Prospects for detecting new dark physics with the next generation of atomic clocks

TL;DR

The paper investigates how next-generation atomic clocks can detect EP-violating new physics that manifest as time variations in the electron-proton mass ratio $\mu$. It develops a scalar-field framework linking clock observables to three main signal classes—modified gravity, dynamical dark energy, and ultralight dark matter—and uses public Circular T data, Fisher forecasts, and simulated datasets to derive projected bounds. An open-source forecast tool translates clock characteristics into quantitative limits on fundamental-physics parameters, guiding experimental design and cross-comparisons with MICROSCOPE, LLR, Planck, and other probes. The work highlights the potential for clock networks to significantly advance constraints on dynamical dark energy and dark matter, and to compete with or surpass existing tests in certain modified-gravity regimes, while providing a practical framework for ongoing and future clock-based searches for new physics.

Abstract

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.

Figures (8)

• Figure 1: Comparison of projected and existing constraints on oscillations in $\mu_\mathrm{eff}(t) / \bar{\mu} = 1 + A / \omega \cos (\omega t + \delta)$. This signal is associated with ultralight dark matter theories. Also shown are currently-leading constraints from clocks in this frequency range Kennedy:2020bacKobayashi_2022Sherrill_2023. Note that this figure is in terms of the ordinary frequency $f$, not the angular frequency $\omega = 2 \pi f$.
• Figure 2: Constraints on Galileon parameter space from a CaF/Sr clock pair over a period of three years. The different power laws in the curve correspond to regions where quadratic, cubic, and quartic terms of Eq. \ref{['Galileon-eom']} each dominate. The gray regions are ruled out by the MICROSCOPE experiment and lunar laser ranging, which are discussed in Appendix \ref{['app:Galileon']}. Also indicated are $M = M_\mathrm{Pl}$, which corresponds to a gravitational-strength matter-scalar coupling, and the $\Lambda$ scale that corresponds to a graviton mass proportional to the current Hubble scale, as given by Eq. \ref{['graviton-mass-scale']}.
• Figure 3: Upper panel: constraints on the space of parameters $(\Lambda,M)$ in the generalized interaction modified gravity model \ref{['generalized-profile']}. The lines define the lower bounds in the region of parameters $(\Lambda,M)$ that can be ruled out by a CaF/Sr clock pair over a three-year observation time. Particular theories are highlighted: the free scalar, cubic Galileon, and quartic Galileon corresponding to each of the three regimes identified in Eq. \ref{['Galileon-eom']}, and also generalized ones that include DBI deRham:2010eu.
• Figure 4: Projected bounds from clocks on quintessence dark energy, over an observation time of 3 years. A CaF/Sr clock pair was used for the bottom plot.
• Figure 5: Constraints on the space of parameters $(M,m)$ in the Dark Matter model defined in \ref{['dm-background']} after marginalizing over the unknown phase $\delta$, for an observation time of $T = 3~\mathrm{yr}$. Also plotted are constraints from NANOGrav NANOGrav:2023hvm and Yb/Cs clocks Kobayashi_2022Sherrill_2023 which were drawn from AxionLimits, as well as Sr/H/Si clocks Kennedy:2020bac, and the MICROSCOPE satellite MICROSCOPE:2022doy. The best torsion balance curves Adelberger:2003zx sit approximately one order of magnitude below the MICROSCOPE line and hence are not included in the figure. Planned atom interferometry experiments will also be sensitive to the higher end of this mass range ($10^{-19}~\mathrm{eV} \lesssim m \lesssim 10^{-11}~\mathrm{eV}$) within the next few years Buchmueller:2023nll.