New approach to find exact solutions for cosmological models with a scalar field

Extended f(R) theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended f(R) theories: f(R, T) theory, in which curvature is coupled non-minimally to the trace of energy–momentum tensor Tμν and mimetic f(R) gravity, a theory with a scalar field degree of freedom, but ghost-free and with internal conformal symmetry. In both cases we write point-like Lagrangian for flat Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological background in the presence of ordinary matter. We have been shown that some classes of models existed with Noether symmetry in these viable extensions of f(R) gravity. As a motivated idea, we have been investigating the stability of the solutions and the bouncing and ΛCDM models using the Noether symmetries. We have been shown that in mimetic f(R) gravity bouncing and ΛCDM solutions are possible. Also a class of solutions with future singularities has been investigated.

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“…What we call it as Noether Symmetry Approach [47]- [49] is the existence of a "unique" vector field X on tangent space T Q ≡ {q i ,q i }): :…”

Section: Noether Symmetry Approach To Dynamical Systemsmentioning

confidence: 99%

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Momeni

Myrzakulov

Güdekli

2015

Int. J. Geom. Methods Mod. Phys.

114

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“…Applying the Noether Symmetry Aproach [18][19][20][21], it can be shown that the new variables we should introduce to simplify the field equations are the same used in [12]:…”

Section: An Exponential Potentialmentioning

confidence: 99%

Model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

et al. 2003

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In this work we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a collapsing universe (for a given region of the parameter space), which is necessary for an adequate definition of string theory. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.

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“…The well known Noether symmetry has broad applications in mathematics, dynamics, and physics [1][2][3][4][5][6][7], it always can lead to conserved quantities. In fact, it is also named variational symmetry [3].…”

Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Wang

Feng

2017

Acta Phys. Pol. A

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Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.

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New approach to find exact solutions for cosmological models with a scalar field

Cited by 163 publications

References 12 publications

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

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