Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

Abstract

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

Minor changes; accepted for publication by General Relativity and Gravitation

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Cited by in corpus (30)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Teleparallel Gravity: From Theory to Cosmology
• Model-independent reconstruction of $f(T)$ gravity from Gaussian Processes
• Bayesian analysis of $f(T)$ gravity using $f{\sigma }_8$ data
• The past and future dynamics of quintom dark energy models
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• Noether Symmetries as a geometric criterion to select theories of gravity
• Stability of motion and thermodynamics in charged black holes in $f(T)$ gravity
• No constraints for $f(T)$ gravity from gravitational waves induced from primordial black hole fluctuations
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• Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
• Deflection angle and lensing signature of covariant f(T) gravity
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• Dynamical complexity of the Teleparallel gravity cosmology
• Extended phase-space analysis of the Horava-Lifshitz cosmology
• Unified dark sectors in scalar-torsion theories of gravity
• Exact spherically symmetric solutions in modified Gauss-Bonnet gravity from Noether symmetry approach
• Scalar induced gravitational waves in modified teleparallel gravity theories
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• Addressing the Hubble tension in Yukawa cosmology?
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions