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Effective field theory analysis of the self-interacting chameleon

Hillary Sanctuary, Riccardo Sturani

TL;DR

The paper addresses whether self-interactions of a chameleon scalar can spoil its ability to mediate long-range forces while evading equivalence principle tests. It adopts an effective field theory approach, adapting Goldberger-Rothstein methods to a scalar-tensor context, to compute corrections from non-derivative self-interactions, focusing on a cubic $\phi^3$ term. The main result is that cubic self-interactions introduce a logarithmic correction to the chameleon potential that grows with distance but remains subdominant for realistic parameters; higher-order interactions are progressively suppressed, and the backreaction on gravity is negligible. Consequently, the chameleon mechanism remains compatible with solar-system constraints, while the EFT framework provides a systematic way to assess nonlinearities in scalar-tensor theories.

Abstract

We analyse the phenomenology of a self-interacting scalar field in the context of the chameleon scenario originally proposed by Khoury and Weltman. In the absence of self-interactions, this type of scalar field can mediate long range interactions and simultaneously evade constraints from violation of the weak equivalence principle. By applying to such a scalar field the effective field theory method proposed for Einstein gravity by Goldberger and Rothstein, we give a thorough perturbative evaluation of the importance of non-derivative self-interactions in determining the strength of the chameleon mediated force in the case of orbital motion. The self-interactions are potentially dangerous as they can change the long range behaviour of the field. Nevertheless, we show that they do not lead to any dramatic phenomenological consequence with respect to the linear case and solar system constraints are fulfilled.

Effective field theory analysis of the self-interacting chameleon

TL;DR

The paper addresses whether self-interactions of a chameleon scalar can spoil its ability to mediate long-range forces while evading equivalence principle tests. It adopts an effective field theory approach, adapting Goldberger-Rothstein methods to a scalar-tensor context, to compute corrections from non-derivative self-interactions, focusing on a cubic term. The main result is that cubic self-interactions introduce a logarithmic correction to the chameleon potential that grows with distance but remains subdominant for realistic parameters; higher-order interactions are progressively suppressed, and the backreaction on gravity is negligible. Consequently, the chameleon mechanism remains compatible with solar-system constraints, while the EFT framework provides a systematic way to assess nonlinearities in scalar-tensor theories.

Abstract

We analyse the phenomenology of a self-interacting scalar field in the context of the chameleon scenario originally proposed by Khoury and Weltman. In the absence of self-interactions, this type of scalar field can mediate long range interactions and simultaneously evade constraints from violation of the weak equivalence principle. By applying to such a scalar field the effective field theory method proposed for Einstein gravity by Goldberger and Rothstein, we give a thorough perturbative evaluation of the importance of non-derivative self-interactions in determining the strength of the chameleon mediated force in the case of orbital motion. The self-interactions are potentially dangerous as they can change the long range behaviour of the field. Nevertheless, we show that they do not lead to any dramatic phenomenological consequence with respect to the linear case and solar system constraints are fulfilled.

Paper Structure

This paper contains 4 sections, 34 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Chameleon in brief
  3. Corrections to the potential from chameleon self-interactions
  4. Conclusions

Figures (2)

  • Figure 1: Feynman diagram displaying the contribution to the effective potential proportional to the tri-linear interaction $g_3M\phi^3$.
  • Figure 2: Feynman diagram displaying the generic contribution to the effective potential proportional to the n-point interaction $g_nM^{4-n}\phi^n$.