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Teleparallel gravity: from theory to cosmology.

Sebastian Bahamonde1,2, Konstantinos F Dialektopoulos3,4,5, Celia Escamilla-Rivera6

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Teleparallel gravity (TG), an alternative to general relativity, is explored as a gauge theory. This review details modified TG theories, their astrophysical and cosmological implications, and machine learning applications in gravity research.

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Area of Science:

  • Theoretical Physics
  • Cosmology
  • Gravitational Theory

Background:

  • Teleparallel gravity (TG) is gaining prominence as an alternative to Einstein's general relativity (GR).
  • TG can be developed as a gauge theory of translations, linking it to metric-affine gravity frameworks.
  • Understanding TG is crucial for exploring gravitational theories beyond GR, including quantum gravity.

Purpose of the Study:

  • To provide a comprehensive introduction to teleparallel geometry and its development as a gauge theory.
  • To systematically construct consistent teleparallel theories respecting physical conditions like local Lorentz invariance.
  • To review modified teleparallel gravity theories, their astrophysical and cosmological consequences, and applications of machine learning.

Main Methods:

  • Formulating a teleparallel equivalent of GR dynamically equivalent to GR.
  • Classifying modified teleparallel gravity theories and highlighting specific models like the teleparallel analogue of Horndeski gravity.
  • Analyzing cosmological implications using dynamical systems, Noether symmetries, perturbation theory, and observational cosmology data.
  • Exploring machine learning applications, including deep learning and Gaussian processes.

Main Results:

  • A teleparallel equivalent of GR is presented, offering potential differences in scenarios like quantum gravity.
  • Various modified teleparallel gravity theories are categorized, with a focus on a teleparallel analogue of Horndeski gravity.
  • Cosmological consequences are explored through background and perturbation theory, with potential to address cosmological tensions.
  • Recent advances in applying machine learning to gravity are surveyed.

Conclusions:

  • Teleparallel gravity offers a rich framework for developing alternative gravitational theories with diverse applications.
  • Modified TG theories show promise in addressing astrophysical phenomena and cosmological puzzles.
  • The integration of machine learning presents new avenues for gravitational research.