[Paper Review] Lectures on Screened Modified Gravity

Philippe Brax|arXiv (Cornell University)|Nov 22, 2012

Cosmology and Gravitation Theories26 references8 citations

TL;DR

This paper presents a unified framework for screened modified gravity models—chameleon, dilaton, and symmetron—using f(R) gravity as a template. It explains how scalar fields with environment-dependent masses evade solar system tests via screening mechanisms, while predicting observable deviations in astrophysical structures, neutron interactions, and Casimir experiments due to unscreened forces.

ABSTRACT

The acceleration of the expansion of the Universe has led to the construction of Dark Energy models where a light scalar field may have a range reaching up to cosmological scales. Screening mechanisms allow these models to evade the tight gravitational tests in the solar system and the laboratory. I will briefly review some of the salient features of screened modified gravity models of the chameleon, dilaton or symmetron types using $f(R)$ gravity as a template.

Motivation & Objective

• To unify the description of chameleon, dilaton, and symmetron models under a common theoretical framework using f(R) gravity as a prototype.
• To explain how screening mechanisms allow scalar-tensor theories to evade constraints from solar system and laboratory tests despite long-range scalar interactions.
• To identify observational windows—such as astrophysical structures, neutron interactions, and Casimir experiments—where screening may break down and deviations from ΛCDM emerge.
• To analyze the implications of Lorentz-violating disformal couplings in scalar-tensor theories, particularly the potential for superluminal fermion propagation in dense environments.
• To assess the viability of modified gravity models in light of low-energy effective field theory constraints and cosmological observations.

Proposed method

• Use f(R) gravity as a template to derive the Einstein frame action with a scalar field φ, showing the emergence of a potential V(φ) and kinetic term.
• Derive the mapping between the Ricci scalar R and the scalar field φ via f_R = df/dR = exp(-2βφ/m_Pl), with β = 1/√6.
• Analyze the chameleon mechanism by showing that the effective mass of φ depends on the local energy density, leading to screening in high-density regions.
• Introduce the disformal coupling term ∂_μφ∂_νφ / M^4 T^{μν} in the matter action, which breaks Lorentz invariance and modifies fermion propagation.
• Compute the modified Dirac equation and dispersion relation in the presence of a static scalar field gradient, revealing anisotropic fermion speeds with c_d = 1 + |d|^2.
• Assess constraints from the absence of superluminal fermions, implying M must be large enough to prevent observable tachyonic effects.

Experimental results

Research questions

• RQ1 How do screening mechanisms in scalar-tensor theories like chameleon, dilaton, and symmetron models allow long-range scalar interactions to evade solar system constraints?
• RQ2 What are the key differences and unifying features between f(R) gravity and other screened modified gravity models in the Einstein frame?
• RQ3 In what astrophysical or laboratory environments might screening fail, leading to observable deviations from general relativity?
• RQ4 How do disformal couplings between the scalar field and matter lead to Lorentz violation, and what are the implications for fermion propagation?
• RQ5 What experimental bounds can be derived from the absence of superluminal fermion speeds in dense matter environments?

Key findings

• The scalar field in f(R) gravity acquires a potential V(φ) that depends on the Ricci scalar, with V(φ) ≈ ρ_Λ(1 + 4βφ/m_Pl) − (n+1)/(2n) f_R0 m_Pl^2 R_0 (2βφ/(m_Pl f_R0))^{n/(n+1)} in the large-curvature limit.
• Screening occurs via the chameleon mechanism: the scalar field’s effective mass increases in high-density regions, suppressing its coupling to matter.
• In static, non-relativistic environments, the disformal coupling ∂_μφ∂_νφ / M^4 T^{μν} does not affect the static potential but modifies fermion propagation.
• The modified Dirac equation leads to a dispersion relation with anisotropic group velocities, where fermions can travel faster than light along the gradient of φ with Δc = |d|^2.
• The absence of observed superluminal fermions implies the suppression scale M must be large enough to prevent observable deviations, constraining the disformal coupling.
• Potential probes of unscreened forces include bumps in the matter power spectrum at Mpc scales, stellar structure deviations, satellite tests of the equivalence principle, and neutron interactions in low-energy experiments.