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Homogeneous and isotropic cosmology in general teleparallel gravity.

Lavinia Heisenberg1,2,3, Manuel Hohmann4, Simon Kuhn2,3

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We explored homogeneous and isotropic teleparallel geometries, finding five connection solution branches. These solutions simplify in certain cases, impacting cosmological dynamics in teleparallel gravity theories.

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Area of Science:

  • Cosmology
  • Theoretical Physics
  • General Relativity

Background:

  • Teleparallel gravity theories offer alternative frameworks to General Relativity.
  • Understanding the geometry of these theories is crucial for cosmological applications.
  • Previous studies have explored specific subclasses of teleparallel geometries.

Purpose of the Study:

  • To derive the most general homogeneous and isotropic teleparallel geometries.
  • To classify the possible connection solutions within these geometries.
  • To investigate the cosmological dynamics of various teleparallel gravity theories based on these geometries.

Main Methods:

  • Derivation of general homogeneous and isotropic teleparallel geometries using a metric and a flat, affine connection.
  • Classification of five distinct branches of connection solutions.
  • Analysis of torsion-free and metric-compatible restrictions.
  • Application to cosmological dynamics of general teleparallel gravity theories.

Main Results:

  • Identified five branches of homogeneous and isotropic teleparallel connection solutions.
  • Demonstrated that many subclasses reduce to known metric or symmetric teleparallel gravity dynamics.
  • Discovered that some subclasses involve up to two new scalar degrees of freedom in cosmological dynamics.

Conclusions:

  • The derived general teleparallel geometries provide a comprehensive framework for studying cosmological dynamics.
  • The classification of connection solutions reveals connections to simpler, established theories.
  • The emergence of new scalar degrees of freedom in certain teleparallel gravity subclasses opens avenues for new cosmological models.