F(R) cosmology via Noether symmetry and Λ-Chaplygin Gas like model

Fazlollahi, H. R.

doi:10.1016/j.physletb.2018.04.031

Cited by 10 publications

(8 citation statements)

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“…Clearly, the system can be solved only after selecting the corresponding model. To this purpose, the application of the Noether Symmetry Approach to Lagrangian (10) yields a system of 9 partial differential equations, not all independent [79,82]. Decomposing η i as η i → {α, β}, the Noether symmetry existence condition allows to select 8 models with symmetries.…”

Section: Selecting F (R) Modelsmentioning

confidence: 99%

Early and late time cosmology: the f(R) gravity perspective

et al. 2022

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Discrepancies between observations at early and late cosmic epochs, and the vacuum energy problem associated with the interpretation of cosmological constant, are questioning the ΛCDM model. Motivated by these conceptual and observational facts, extensions of Einstein's gravity are recently intensively considered in view of curing unsolved issues suffered by General Relativity at ultraviolet and infrared scales. Here, we provide a short overview of some aspects of f (R) gravity, focusing, in particular, on cosmological applications. Specifically, Noether symmetries are adopted as a criterion to select viable models and investigate the corresponding dynamics. We thus find solutions to the cosmological field equations, analyzing the behaviour of selected models from the matter-dominated to the present epoch. Moreover, constraints coming from energy conditions and the so-called swampland criteria are also considered. In particular, we qualitatively discuss the possibility of f (R) gravity to account for fixing cosmic tensions.

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Section: Selecting F (R) Modelsmentioning

confidence: 99%

Early and late time cosmology: the f(R) gravity perspective

et al. 2022

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“…The Noether Symmetry Approach is widely used to deal with cosmologies coming from different theories of gravity. For example, in [65][66][67][68][69][70][71], the approach has been used to deal with f (R) gravity. In [72][73][74][75][76][77], extended f (T ) TEGR models have been discussed in cosmology and spherical symmetry.…”

Section: Appendix A: the Noether Symmetry Approachmentioning

confidence: 99%

Equivalence of non-minimally coupled cosmologies by Noether symmetries

Bajardi,

Capozziello

2020

Preprint

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We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss-Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different non-minimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are a selection criterion to compare different theories of gravity.

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“…Bahamonde and Capozziello [64,65] have adopted the Noether symmetry approach to study the related dynamical systems and to find cosmological solutions using FRW and static spherically symmetric metrics. In another study, Fazlollahi [66] have discussed the behavior of effective EoS parameter for the obtained cosmology by exploring existence of Noether gauge symmetries in f (R) theory. They have also shown significance of the obtained cosmic scale factor by taking observational data into account.…”

Section: Introductionmentioning

confidence: 99%

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

2021

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The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

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F(R) cosmology via Noether symmetry and Λ-Chaplygin Gas like model

Cited by 10 publications

References 50 publications

Early and late time cosmology: the f(R) gravity perspective

Early and late time cosmology: the f(R) gravity perspective

Equivalence of non-minimally coupled cosmologies by Noether symmetries

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

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