$f(\mathcal{R},\phi ,\chi )$ Cosmology with Noether Symmetry

Abstract

This paper is devoted to explore modified $f(\mathcal{R})$ theories of gravity using Noether symmetry approach. For this purpose, Friedmann-Robertson-Walker spacetime is chosen to investigate the cosmic evolution. The study is mainly divided into two parts: Firstly Noether symmetries of metric $f(\mathcal{R})$ gravity are revisited and some new class of solutions with the help of conserved quantities are reported. It is shown that different scenarios of cosmic evolution can be discussed using Noether symmetries and one of the case indicates the chances for the existence of Big Rip singularity. Secondly, $f(\mathcal{R})$ theory coupled with scalar field has been discussed in detail. The Noether equations of modified gravity are reported with three subcases for flat Friedmann-Robertson-Walker universe. It is concluded that conserved quantities are quite helpful to find some important exact solutions in the cosmological contexts. Moreover, the scalar field involved in the modified gravity plays a vital role in the cosmic evolution and an accelerated expansion phase can be observed for some suitable choices of $f(\mathcal{R},\phi ,\chi )$ gravity models.

arXiv comment11 pages, 3 figures

References in corpus (20)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• f(R,T) gravity
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Curvature Quintessence
• Gravity assisted dark energy dominance and cosmic acceleration
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• Phantom Cosmology without Big Rip Singularity
• Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach
• Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity
• Some Exact Solutions in $f(\mathcal{G},T)$ Gravity via Noether Symmetries
• Noether Gauge Symmetry Approach in f(R) Gravity
• Generalized $f(R,\varphi ,X)$ gravity and the late-time cosmic acceleration
• Conserved Quantities in $f(R)$ Gravity via Noether Symmetry
• LRS Bianchi type I universes exhibiting Noether symmetry in the scalar-tensor Brans-Dicke theory
• New Exact Spherically Symmetric Solutions in $f(R,\varphi ,X)$ gravity by Noether's symmetry approach
• Re-Scaling of Energy in the Stringy Charged Black Hole Solutions using Approximate Symmetries
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• F(R) cosmology via Noether symmetry and lambda-Chaplygin Gas like model

Cited by in corpus (3)

• Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries
• Exploring the Cosmological Model in $f(R,T^{\varphi })$ Gravity with Observational Constraints
• Unified dynamical system formulations for $f(R,\varphi ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation