Revisiting Cosmologies in Teleparallelism

Abstract

We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(\mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(\mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(\mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.

17 pages, no figures

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Cited by in corpus (50)

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• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• Forecasting constraints on deviations from general relativity in $f(Q)$ gravity with standard sirens
• On the viability of $f(Q)$ gravity models
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Data reconstruction of the dynamical connection function in $f(Q)$ cosmology
• Homogeneous and isotropic cosmology in general teleparallel gravity
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• Possible consistent model of parity violations in the symmetric teleparallel gravity
• Anisotropic LRS-BI Universe with $f(Q)$ gravity theory
• Anisotropic Universe in $f(Q,T)$ gravity, a novel study
• Symmetric Teleparallel Geometries
• Torsion in string-inspired cosmologies and the universe dark sector
• Constraints on $f(Q)$ logarithmic model using gravitational wave standard sirens
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• How different connections in flat FLRW geometry impact energy conditions in $f(Q)$ theory?
• Dark Energy within the Generalized Uncertainty Principle in Light of DESI DR2
• Dynamical system analysis of scalar field cosmology in coincident $f(Q)$ gravity
• Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
• Teleparallel gravity
• Spatial curvature in coincident gauge $f(Q)$ cosmology
• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Dynamical system analysis of Dirac-Born-Infeld scalar field cosmology in coincident $f(Q)$ gravity
• Observational Constraints and Cosmographic Analysis of $f(T,T_G)$ Gravity and Cosmology
• $f(Q,T)$ gravity, its covariant formulation, energy conservation and phase-space analysis
• Teleparallel Robertson-Walker geometries and applications
• Dynamical system analysis of LRS-BI Universe with f(Q) gravity theory
• Viscous fluid cosmology in symmetric teleparallel gravity
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity
• Effects of the matter Lagrangian degeneracy in $f(Q,T)$ gravity
• Observational constraints on the growth index parameters in $f(Q)$ gravity
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Extended Bose-Einstein condensate dark matter in $f(Q)$ gravity
• Comparing measures of the Hubble and BAO tensions in $\Lambda$CDM and possible solutions in $f(Q)$ gravity
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• Reconstructing modified and alternative theories of gravity
• Conventionalism, cosmology and teleparallel gravity
• Cosmological dynamics of interacting dark energy and dark matter in $f(Q)$ gravity
• Probing symmetric teleparallel gravity in the early universe
• Cosmological constraints in symmetric teleparallel gravity with bulk viscosity
• Neutron stars in $f(\mathbb{Q})$ gravity
• Lost in translation: the Abelian affine connection (in the coincident gauge)
• Insights in $f(Q)$ cosmology: the relevance of the connection