Probing Spin-2 Ultralight Dark Matter with Space-based Gravitational Wave Detectors in the mHz Regime

TL;DR

The paper addresses the search for spin-2 ultralight dark matter (ULDM) by exploiting space-based gravitational-wave interferometers in the millihertz band. It models a direct coupling between spin-2 ULDM and ordinary matter, derives the resulting Shapiro-like frequency shifts, and computes the detector response for single links, Michelson configurations, and TDI channels. By constructing sensitivity curves and an optimal combination of TDI channels, the authors show that upcoming detectors like Taiji can constrain the coupling $α$ to about $10^{-10}$ near $m \sim 10^{-17}\,{ m eV}$, surpassing current ground-based and pulsar timing bounds. The work highlights that fully symmetric TDI channels have weaker ULDM responses, offering a potential handle to distinguish ULDM signals from GWs, and discusses coherent versus semi-coherent analysis approaches for ULDM signals in the presence of finite coherence time and velocity distributions.

Abstract

Spin-2 ultralight dark matter (ULDM) is a viable dark matter candidate and it can be constrained using gravitational wave (GW) observations. In this paper, we investigate the detectability of spin-2 ULDM by space-based GW interferometers. By considering a direct coupling between spin-2 ULDM and ordinary matter, we derive the corresponding response functions and sensitivity curves for various time-delay interferometry channels and calculate the optimal sensitivity curves for future millihertz GW detectors. Our results demonstrate that the space-based detectors can place stringent constraints on the coupling constant of spin-2 ULDM, reaching $α\sim 10^{-10}$ around a mass of $m \sim 10^{-17} \rm eV$, surpassing current limits from ground-based detectors and pulsar timing arrays. Thus, the space-based GW detectors can serve as powerful tools not only for detecting GWs but also for probing fundamental properties of ultralight dark matter.

Figures (7)

• Figure 1: A schematic diagram illustrating the configuration of three detectors, where the vertices {1, 2, 3} represent the distinct detectors, and $\psi = \pi/3$.
• Figure 2: The response functions for single link(left) and Michelson combinations(right).
• Figure 3: The response functions for different TDI channels.
• Figure 4: The sensitivity curves of GWIs for the detection of spin-2 ULDM in different TDI channels, compared with the performance of GWs. We assume $L=3\times 10^9~{\mathrm m}$ and $v=10^{-3}$.
• Figure 5: The comparison between sensitivity curves of different channels for spin-2 ULDM.