Noether Symmetries in $f(T,T_G)$ Cosmology

Abstract

All degrees of freedom related to the torsion scalar can be explored by analysing, the $f(T,T_G)$ gravity formalism where, $T$ is a torsion scalar and $T_G$ is the teleparallel counterpart of the Gauss-Bonnet topological invariant term. The well-known Noether symmetry approach is a useful tool for selecting models that are motivated at a fundamental level and determining the exact solution to a given Lagrangian, hence we explore Noether symmetry approach in $f(T,T_G)$ gravity formalism with three different forms of $f(T,T_G)$ and study how to establish nontrivial Noether vector form for each one of them. We extend the analysis made in \cite{capozziello2016noether} for the form $f(T,T_G)=b_0{T}_G^k+t_0{T}^m$ and discussed the symmetry for this model with linear teleparallel equivalent of the Gauss-Bonnet term, followed by the study of two models containing exponential form of the teleparallel equivalent of the Gauss-Bonnet term. We have shown that all three cases will allow us to obtain non-trivial Noether vector which will play an important role to obtain the exact solutions for the cosmological equations.

12 pages

References in corpus (32)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• The trouble with $H_0$
• Cosmology Intertwined II: The Hubble Constant Tension
• Teleparallel Gravity: From Theory to Cosmology
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Good and bad tetrads in f(T) gravity
• Solar system constraints on f(T) gravity
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Dynamical behavior in $f(T,T_G)$ cosmology
• The Pantheon+ Analysis: SuperCal-Fragilistic Cross Calibration, Retrained SALT2 Light Curve Model, and Calibration Systematic Uncertainty
• Cosmological applications of $F(T,T_G)$ gravity
• Using the Noether symmetry approach to probe the nature of dark energy
• Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
• Dynamical Stability Analysis of Accelerating f(T) Gravity Models
• Stability of the flat FLRW metric in $f(T)$ gravity
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• f(R) gravity: successes and challenges
• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Dynamical systems analysis in $f(T,\varphi )$ gravity
• Noether symmetries and stability of ideal gas solution in Galileon Cosmology
• Analyzing the geometrical and dynamical parameters of modified Teleparallel-Gauss-Bonnet model
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity

Cited by in corpus (6)

• Dynamical system analysis in teleparallel gravity with boundary term
• Noether Symmetry Approach in Scalar-Torsion $f(T,\varphi )$ Gravity
• Observational Constraints and Cosmographic Analysis of $f(T,T_G)$ Gravity and Cosmology
• Dynamical Complexity in Teleparallel Gauss-Bonnet Gravity
• Constraining $f(T,B,T_G,B_G)$ gravity by dynamical system analysis
• Propagating Gravitational Waves in Teleparallel Gauss-Bonnet Gravity