Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology

Abstract

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or $\Lambda$CDM as separate scenarios. We reconstruct the $f(T)$ gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and standard model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular $f(T)$ gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

arXiv commentMinor modifications, some references added to match the published version

References in corpus (45)

• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• f(T) Gravity and local Lorentz invariance
• Matter Bounce Cosmology with the f(T) Gravity
• Towards a Nonsingular Bouncing Cosmology
• The covariant formulation of f(T) gravity
• Gravitational Waves From a Dark (Twin) Phase Transition
• A Critical Review of Classical Bouncing Cosmologies
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Exploring Bouncing Cosmologies with Cosmological Surveys
• Two Field Matter Bounce Cosmology
• New observational constraints on f(T) gravity from cosmic chronometers
• Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field
• Regular black holes in $f(T)$ Gravity through a nonlinear electrodynamics source
• Accelerating f(T) gravity models constrained by recent cosmological data
• Bouncing cosmologies with dark matter and dark energy
• A spherically-symmetric charged-dS solution in f(T) gravity theories
• $f(T)$ gravitational baryogenesis
• A Built-in Inflation in the $f(T)$-Cosmology
• Inflationary cosmology in unimodular $F(T)$ gravity
• Evolution of curvature and anisotropy near a nonsingular bounce
• Exact Teleparallel Gravity of Binary Black Holes
• Constraining $f(T)$ Theories with the Varying Gravitational Constant
• Generalized teleparallel cosmology and initial singularity crossing
• Generalized Noether symmetry in f(T) gravity
• The Hidden Flat Like Universe: Starobinsky-like inflation induced by f(T) gravity
• Stationary Axisymmetric Solutions and their Energy Contents in Teleparallel Equivalent of Einstein Theory
• Equivalence principle in the new general relativity
• Spherically Symmetric Solutions on a Non-Trivial Frame in f(T) Theories of Gravity
• Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation
• Analytic rotating black hole solutions in $N$-dimensional $f(T)$ gravity
• Detectability of Torsion Gravity via Galaxy Clustering and Cosmic Shear Measurements
• Power-law and intermediate inflationary models in f(T)-gravity
• Anisotropic 'hairs' in string cosmology
• Quantum Features of Non-Symmetric Geometries
• Light bending in $f(T)$ gravity
• Teleparallel gauge theory of gravity
• Analyzing modified unimodular gravity via Lagrange multipliers
• Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry
• $f(T)$ non-linear massive gravity and the cosmic acceleration
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Effects of Finite-time Singularities on Gravitational Waves
• Pure Geometric Field Theory: Description of Gravity and Material Distribution

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• Teleparallel Gravity: From Theory to Cosmology
• Cosmological bouncing solutions in f(T,B) gravity
• Constant-roll Inflation in $f(T)$ Teleparallel Gravity
• Non-trivial class of anisotropic compact stellar model in Rastall gravity
• Phase Portraits of general f(T) Cosmology
• Accelerating Universe in Hybrid and Logarithmic Teleparallel Gravity
• Higgs inflation and teleparallel gravity
• $H_0$ Tension and the Phantom Regime: A Case Study In Terms of an Infrared $f(T)$ Gravity
• Phenomenological Reconstruction of $f(T)$ Teleparallel Gravity
• Transit cosmological models in Myrzakulov F(R,T) gravity theory
• A Complete Cosmological Scenario in Teleparallel Gravity
• New anisotropic star solutions in mimetic gravity
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• Effect of nonlocal transformations on the linearizability and exact solvability of the nonlinear generalized modified Emden type equations