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 Scalar–tensor teleparallel gravity with boundary term by Noether symmetries

2018 ◽  
Vol 15 (09) ◽  
pp. 1850151 ◽  
Author(s):  
G. Gecim ◽  
Y. Kucukakca
Keyword(s):  
Scalar Field ◽  
Teleparallel Gravity ◽  
Boundary Term ◽  
Noether Symmetry ◽  
Late Time ◽  
Field Equations ◽  
Symmetry Approach ◽  
Tensor Theory ◽  
Accelerating Expansion ◽  
Frw Cosmological Model

In the framework of teleparallel gravity, the Friedman–Robertson–Walker (FRW) cosmological model with scalar tensor theory, where scalar field is non-minimally coupled to both the torsion scalar and boundary term, is studied. Utilizing the Noether symmetry approach in such a theory, we obtain the explicit forms of the couplings and potential as a function of the scalar field. We present some important cosmological solutions for the modified field equations using these functions gotten via the Noether symmetry approach. Finally, the interesting cosmological properties of these solutions are discussed in detail, and it is shown that they can describe a universe leading to the late-time accelerating expansion.

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.

Early inflation to late-time acceleration in f(G) model

2016 ◽  
Vol 31 (33) ◽  
pp. 1650187
Author(s):  
Malay Krishna Dutta ◽  
Kaushik Sarkar ◽  
B. Modak
Keyword(s):  
Ideal Fluid ◽  
Deceleration Parameter ◽  
Accelerating Universe ◽  
Late Time ◽  
Evolution Of The Universe ◽  
Late Time Acceleration ◽  
Modified Theory Of Gravity ◽  
Theory Of Gravity ◽  
The Universe ◽  
Modified Theory

We present some solutions in Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime in the modified theory of gravity with a general Gauss–Bonnet (GB) term f(G) and R2 including an ideal fluid. We present evolution of the universe introducing an ansatz without a prior choice of f(G) in one approach, while in other class of model, the solutions are obtained assuming few simple forms of f(G). Some of the solutions show early inflationary expansion, further in one solution the fluctuation of the deceleration parameter q is evident at the end of inflation. In all cases, late-time transition to accelerating universe at redshift z [Formula: see text] 0.7 is realizable.

Cosmological constant Λ in f(R,T) modified gravity

2016 ◽  
Vol 13 (05) ◽  
pp. 1650058 ◽  
Author(s):  
Gyan Prakash Singh ◽  
Binaya Kumar Bishi ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Modified Gravity ◽  
Bianchi Type ◽  
Field Equations ◽  
Type Iii ◽  
Expansion Scalar ◽  
Modified Theory Of Gravity ◽  
Shear Scalar ◽  
Modified Theory

In this paper, we have studied the Bianchi type-III cosmological model in the presence of cosmological constant in the context of [Formula: see text] modified theory of gravity. Here, we have discussed two classes of [Formula: see text] gravity, i.e. [Formula: see text] and [Formula: see text]. In both classes, the modified field equations are solved by the relation expansion scalar [Formula: see text] that is proportional to shear scalar [Formula: see text] which gives [Formula: see text], where [Formula: see text] and [Formula: see text] are metric potentials. Also we have discussed some physical and kinematical properties of the models.

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.

Transit dark energy string cosmological models with perfect fluid in F(R,T)-gravity

2018 ◽  
Vol 15 (10) ◽  
pp. 1850168 ◽  
Author(s):  
Rashid Zia ◽  
Dinesh Chandra Maurya ◽  
Anirudh Pradhan
Keyword(s):  
Dark Energy ◽  
Early Time ◽  
Momentum Tensor ◽  
Late Time ◽  
Field Equations ◽  
Accelerating Expansion ◽  
Type Ia ◽  
Dynamical Parameters ◽  
The Stability ◽  
The Universe

In this paper, spatially homogeneous and anisotropic Bianchi type-[Formula: see text] dark energy (DE) cosmological transit models with string fluid source in [Formula: see text] gravity [T. Harko et al., Phys. Rev. D 84 (2011) 024020], where [Formula: see text] is the Ricci scalar and [Formula: see text] the trace of the stress energy–momentum tensor, have been studied in the context of early time decelerating and late-time accelerating expansion of the Universe as suggested by the recent observations. The exact solutions of the field equations are obtained first by using generalized hybrid expansion law (HEL) [Formula: see text] which yields a time-dependent deceleration parameter [Formula: see text] and second by considering the metric coefficient [Formula: see text]. By using recent constraints from supernovae type-Ia union data [Cunha, arXiv:0811.2379[astro-ph]], we obtain [Formula: see text] and [Formula: see text] for transit model [Formula: see text]. The Universe has an initial singularity and is anisotropic closed and it tends to be flat at the late time, i.e. our Universe is in accelerating expansion. Our model shows a phase transition property from decelerating to accelerating. It is remarkable to mention here that our Universe is homogeneous and anisotropic in the early phase whereas it becomes homogeneous and isotropic for [Formula: see text]. We have also discussed the stability of the background solution with respect to perturbations of the metric along with the properties of future singularities in the Universe dominated by DE including the phantom-type fluid. Various physical and dynamical parameters are also calculated and investigated in terms of time and redshift both.

scholarly journals Noether Gauge Symmetry of Dirac Field in (2 + 1)-Dimensional Gravity

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganim Gecim ◽  
Yusuf Kucukakca ◽  
Yusuf Sucu
Keyword(s):  
Gauge Symmetry ◽  
Early Time ◽  
Gravitational Theory ◽  
Dirac Field ◽  
Late Time ◽  
Field Equations ◽  
Dynamical Equations ◽  
Symmetry Approach ◽  
Cosmological Solutions ◽  
Dimensional Gravity

We consider a gravitational theory including a Dirac field that is nonminimally coupled to gravity in 2 + 1 dimensions. Noether gauge symmetry approach can be used to fix the form of coupling functionF(Ψ)and the potentialV(Ψ)of the Dirac field and to obtain a constant of motion for the dynamical equations. In the context of (2 + 1)-dimensional gravity, we investigate cosmological solutions of the field equations using these forms obtained by the existence of Noether gauge symmetry. In this picture, it is shown that, for the nonminimal coupling case, the cosmological solutions indicate both an early-time inflation and late-time acceleration for the 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 Dirac Field as a Source of the Inflation in2+1Dimensional Teleparallel Gravity

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ganim Gecim ◽  
Yusuf Sucu
Keyword(s):  
Early Time ◽  
Teleparallel Gravity ◽  
Noether Symmetry ◽  
Dirac Field ◽  
Late Time ◽  
Late Time Acceleration ◽  
Symmetry Approach ◽  
Gauge Term ◽  
Acceleration Of The Universe ◽  
The Universe

In this paper, we study early-time inflation and late-time acceleration of the universe by nonminimally coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with that of the3+1dimensional teleparallel gravity under Noether symmetry approach. And we see that the study explains early-time inflation and late-time acceleration of the universe.

Phase transition of LRS Bianchi type-I cosmological model in f(R,T) gravity

2020 ◽  
Vol 17 (12) ◽  
pp. 2050187
Author(s):  
R. K. Tiwari ◽  
D. Sofuoğlu ◽  
V. K. Dubey
Keyword(s):  
Cosmological Model ◽  
Bianchi Type ◽  
Early Time ◽  
Momentum Tensor ◽  
Late Time ◽  
Type I ◽  
Field Equations ◽  
Bianchi Type I ◽  
Accelerating Expansion ◽  
Acceleration Of The Universe

In this work, LRS Bianchi type-I cosmological model with perfect fluid source in [Formula: see text] gravity theory, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the stress energy-momentum tensor, has been studied in order to investigate early time deceleration and late time acceleration of the universe. By proposing a new special form of time-varying deceleration parameter in terms of Hubble parameter, the exact solution of the field equations has been obtained. The physical and geometric quantities of the model have been derived and their evolution has been discussed. Our model has an initial singularity and initially exhibits decelerating expansion and transits to accelerating expansion phase at last eras. The nature of the matter source of the model is consistent with the standard model in frame of the structure formation.

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