Abstract

Over the past few decades, general relativity and the concordance ΛCDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets (precision cosmology). Despite their successes, some shortcomings emerge due to the fact that general relativity should be revised at infrared and ultraviolet limits and to the fact that the fundamental nature of dark matter and dark energy is still a puzzle to be solved. In this perspective, ƒ(R) gravity has been extensively investigated, being the most straightforward way to modify general relativity and to overcame some of the above shortcomings. In this paper, we review various aspects of ƒ(R) gravity at extragalactic and cosmological levels. In particular, we consider a cluster of galaxies, cosmological perturbations and N-body simulations, focusing on those models that satisfy both cosmological and local gravity constraints. The perspective is that some classes of ƒ(R) models can be consistently constrained by the large-scale structure.

Highlights

  • The concordance ΛCDM cosmological model is based on Einstein’s general relativity (GR), the standard model of particles with the inclusion of two new ingredients, which are the cosmological constant Λ and dark matter

  • It represents the distance from the DM halo center where the screening mechanism acts and it is not possible to distinguish between chameleon gravity and GR [51]

  • It is mandatory to search for the answer to one of the fundamental questions in modern cosmology: is GR the effective theory of gravitation? This question comes from the evidence that GR is not enough to fully explain the cosmological evolution of the Universe and the emergence of the clustered structures, and it needs the addition of two unknown components

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Summary

Introduction

The concordance ΛCDM cosmological model is based on Einstein’s general relativity (GR), the standard model of particles with the inclusion of two new ingredients, which are the cosmological constant Λ and dark matter. The particularity of these f (T ) models is that they include torsion as the source of DE without considering a cosmological constant, and they give rise to second order field equations that are easier to solve than the fourth order ones from f (R) gravity [66,67,68,69,70,71,72,73,74,75,76,77] These models have been widely investigated from fundamental to cosmological scales [76,78,79,80,81,82,83,84]. Models, which are designed to satisfy cosmological and Solar System constraints

Chameleon Models
Pressure Profile from Yukawa-Like Gravitational Potential
Data and Results
Chameleon Gravity
G MPl dr
Testing Gravity Using the Cosmic Microwave Background Data
Discussion and Future

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