A flavour on f(R) theories: theory and observations

  1. de la Cruz-Dombriz, Álvaro 12
  1. 1 Cosmology and Gravity Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town, 7701, South Africa
  2. 2 Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, Salamanca, Spain
Libro:
Modified gravity and cosmology
  1. Emmanuel N. Saridakis (ed. lit.)
  2. Ruth Lazkoz (ed. lit.)
  3. Vincenzo Salzano (ed. lit.)
  4. Paulo Vargas Moniz (ed. lit.)
  5. Salvatore Capozziello (ed. lit.)
  6. Jose Beltrán Jiménez (ed. lit.)
  7. Mariafelicia De Laurentis (ed. lit.)
  8. Gonzalo J. Olmo (ed. lit.)

Editorial: Springer

ISBN: 9783030837143,  9783030837150

Año de publicación: 2021

Páginas: 43-78

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-030-83715-0_5 GOOGLE SCHOLAR lock_openAcceso abierto editor

Objetivos de desarrollo sostenible

Resumen

Modifications to the General Theory of Relativity emerged almost immediately upon its acceptance by the scientific community. This chapter aims at providing a detailed review on the foundations on f(R) theories, one of the simplest modifications to Einsteinian gravity in the context of addressing the underlying nature of dark energy in the Cosmological Concordance Model. Therein, we shall first revise the equivalence between f(R) theories and a subclass of scalar-tensor theories; namely, Brans–Dicke gravity. We shall also summarise the most relevant formalisms to study such theories and the viability requirements that f(R) theories need to obey to be considered as a viable alternative to Einsteinian gravity. Then, we shall present the expected cosmological expansion history evolution of these theories within the usual metric formalism and revise on how the use of the so-called 1+3 covariant gauge-invariant variables can be naturally applied to f(R) theories and consequently, how the analysis of cosmological scalar perturbations becomes highly transparent in this context. The use of both cosmological distance data as well as large-scale structure data can be used to place constraints on the values of the parameters of specific f(R) models claimed as viable. To conclude we shall illustrate two paradigmatic gravitational features of f(R) theories. First, the equivalent geodesic deviation equation for these theories and the consequences for the observer area distance extracted, a fact with relevant cosmological implications in the measure of distances and comparison with eventual data. Second, the attractive or repulsive character that these theories exhibit in a cosmological context and its relation to the so-called energy conditions in the context of extended theories of gravity

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