Screened scalars are ubiquitous in many dark-sector models. They give rise to nontrivial fifth forces while evading experimental constraints through density-dependent screening mechanisms. We propose equipping a 10 m-scale long-baseline atom interferometer with an annular planar source mass inside the vacuum chamber to search for such screened fifth forces. Two key challenges arise: distinguishing the static fifth force from backgrounds, and isolating it from the plate's Newtonian gravity. We introduce the Q-flip protocol, which alternates between interferometry sequences to induce controllable time-dependence, aiding signal extraction and detrending of transient noise. We further develop an in situ calibration procedure to characterize the plate's Newtonian gravity and reach shot-noise-limited sensitivity. We show that our proposal could test theoretically motivated parameter space, advancing existing bounds on chameleon and symmetron screened scalar models by 1 to 1.5 orders of magnitude. Our proposal is directly applicable to forthcoming experiments, such as AION-10 or VLBAI, and is readily extensible to broader theoretical models and longer baselines.

Wide classes of new fundamental physics theories cause apparent variations in particle mass ratios in space and time. In theories that violate the weak equivalence principle (EP), those variations are not uniform across all particles and may be detected with atomic and molecular clock frequency comparisons. In this work we explore the potential to detect those variations with near-future clock comparisons. We begin by searching published clock data for variations in the electron-proton mass ratio. We then undertake a statistical analysis to model the noise in a variety of clock pairs that can be built in the near future according to the current state of the art, determining their sensitivity to various fundamental physics signals. Those signals are then connected to constraints on fundamental physics theories that lead directly or indirectly to an effective EP-violating, including those motivated by dark matter, dark energy, the vacuum energy problem, unification or other open questions of fundamental physics. This work results in projections for tight new bounds on fundamental physics that could be achieved with atomic and molecular clocks within the next few years. Our code for this work is packaged into a forecast tool that translates clock characteristics into bounds on fundamental physics.

Wavelike dark matter may feature quadratic couplings to ordinary matter. This carries profound consequences for the phenomenologies of such models. It changes the dark matter density around dense objects made from ordinary matter such as planets and stars, thereby changing the sensitivity of direct detection experiments on Earth as well as implying forces on other ordinary matter objects in the vicinity. In this paper we study the time dependence of the dark matter field around spherical objects of ordinary matter. This work indicates the timescale on which accelerating objects settle into a stationary state and delineates the applicability of stationary solutions for experimental dark matter tests. We also use this to understand (and effectively eliminate) the infinities in energies, forces, and pressures that appear when naively comparing the total energy around objects with different size but the same total number of ordinary matter particles.

We compute bounds from atomic spectroscopy on chameleon fields that couple to the photon. Chameleons are a wide class of scalar field models that generically lead to screened fifth forces and a host of novel phenomenologies, particularly when the photon coupling is included. We account for perturbations to the atomic energy levels from both the scalar field "fifth force" and the scalar field's correction to the electric field. We also account for the electromagnetic interaction's contribution to the scalar charge of the proton, which enables a considerably wider class of models to be tested than without this effect. We find bounds that cover different areas of chameleon parameter space. Some regions are redundant with existing experiments, particularly $g - 2$, confirming that those models are ruled out. Other regions were previously unconstrained, and a range of models spanning approximately four orders of magnitude in chameleon coupling parameters are excluded for the first time.

Light scalar fields, with double well potentials and direct matter couplings, undergo density driven phase transitions, leading to the formation of domain walls. Such theories could explain dark energy or dark matter or source the nanohertz gravitational-wave background. We describe an experiment that could be used to detect such domain walls in a laboratory environment, solving for the scalar field profile and showing how the domain wall affects the motion of a test particle. We find that, in currently unconstrained regions of parameter space, the domain walls leave detectable signatures. Published by the American Physical Society 2024

We compute bounds and forecasts on screened modified gravity theories, specialising to the chameleon model in Casimir force experiments. In particular, we investigate the classical interaction between a plate and sphere subject to a screened interaction of the chameleon type. We compare numerical simulations of the field profile and the classical pressure exerted on the sphere to analytical approximations for these non-linear field theories. In particular, we focus on the proximity force approximation (PFA) and show that, within the range of sphere sizes $R$ and plate-sphere distance $D$ simulated numerically, the PFA does not reproduce the numerical results. This differs from the case of linear field theories such as Newtonian gravity and a Yukawa model where the PFA coincides with the exact results. We show that for chameleon theories, the screening factor approximation (SFA) whereby the sphere is modelled as a screened sphere embedded in the external field due to the plates, fares better and can be used in the regime $D\gtrsim R$ to extract constraints and forecasts from existing and forthcoming data. In particular, we forecast that future Casimir experiments would corroborate the closing of the parameter space for the simplest of chameleon models at the dark energy scale.

Light scalar fields, with double well potentials and direct matter couplings, undergo density driven phase transitions, leading to the formation of domain walls. Such theories could explain dark energy, dark matter or source the nanoHz gravitational-wave background. We describe an experiment that could be used to detect such domain walls in a laboratory experiment, solving for the scalar field profile, and showing how the domain wall affects the motion of a test particle. We find that, in currently unconstrained regions of parameter space, the domain walls leave detectable signatures.

We compute bounds on screened scalar field theories from hydrogenlike systems. New light scalar fields generically have a direct coupling to matter. Such a coupling is strongly constrained by myriad experimental measurements. However, certain theories possess a screening mechanism that allows the effects of this coupling to weaken dynamically, and to evade many such bounds. We compute the perturbations to the energy levels of hydrogenlike systems due to screened scalar fields. We then use this result in two ways. First, we compute bounds from hydrogen spectroscopy, finding significantly weaker bounds than have been reported before as screening effects were overlooked. Second, we show that muonium is an intrinsically much more sensitive probe of screened scalar fields. For chameleon models, muonium experiments probe a large part of the parameter space that is as yet unexplored by low-energy physics and has so far only been tested by high-energy particle physics experiments.

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.

We derive the weak field limit of scalar-Gauss-Bonnet theory and place novel bounds on the parameter space using terrestrial and space-based experiments. In order to analyze the theory in the context of a wide range of experiments, we compute the deviations from Einstein gravity around source masses with planar, cylindrical, and spherical symmetry. We find a correction to the Newtonian potential around spherical and cylindrical sources that can be larger than PPN corrections sufficiently close to the source. We use this to improve on laboratory constraints on the scalar-Gauss-Bonnet coupling parameter $Λ$ by two orders of magnitude. Present laboratory and Solar System bounds reported here are superseded by tests deriving from black holes.

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory.

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.

Many non-linear scalar field theories possess a screening mechanism that can suppress any associated fifth force in dense environments. As a result, these theories can evade local experimental tests of new forces. Chameleon-like screening, which occurs because of non-linearities in the scalar potential or the coupling to matter, is well understood around extended objects. However, many experimental tests of these theories involve objects with spatial extent much smaller than the scalar field's Compton wavelength, and which could therefore be considered point-like. In this work, we determine how the fifth forces are screened in the limit that the source objects become extremely compact.

Within the landscape of modified theories of gravity, progress in understanding the behaviour of, and developing tests for, screening mechanisms has been hindered by the complexity of the field equations involved, which are nonlinear in nature and characterised by a large hierarchy of scales. This is especially true of Vainshtein screening, where the fifth force is suppressed by high-order derivative terms which dominate within a radius much larger than the size of the source, known as the Vainshtein radius. =-1 In this work, we present the numerical code φenics, building on the FEniCS library, to solve the full equations of motion from two theories of interest for screening: a model containing high-order derivative operators in the equation of motion and one characterised by nonlinear self-interactions in two coupled scalar fields. We also include functionalities that allow the computation of higher-order operators of the scalar fields in post-processing, enabling us to check that the profiles we find are consistent solutions within the effective field theory. These two examples illustrate the different challenges experienced when trying to simulate such theories numerically, and we show how these are addressed within this code. The examples in this paper assume spherical symmetry, but the techniques may be straightforwardly generalised to asymmetric configurations. This article therefore also provides a worked example of how the finite element method can be employed to solve the screened equations of motion. φenics is publicly available and can be adapted to solve other theories of screening.

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''.

The symmetron is a typical example of screened modified gravity, wherein the symmetron force is dynamically suppressed in dense environments. This allows it to hide in traditional tests of gravity. However, the past decade has seen great experimental progress towards measuring screened forces in the laboratory or in space. Screening relies on nonlinearities in the equation of motion, which significantly complicates the theoretical analysis of such forces. Here, we present a calculation of the symmetron force between a dense plate and sphere surrounded by vacuum. This is done via semi-analytical approaches in two limiting cases, based on the size of the sphere: large spheres are analyzed via the proximity force approximation, whilst small spheres are treated as screened test particles. In the intermediate regime we solve the problem numerically. Our results allow us to make contact with Casimir force experiments, which often employ a plate and sphere configuration for practical reasons, and may therefore be used to constrain symmetrons. We use our results to forecast constraints on the symmetron's parameters for a hypothetical Casimir experiment that is based on the current state of the art. The forecasts compare favorably to other leading laboratory tests of gravity, particularly atom interferometry and bouncing neutrons. We thus conclude that near-future Casimir experiments will be capable of placing tight new bounds on symmetrons. Our results for the symmetron force are derived in a scale-invariant way, such that although we here focus on Casimir experiments, they may be applied to any other plate-sphere system, ranging from microscopic to astrophysical scales.

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.

Precision measurements in space can help our understanding of physics in areas such as the nature of gravity, dark matter, dark energy, and fundamental physics in general. The white paper discusses emerging roles of space laboratory missions for discovery and a mission concept of gravity observation and detection of dark energy in the Solar System.

We investigate how nonlinear scalar field theories respond to point sources. Taking the symmetron as a specific example of such a theory, we solve the nonlinear equation of motion in one spatial dimension for (i) an isolated point source and (ii) two identical point sources with arbitrary separation. We find that the mass of a single point source can be screened by the symmetron field, provided that its mass is above a critical value. We find that two point sources behave as independent, isolated sources when the separation between them is large, but, when their separation is smaller than the symmetron's Compton wavelength, they behave much like a single point source with the same total mass. Finally, we explore closely related behavior in a toy Higgs-Yukawa model and find indications that the maximum fermion mass that can be generated consistently via a Yukawa coupling to the Higgs in 1+1 dimensions is roughly the mass of the Higgs itself, with potentially intriguing implications for the hierarchy problem.