Embedding Non-Linear Structures in f(R) Cosmologies

TL;DR

This paper explores how embedding non-linear structures in cosmological models within f(R) gravity theories affects large-scale universe expansion, revealing constraints and interdependencies between solutions.

Contribution

It analyzes the applicability of Swiss cheese and lattice models in f(R) gravity, highlighting constraints on cosmological solutions not present in standard General Relativity.

Findings

Embedding methods impose constraints on universe expansion in f(R) theories

Friedmann and weak-field solutions may not be independent in f(R) gravity

Standard embedding techniques require modifications for f(R) models

Abstract

When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann solutions, and lattice models, in which weak-field regions are joined together directly. In this talk we will consider how these methods work in f(R) theories of gravity. We will show that their existence places constraints on the large-scale expansion of the universe, and that it may not always be possible to consider the Friedmann solutions and weak-field solutions of a theory independently from each other.