Chameleon Cosmology

TL;DR

Chameleon Cosmology introduces a density-dependent scalar field whose mass increases with local matter density, allowing $\beta_i=\mathcal{O}(1)$ couplings while suppressing Earth-based EP violations via a thin-shell mechanism. The framework yields a heavy, short-ranged field on Earth but a light, long-ranged field in space, predicting strong signals for upcoming satellite experiments such as STEP, GG, MICROSCOPE, and SEE, including possible sizable deviations in Newton's constant. The authors derive exterior $\phi$-profiles for compact objects, constrain model parameters under a power-law potential, and demonstrate compatibility with solar-system tests and strong EP constraints, while providing striking, falsifiable predictions for near-future experiments. Overall, the work offers a concrete mechanism to reconcile cosmological scalar fields with terrestrial gravity tests and motivates dedicated space-based probes of gravity.

Abstract

The evidence for the accelerated expansion of the universe and the time-dependence of the fine-structure constant suggests the existence of at least one scalar field with a mass of order H_0. If such a field exists, then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the Equivalence Principle (EP). In this paper, we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity. In our scenario, the mass of the fields depends on the local matter density: the interaction range is typically of order 1 mm on Earth (where the density is high) and of order 10-10^4 AU in the solar system (where the density is low). All current bounds from tests of General Relativity are satisfied. Nevertheless, we predict that near-future experiments that will test gravity in space will measure an effective Newton's constant different by order unity from that on Earth, as well as EP violations stronger than currently allowed by laboratory experiments. Such outcomes would constitute a smoking gun for our scenario.

Figures (5)

• Figure 1: Example of a runaway potential.
• Figure 2: The chameleon effective potential $V_{eff}$ (solid curve) is the sum of two contributions: one from the actual potential $V(\phi)$ (dashed curve), and the other from its coupling to the matter density $\rho$ (dotted curve).
• Figure 3: Chameleon effective potential for large and small $\rho$, respectively. This illustrates that, as $\rho$ decreases, the minimum shifts to larger values of $\phi$ and the mass of small fluctuations decreases. (Line styles are the same as in Fig. \ref{['poteff']}.)
• Figure 4: For large objects, the $\phi$-field a distance $r>R_c$ from the center is to a good approximation entirely determined by the contribution from infinitesimal volume elements $dV$ (dark rectangle) lying within a thin shell of thickness $\Delta R_c$ (shaded region). This thin-shell effect suppresses the resulting chameleon force.
• Figure 5: The inverted potential $-V_{eff}$ for a compact object of radius $R_c$ is discontinuous at $r=R_c$ since the matter density equals: a) $\rho_c$ for $r<R_c$; b) $\rho_\infty$ for $r>R_c$. The dots represent the position of the particle at some value of $r$.