Probing modified gravity with atom-interferometry: A numerical approach

Abstract

Refined constraints on chameleon theories are calculated for atom-interferometry experiments, using a numerical approach consisting in solving for a four-region model the static and spherically symmetric Klein-Gordon equation for the chameleon field. By modeling not only the test mass and the vacuum chamber but also its walls and the exterior environment, the method allows to probe new effects on the scalar field profile and the induced acceleration of atoms. In the case of a weakly perturbing test mass, the effect of the wall is to enhance the field profile and to lower the acceleration inside the chamber by up to one order of magnitude. In the thin-shell regime, results are found to be in good agreement with the analytical estimations, when measurements are realized in the immediate vicinity of the test mass. Close to the vacuum chamber wall, the acceleration becomes negative and potentially measurable. This prediction could be used to discriminate between fifthforce effects and systematic experimental uncertainties, by doing the experiment at several key positions inside the vacuum chamber. For the chameleon potential V (φ) = Λ 4+α /φ α and a coupling function A(φ) = exp(φ/M ), one finds M 7 × 10 16 GeV, independently of the power-law index. For V (φ) = Λ 4 (1 + Λ/φ), one finds M 10 14 GeV. A sensitivity of a ∼ 10 −11 m/s 2 would probe the model up to the Planck scale. Finally, a proposal for a second experimental set-up, in a vacuum room, is presented. In this case, Planckian values of M could be probed provided that a ∼ 10 −10 m/s 2 , a limit reachable by future experiments. Our method can easily be extended to constrain other models with a screening mechanism, such as symmetron, dilaton and f(R) theories.

Chameleon dark energy and atom interferometry

“…The motivations for this work are three-fold. Firstly, the exact approach followed here allows us to quantify the validity of the approximations made in [54], as well to place rigorous constraints on chameleon theories from the experimental bound on a. Secondly, it allows us to check claims in the literature that accounting for the chamber walls leads to a significant effect on the field profile deep inside the chamber [55] or that the thin-shell expression that goes back to [2,3] gives a poor approximation to the chameleon force [56]. We will see that these claims are wrong.…”

Numerical forecasts for lab experiments constraining modified gravity: The chameleon model

“…The same numerical method has been used to derive constraints on other chameleon potentials in Ref. 5 for the thin shell regime. Our numerical method could be easily extended to other modified gravity models like the symmetron.…”

Red giant evolution in modified gravity

“…Although tests of general relativity in the solar system would exclude the corresponding parameter space for the chameleon field but in order to find significant deviations for the dynamical chameleon scalar field with attractor behaviour 1 in astrophysical scales we have focused on greater values of the constant taken from cosmology. It's order of magnitude for different values of n can be found using the following relation [33,34] logM…”