe prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$ F ( R , G ) theories are given as examples.

A NOETHER SYMMETRY STUDY IN SCALAR-TENSOR THEORY

1998 ◽  
Vol 13 (24) ◽  
pp. 4163-4171 ◽  
Author(s):  
B. MODAK ◽  
S. KAMILYA ◽  
S. BISWAS
Keyword(s):  
General Relativity ◽  
Functional Form ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Exponential Expansion ◽  
General Scalar ◽  
Spatially Homogeneous ◽  
The Universe

In this work we study a general scalar-tensor theory in which the coupling and potential functions are determined from Noether symmetry arguments. We also obtain exact solutions of the field equations and found that the universe asymptotically follows an exponential expansion having no graceful exit. The study of the functional form of ω(φ) reveals that the theory asymptotically becomes an attractor of general relativity. We restrict ourselves to spatially homogeneous, isotropic flat universe.

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.

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 Similarity solutions for the Wheeler–DeWitt equation in $$f\left( R\right) $$-cosmology

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Quantum Cosmology ◽  
Classical Limit ◽  
Functional Form ◽  
Similarity Solutions ◽  
Bäcklund Transformations ◽  
Field Equations ◽  
Backlund Transformations ◽  
Classical Models

AbstractIn the case of a spatially flat Friedmann–Lemaître–Robertson–Walker Universe in $$f\left( R\right) $$fR-gravity we write the Wheeler–DeWitt equation of quantum cosmology. The equation depends upon the functional form of $$f\left( R\right) $$fR. We choose to work with four specific functions of $$f\left( R\right) $$fR in which the field equations for the classical models are integrable and solvable through quadratures. For these models we determine similarity solutions for the Wheeler–DeWitt equation by determining Lie–Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler–DeWitt equation.

Noether symmetry of Palatini F(ℜ) gravity

2018 ◽  
Vol 15 (03) ◽  
pp. 1850046 ◽  
Author(s):  
Nayem Sk
Keyword(s):  
Noether Symmetry ◽  
Field Equations ◽  
Walker Metric ◽  
Conserved Current ◽  
Theory Of Gravity ◽  
Friedmann Robertson Walker

In metric formalism, Noether symmetry of [Formula: see text] theory of gravity in vacuum and in the presence of pressureless dust yields [Formula: see text] along with the conserved current [Formula: see text] in Robertson–Walker metric and nothing else. However, Roshan and Shojai have claimed in [Palatini [Formula: see text] gravity and Noether symmetry, Phys. Lett. B 668 (2008) 238–240] that Noether symmetry in the context of Palatini [Formula: see text] theory of gravity admits [Formula: see text], (where [Formula: see text] is arbitrary) in matter domain era in Friedmann–Robertson–Walker universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general. Here, it is shown that Noether Symmetry admits [Formula: see text] along with a conserved current [Formula: see text] in Palatini gravity. Thus, their claim is not right.

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.

scholarly journals Noether symmetries of Einstein-aether scalar field cosmology

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Yusuf Kucukakca ◽  
Amin Rezaei Akbarieh
Keyword(s):  
Scalar Field ◽  
Noether Symmetry ◽  
Accelerated Expansion ◽  
Noether Symmetries ◽  
Field Equations ◽  
Symmetry Approach ◽  
Expansion Of The Universe ◽  
Frw Metric ◽  
Scalar Field Cosmology ◽  
The Universe

AbstractIn this paper, we explore an Einstein-aether cosmological model by adding the scalar field in which it has an interaction with the aether field. For the cosmological implications of the model, we consider that the universe can be described by the spatially flat FRW metric together with the matter dominated universe. Applying Noether symmetry approach to the point-like Lagrangian we determine the explicit forms of unknown functions i.e. the potential and coupling function. We solve the analytical cosmological solutions of the field equations admitting the Noether symmetry, basically divided into two parts. Our results show that the obtained solutions lead to an accelerated expansion of the universe. We also discuss the tensor perturbations within the framework of this model in order to get information about the mass of gravitational waves.

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