Focusing conditions for extended teleparallel gravity theories
arXiv:2009.04353 · doi:10.1088/1475-7516/2020/12/020
Abstract
In the context of extended theories of teleparallel gravity we derive the focusing conditions for a one-parameter dependent congruence of timelike auto-parallels of the Levi-Civita connection. We also consider the field equations for a general metric tensor before moving on to consider a spatially flat Robertson-Walker space-time. Following this, we study the expansion rate for a one-parameter dependent congruence of timelike auto-parallel curves of the Levi-Civita connection. Given the fact that test particles follow auto-parallels of the Levi-Civita connection, the torsion-free Raychaudhuri equation is used in order to determine the desired focusing conditions. Finally we study the obtained focusing conditions for three paradigmatic cosmological models and discuss the satisfaction or violation of these conditions. Through this, we find models that allow for the weak and strong focusing conditions to be satisfied or violated. It is mentioned that this behaviour can also be found in the so-called and theories.
arXiv comment31 pages, 9 figures, JCAP format, minor changes, matches published version in JCAP
References in corpus (49)
- f(R) Theories Of Gravity
- f(T) teleparallel gravity and cosmology
- Dark torsion as the cosmic speed-up
- Einstein's Other Gravity and the Acceleration of the Universe
- Dark Energy after GW170817: dead ends and the road ahead
- Can modified gravity explain accelerated cosmic expansion?
- Physical Aspects of the Space-Time Torsion
- Modified teleparallel theories of gravity
- Extended Gravity Cosmography
- Reconstruction of gravity: Rip cosmology, finite-time future singularities and thermodynamics
- Energy conditions in f(R)-gravity
- Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
- Gravitational Lorentz Force and the Description of the Gravitational Interaction
- Good and bad tetrads in f(T) gravity
- Torsion Gravity: a Reappraisal
- models with phantom divide line crossing
- Energy Conditions in gravity
- Spherically symmetric static spacetimes in vacuum f(T) gravity
- Generalized energy conditions in Extended Theories of Gravity
- The role of energy conditions in cosmology
- The Raychaudhuri equations: a brief review
- Energy conditions in modified gravity
- Noether Symmetry Approach in teleparallel cosmology
- New types of gravity
- Cosmological applications of gravity
- Energy conditions bounds on f(T) gravity
- gravity after GW170817 and GRB170817A
- New observational constraints on f(T) gravity from cosmic chronometers
- Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
- Weak Field Limit and Gravitational Waves in Teleparallel Gravity
- Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions
- Birkhoff's theorem in the f(T) gravity
- Gauge Structure of Teleparallel Gravity
- Cosmological bouncing solutions in extended teleparallel gravity theories
- On the non-attractive character of gravity in f(R) theories
- Junction conditions in extended Teleparallel gravities
- Effective gravitational coupling in modified teleparallel theories
- The Raychaudhuri equation in spacetimes with torsion and non-metricity
- Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
- Spacetime thermodynamics in the presence of torsion
- Focusing of geodesic congruences in an accelerated expanding Universe
- Raychaudhuri equation in spacetimes with torsion
- Modified teleparallel gravity with higher-derivative torsion terms
- Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
- Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
- Teleparallel theory as a gauge theory of translations: comments and issues
- Constraining teleparallel gravity from energy conditions
- Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories
- Singularity theorems and the inclusion of torsion in affine theories of gravity