## Search for domain wall dark matter with atomic clocks on board global positioning system satellites

Benjamin M. Roberts, Geoffrey Blewitt, Conner Dailey, Mac Murphy, Maxim Pospelov, Alex Rollings, Jeff Sherman, Wyatt Williams, & Andrei Derevianko

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### Abstract

Cosmological observations indicate that dark matter makes up $85\%$ of all matter in the universe yet its microscopic composition remains a mystery. Dark matter could arise from ultralight quantum fields that form macroscopic objects. Here we use the global positioning system as a $\sim 50,000 \mathrm{km}$ aperture dark matter detector to search for such objects in the form of domain walls. Global positioning system navigation relies on precision timing signals furnished by atomic clocks. As the Earth moves through the galactic dark matter halo, interactions with domain walls could cause a sequence of atomic clock perturbations that propagate through the satellite constellation at galactic velocities $\sim 300 \mathrm{km/s}$. Mining $16$ years of archival data, we find no evidence for domain walls at our current sensitivity level. This improves the limits on certain quadratic scalar couplings of domain wall dark matter to standard model particles by several orders of magnitude.

## Introduction

Despite the overwhelming cosmological evidence for the existence of dark matter (DM), there is as of yet no definitive evidence for DM in terrestrial experiments. Multiple cosmological observations suggest that ordinary matter makes up only about $15\%$ of the total matter in the universe, with the remaining portion composed of DM. All the evidence for DM (e.g., galactic rotation curves, gravitational lensing, cosmic microwave background) comes from galactic or larger scale observations through the gravitational pull of DM on ordinary matter. Extrapolation from the galactic to laboratory scales presents a challenge because of the unknown nature of DM constituents. Various theories postulate additional non-gravitational interactions between standard model (SM) particles and DM. Ambitious programs in particle physics have mostly focused on (so far unsuccessful) searches for weakly interacting massive particle (WIMP) DM candidates with $10-10^3 \mathrm{GeV}\,c^{−2}$ masses ($c$ is the speed of light) through their energy deposition in particle detectors. The null results of the WIMP searches have partially motivated an increased interest in alternative DM candidates, such as ultralight fields. These fields, in contrast to particle candidates, act as coherent entities on the scale of an individual detector.

Here we focus on ultralight fields that may cause apparent variations in the fundamental constants of nature. Such variations in turn lead to shifts in atomic energy levels, which may be measurable by monitoring atomic frequencies. Such monitoring is performed naturally in atomic clocks, which tell time by locking the frequency of externally generated electromagnetic radiation to atomic frequencies. Here, we analyze time as measured by atomic clocks on board global positioning system (GPS) satellites to search for DM-induced transient variations of fundamental constants. In effect we use the GPS constellation as a $\sim 50,000 \mathrm{km}$-aperture DM detector. Our DM search is one example of using GPS for fundamental physics research. Another recent example includes placing limits on gravitational waves.