Noether Symmetry Approach in Scalar-Torsion $f(T,\varphi )$ Gravity

Abstract

The Noether Symmetry approach is applied to study an extended teleparallel $f(T,\varphi )$ gravity that contains the torsion scalar $T$ and the scalar field $\varphi$ in the context of an Friedmann-Lemaître-Robertson-Walker space-time. We investigate the Noether symmetry approach in $f(T,\varphi )$ gravity formalism with the specific form of $f(T,\varphi )$ and analyze how to demonstrate a nontrivial Noether vector. The Noether symmetry method is a helpful resource for generating models and finding out the exact solution of the Lagrangian. In this article, we go through how the Noether symmetry approach enables us to define the form of the function $f(T,\varphi )$ and obtain exact cosmological solutions. We also find the analytical cosmological solutions to the field equations, that is consistent with the Noether symmetry. Our results demonstrate that the obtained solutions enable an accelerated expansion of the Universe. We have also obtained the present value of the Hubble parameter, deceleration parameter, and effective equation of state parameter, which is fit in the range of current cosmological observations.

12 pages, Accepted version European Physical Journal C

References in corpus (15)

• 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
• 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 trouble with $H_0$
• Teleparallel Gravity: From Theory to Cosmology
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Dynamical Stability Analysis of Accelerating f(T) Gravity Models
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Noether Symmetries in $f(T,T_G)$ Cosmology

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• Teleparallel Gravity and Quintessence: The Role of Nonminimal Boundary Couplings
• Dynamical System Analysis for Scalar Field Potential in Teleparallel Gravity
• Late Time Phenomena in $f(T,\mathcal{T})$ Gravity Framework: Role of $H_0$ Priors
• Quantum cosmology in teleparallel gravity with a boundary term