Energy bounds in f(R,G) gravity with anisotropic background

Abstract

This paper investigates the energy bounds in modified GaussBonnet gravity with anisotropic background. Locally rotationally symmetric Bianchi type I cosmological model in f (R, G) gravity is considered to meet this aim. Primarily, a general f (R, G) model is used to develop the field equations. In this aspect, we investigate the viability of modified gravitational theory by studying the energy conditions. We take in account four f (R, G) gravity models commonly discussed in the literature. We formulate the inequalities obtained by energy conditions and investigate the viability of the above mentioned models using the Hubble, deceleration, jerk and snap parameters. Graphical analysis shows that for first two f (R, G) gravity models, NEC, WEC and SEC are satisfied under suitable values of anisotropy and model parameters involved. Moreover, SEC is violated for the third and fourth models which predicts the cosmic expansion.

A signature invariant geometric algebra framework for spacetime physics and its applications in relativistic dynamics of a massive particle and gyroscopic precession

“…As two successful paradigms, the treatment of relativistic dynamics of a massive particle and gyroscopic precession clearly shows that the GA techniques constructed in this paper are efficient and reliable. Being straightforward generalizations, these techniques could also be applied to gyroscopic precession in alternative theories of gravity, such as f ( R ) gravity 30 , 37 – 39 , gravity 40 , 41 , and f ( X , Y , Z ) gravity 42 . However, since these topics are usually explored by making use of some complicated mathematical tools (e.g., the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors 30 ), it is crucial to develop new techniques to apply these tools in STA.…”

“…The treatment of relativistic dynamics of a massive particle and gyroscopic precession intuitively displays the basic method of dealing with specific topics in curved spacetime within the signature invariant GA framework, which suggests that the GA techniques established in this paper are efficient and reliable. No doubt, if these techniques are directly applied to gyroscopic precession in alternate theories of gravity, such as f ( R ) gravity 30 , 37 – 39 , gravity 40 , 41 , and f ( X , Y , Z ) gravity 42 , they will definitely facilitate the relevant studies, where is the Gauss-Bonnet invariant, is the Ricci scalar, is the quadratic contraction of two Ricci tensors, and is the quadratic contraction of two Riemann tensors. Furthermore, by developing other types of techniques, the method in this paper could also be applied to more fields, and in fact, some topics in classical mechanics and electrodynamics have been described in such a manner.…”

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

“…Here is called as Gauss-Bonnet curvature invariant which is defined by a combination formed from the Riemann curvature tensor which are contractions of the = Ricci curvature tensor and the = Ricci curvature scalar as = − 4 + [4,5,6,7,8]. In the literature; in order to simplify the equations of ( , ) , Locally Rotationally Symmetric (LRS) Bianchi-Type models based on the assumption = (or = or = ) are often considered to reduce the number of unknowns [9,10,11]. Apart from this simplification, which is often made in GRT for scale factors, one of the purposeful assumptions to obtain equations reduced to a single unknown is "to take the shear scalar proportional to the expansion scalar" [9,12,11].…”

“…In the literature; in order to simplify the equations of ( , ) , Locally Rotationally Symmetric (LRS) Bianchi-Type models based on the assumption = (or = or = ) are often considered to reduce the number of unknowns [9,10,11]. Apart from this simplification, which is often made in GRT for scale factors, one of the purposeful assumptions to obtain equations reduced to a single unknown is "to take the shear scalar proportional to the expansion scalar" [9,12,11]. Another assumption is to suggest some relations between the function and a scale factor, such as the powerlaw [13,9,14,1,12].…”

Multipole analysis for linearized $$f(R,{\mathcal {G}})$$ gravity with irreducible Cartesian tensors

“…f (R) gravity [14][15][16][17][18][19] is one of the simplest MGTs, and it replaces the Einstein-Hilbert action by the quantity f (R) in the gravitational Lagrangian, where f is a general funca e-mail: bofengw@pku.edu.cn b e-mail: huangcg@ihep.ac.cn tion of the Ricci scalar R. f (R) gravity has many important implications in cosmology [20,21], and the typical one is that some models of f (R) gravity can explain the inflation in early universe successfully [18]. Recently, a generalized modified Gauss-Bonnet (GB) gravity, whose gravitational Lagrangian is a general function of R and G as f (R, G), has attracted considerable attention [22][23][24][25][26][27], where G is another interesting curvature scalar, and such models can give reasonable gravitational alternative for dark energy [28] and avoid ghost contributions [29].…”