Teleparallel Robertson-Walker geometries and applications

Abstract

In teleparallel geometries the coframe and corresponding spin-connection are the principal geometric objects and consequently the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson-Walker affine symmetries are displayed and discussed. We will refer to such geometries as teleparallel Robertson-Walker (TRW) geometries, where the corresponding derived metric is of Robertson-Walker form and is characterized by the parameter $k=(-1,0,1)$. The field equations are explicitly presented for the $F(T)$ class of teleparallel TRW spacetimes. We are primarily interested in investigating the $k\ne 0$ TRW models. After first studying the $k=0$ models and, in particular, writing their governing field equations in an appropriate form, we then study their late time stability with respect to perturbations in $k$ in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration we consider both quadratic $F(T)$ theories and power-law solutions.

18 pages, no figure, Published in Universe MDPI

References in corpus (8)

• Teleparallel Gravity: From Theory to Cosmology
• Black holes in $f(\mathbb{Q})$ Gravity
• Dynamical behavior in $f(T,T_G)$ cosmology
• Revisiting Cosmologies in Teleparallelism
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Modified gravity: a unified approach to metric-affine models
• Symmetric Teleparallel Geometries
• Scalar induced gravitational waves in modified teleparallel gravity theories

Cited by in corpus (10)

• Attractor behaviour of $f(T)$ modified gravity and the cosmic acceleration
• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• Cosmological solutions in teleparallel $F(T,B)$ gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Scalar field source Teleparallel Robertson-Walker F(T)-gravity solutions
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Scalar Field Static Spherically Symmetric Solutions in Teleparallel $F(T)$ Gravity
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions