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A model for cosmological perturbations in affine gravity

Oscar Castillo-Felisola, Radouane Gannouji, Manuel Morocho-López, Marcelo Rozas-Rojas

Abstract

In this paper, we present the cosmological perturbation formalism for theories within the framework of affine gravity. These theories are distinguished by their connection, devoid of any metric. Our approach involves segregating perturbations into symmetric and antisymmetric components (related to torsion), each further decomposed into irreducible elements, namely scalars, pseudoscalars, vectors, pseudovectors, 2-tensors, and 3-tensors. Finally, we have fully addressed the gauge freedom in this context.

A model for cosmological perturbations in affine gravity

Abstract

In this paper, we present the cosmological perturbation formalism for theories within the framework of affine gravity. These theories are distinguished by their connection, devoid of any metric. Our approach involves segregating perturbations into symmetric and antisymmetric components (related to torsion), each further decomposed into irreducible elements, namely scalars, pseudoscalars, vectors, pseudovectors, 2-tensors, and 3-tensors. Finally, we have fully addressed the gauge freedom in this context.
Paper Structure (13 sections, 61 equations, 3 tables)

This paper contains 13 sections, 61 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Brief review of differential geometry
  3. Cosmological principle and geometrical objects
  4. Analysis of perturbations
  5. $SO(3,\mathbb{R})$ decomposition of the perturbation
  6. $SO(3,\mathbb{R})$ decomposition of $C_{ijk}$
  7. $SO(3,\mathbb{R})$ decomposition of the other components
  8. Summary: $SO(3,\mathbb{R})$ decomposition
  9. Helmholtz decomposition of the perturbation
  10. Gauge invariance
  11. Discussion and Conclusions
  12. Irreducible representations of $SO(3,\mathbb{R})$ using Young tableaux
  13. From $SO(3,\mathbb{R})$ to $SO(2,\mathbb{R})$