Atomic interferometry measurements of the gravitational force on free-falling atoms provide improved constraints on certain scalar field theories trying to explain dark energy. Traditional gravity measurements use bulk masses to both source and probe gravitational fields1. Matter-wave interferometers enable the use of probe masses as small as neutrons2, atoms3 and molecular clusters4, but still require fields generated by masses ranging from hundreds of kilograms5,6 to the entire Earth. Shrinking the sources would enable versatile configurations, improve positioning accuracy, enable tests for beyond-standard-model (‘fifth’) forces, and allow observation of non-classical effects of gravity. Here we detect the gravitational force between freely falling caesium atoms and an in-vacuum, miniature (centimetre-sized, 0.19 kg) source mass using atom interferometry. Sensitivity down to gravitational strength forces accesses the natural scale7 for a wide class of cosmologically motivated scalar field models8,9 of modified gravity and dark energy. We improve the limits on two such models, chameleons9 and symmetrons10,11, by over two orders of magnitude. We expect further tests of dark energy theories, and measurements of Newton’s gravitational constant and the gravitational Aharonov–Bohm effect12.

The accelerated expansion of the universe motivates a wide class of scalar field theories that modify general relativity (GR) on large scales. Such theories require a screening mechanism to suppress the new force in regions where the weak field limit of GR has been experimentally tested. We have used atom interferometry to measure the acceleration of an atom toward a macroscopic test mass inside a high vacuum chamber, where new forces can be unscreened. Our measurement shows no evidence of new forces, a result that places stringent bounds on chameleon and symmetron theories of modified gravity.

Atom interferometry experiments are searching for evidence of chameleon scalar fields with ever-increasing precision. As experiments become more precise, so too must theoretical predictions. Previous work has made numerous approximations to simplify the calculation, which in general requires solving a three-dimensional nonlinear partial differential equation. This paper calculates the chameleonic force using a numerical relaxation scheme on a uniform grid. This technique is more general than previous work, which assumed spherical symmetry to reduce the partial differential equation to a one-dimensional ordinary differential equation. We examine the effects of approximations made in previous efforts on this subject and calculate the chameleonic force in a setup that closely mimics the recent experiment of Hamilton et al. Specifically, we simulate the vacuum chamber as a cylinder with dimensions matching those of the experiment, taking into account the backreaction of the source mass, its offset from the center, and the effects of the chamber walls. Remarkably, the acceleration on a test atomic particle is found to differ by only 20% from the approximate analytical treatment. These results allow us to place rigorous constraints on the parameter space of chameleon field theories, although ultimately the constraint we find is the same as the one we reported in Hamilton et al. because we had slightly underestimated the size of the vacuum chamber. This computational technique will continue to be useful as experiments become even more precise and will also be a valuable tool in optimizing future searches for chameleon fields and related theories.

Long range scalar fields with a coupling to matter appear to violate known bounds on gravitation in the solar system and the laboratory. This is evaded thanks to screening mechanisms. In this short review, we shall present the various screening mechanisms from an effective field theory point of view. We then investigate how they can and will be tested in the laboratory and on astrophysical and cosmological scales.

We construct a theory that admits a time-dependent solution smoothly interpolating between a null energy condition (NEC)-satisfying phase at early times and a NEC-violating phase at late times. We first review earlier attempts to violate the NEC and an argument of Rubakov, presented in [V. A. Rubakov, Phys. Rev. D 88, 044015 (2013)], which forbids the existence of such interpolating solutions in a single-field dilation-invariant theory. We then construct a theory which, in addition to possessing a Poincaré-invariant vacuum, does admit such a solution. For a wide range of parameters, perturbations around this solution are at all times stable, comfortably subluminal and weakly coupled. The theory requires us to explicitly break dilation invariance, so it is unlikely that the theory is fully stable under quantum corrections, but we argue that the existence of a healthy interpolating solution is quantum-mechanically robust.