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

Abstract

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.

Thermodynamics and Perturbative Analysis of Some Newly Developed F(R,Lm,T)$\mathcal {F}(R,L_m, T)$ Theories Under the Scenario of Conserved Energy‐momentum Tensor

“…In recent past, modified gravity theories approach has been emerged as a powerful tool where the modifications in the gravitational part of Einstein‐Lagrangian are introduced to accommodate dark ingredients. In this respect, some well‐known examples include scalar‐tensor extensions of GR, [ 1,2 ] torsion based formulations [ 3,4 ] and Gauss‐Bonnet theory and its extensions, [ 5,6 ] $$\mathcal {F}(R)$$ gravity and theories involving higher‐order curvature corrections [ 7–9 ] and the gravitational frameworks involving coupling of curvature and matter. [ 10–14 ] It is argued in literature that the modified gravitational frameworks can provide a successful explanation to various cosmic issues.…”

Noether Gauge Symmetry Approach Applying for the Non‐Minimally Coupled Gravity to the Maxwell Field

“…[ 33 ] In this regard, the Noether symmetry approach has been applied to study various cosmological scenarios including scalar‐tensor cosmologies, [ 34‐37 ] $$f(R)$$ theories, [ 38, 39 ] nonlocal $$f(T)$$ gravity, [ 40–42 ] $$f(R,T)$$ theories [ 43 ] the theory of $$f(G)$$, [ 44 ] and in $$f(R,Y,\varphi )$$ gravity. [ 45 ] Moreover, the authors in refs. [46, 47] have studied the exact solutions for potential functions, scalar, and the scale factors in the Bianchi models.…”

Perturbed solutions in matter FLRW model with R μ ν R μ ν and R 4 gravity

“…Typically, the inclusion of R μν R μ ν and R μναβ R μ ν α β in the common EH action produces the field equations, which are fourth order differential equations, and such adding of terms in the EH action is classified as a four order theory of gravity [41,44]. f (R, R μν R μ ν , f) gravity theory is a class of scalar-tensor fourth order gravity theory, where the curvature invariants R, R μν R μ ν and scalar field f are considered in the EH action [45][46][47][48]. In f (R, R μν R μ ν ) gravity theory, the scalar field f is not considered [49,50].…”

“…In f (R, R μν R μ ν ) gravity theory, the scalar field f is not considered [49,50]. In the framework of f (R, R μν R μ ν , f) and f (R, R μν R μ ν ) gravity theories, there are several studies [45][46][47][48][49][50] that can successfully explain the late-time accelerating stage of the Universe.…”