Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Emergent Cosmological Expansion in Scalar-Tensor Theories of Gravity

Chad Briddon, Timothy Clifton, Pierre Fleury

Abstract

We consider the emergence of large-scale cosmological expansion in scalar-tensor theories of gravity. This is achieved by modelling sub-horizon regions of space-time as weak-field expansions around Minkowski space, and then subsequently joining many such regions together to create a statistically homogeneous and isotropic cosmology. We find that when the scalar field can be treated perturbatively, the cosmological behaviour that emerges is well modelled by the Friedmann solutions of the theory. When non-perturbative screening mechanisms occur this result no longer holds, and in the case of scalar fields subject to the chameleon mechanism we find significant deviations from the expected Friedmann behaviour. In particular, the screened mass no longer contributes to the Klein-Gordon equation, suppressing deviations from general relativistic behaviour.

Emergent Cosmological Expansion in Scalar-Tensor Theories of Gravity

Abstract

We consider the emergence of large-scale cosmological expansion in scalar-tensor theories of gravity. This is achieved by modelling sub-horizon regions of space-time as weak-field expansions around Minkowski space, and then subsequently joining many such regions together to create a statistically homogeneous and isotropic cosmology. We find that when the scalar field can be treated perturbatively, the cosmological behaviour that emerges is well modelled by the Friedmann solutions of the theory. When non-perturbative screening mechanisms occur this result no longer holds, and in the case of scalar fields subject to the chameleon mechanism we find significant deviations from the expected Friedmann behaviour. In particular, the screened mass no longer contributes to the Klein-Gordon equation, suppressing deviations from general relativistic behaviour.
Paper Structure (7 sections, 49 equations, 4 figures)

This paper contains 7 sections, 49 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Scalar-tensor theories of gravity
  3. Post-Newtonian cosmology
  4. General behaviour
  5. Perturbed scalar fields
  6. Non-perturbative screening mechanisms
  7. Discussion

Figures (4)

  • Figure 1: Two cubic cells of side length $L$ being joined together at a common boundary $\mathcal{B}$, whose union constitutes a solution to the field equations of the theory (\ref{['action']}), with no boundary layer, if Eq. (\ref{['eq:junction']}) is satisfied.
  • Figure 2: The spatial sections of constant $t$ from two neighbouring cells, $\mathcal{C}_1$ and $\mathcal{C}_2$, meeting at their common boundary $\mathcal{B}$. The surfaces do not overlap, and are not orthogonal to the boundary.
  • Figure 3: Scalar field profiles along a line connecting the centre of a cell and the centre of a cell face. Curves correspond to spheres of radius $0.04$ (red), $0.03$ (green), $0.02$ (purple) and $0.01$ (blue), and range from completely unscreened (red) to strongly screened (blue), with the screened value shown in Eq. (\ref{['phiint']}) indicated by dashed horizontal lines. Distances are given in units of the cell length, $L$, and the scalar field is in units of $\phi_{\rm ext}$ (from Eq. (\ref{['phiex']}), and as indicated by the horizontal dashed black line).
  • Figure 4: The magnitude of the gradient of the scalar field, outside of the spherical body at the centre of the cell. Colours correspond to the configurations from Fig. \ref{['spheres']}, with distances in units of the cell length $L$, and $\phi_{\rm ext}$ as defined in Eq. (\ref{['phiex']}). Dashed lines correspond to raw values, and solid lines (stacked very closely together) to values rescaled by the ratio $m/m_{\rm shell}$.