Looking for gravitational waves with orbital dynamics: GUEST mission and the $μ$Hz band of Gravitational Waves

Author(s)

Blas, Diego

Abstract

`Adding colour'' to the gravitational-wave sky by probing unexplored frequency bands has the potential to unveil new and unexpected phenomena in the Universe. The microhertz band, between pulsar timing arrays and LISA, is a particularly attractive target: it should host the extension of the signal recently found by pulsar timing arrays (if it is generated by a family of sources of gravitational waves), and it may harbour signals from the early Universe, primordial black holes or dark matter. In these proceedings, we review how the orbits of gravitationally bound systems act as resonant detectors of microhertz gravitational waves and ultra-light dark matter. We then describe GUEST (Gravitational Universe Exploration with Satellite Tracking), a mission concept recently proposed to the ESA F-class call, consisting of two dense passive spheres covered with retroreflectors, placed in highly eccentric Earth orbits and tracked by a global laser-ranging network.

Figures

The GW landscape in terms of $\Omega_{\rm GW}(f)$. Current facilities (dark grey) and planned missions (light grey) leave the $\mu$Hz band essentially uncovered. TVLBAI and PIXIE lines are estimates with no planned mission. The GUEST line corresponds to the mission concept of Sec.~\ref{sec:guest}. Adapted from~\cite{Blas:2026xol}.
Caption The GW landscape in terms of $\Omega_{\rm GW}(f)$. Current facilities (dark grey) and planned missions (light grey) leave the $\mu$Hz band essentially uncovered. TVLBAI and PIXIE lines are estimates with no planned mission. The GUEST line corresponds to the mission concept of Sec.~\ref{sec:guest}. Adapted from~\cite{Blas:2026xol}.
Power-law-integrated sensitivity of LLR, eccentric lunar orbits (eLO) and eccentric Earth orbits tracked with SLR (eSLR)~\cite{Foster:2025nzf}, compared to NANOGrav 15-year data and future SKA, LISA and AION-km. Black lines: SIGW spectra for two benchmark PBH scenarios with widths $\Delta=0.1$ (solid) and $\Delta=1$ (dashed). From~\cite{Blas:2026xws}.
Caption Power-law-integrated sensitivity of LLR, eccentric lunar orbits (eLO) and eccentric Earth orbits tracked with SLR (eSLR)~\cite{Foster:2025nzf}, compared to NANOGrav 15-year data and future SKA, LISA and AION-km. Black lines: SIGW spectra for two benchmark PBH scenarios with widths $\Delta=0.1$ (solid) and $\Delta=1$ (dashed). From~\cite{Blas:2026xws}.
Our 2025 forecasts for $\Omega_{\rm GW}$ from binary systems~\cite{Foster:2025nzf,Foster:2025csl}: the Moon (LLR), millisecond pulsars (MSPs), existing satellites (SLR LAGEOS), and proposed satellites around the Moon (High-$e$ LO) and the Earth (SLR$_{\rm MMS}$, assuming an MMS-like orbit tracked as well as LAGEOS and an idealised analysis). Dashed lines: pessimistic case with large parameter degeneracies. Possible signals from SMBHBs~\cite{Ellis:2023owy}, cosmic strings and FOPTs are also shown.
Caption Our 2025 forecasts for $\Omega_{\rm GW}$ from binary systems~\cite{Foster:2025nzf,Foster:2025csl}: the Moon (LLR), millisecond pulsars (MSPs), existing satellites (SLR LAGEOS), and proposed satellites around the Moon (High-$e$ LO) and the Earth (SLR$_{\rm MMS}$, assuming an MMS-like orbit tracked as well as LAGEOS and an idealised analysis). Dashed lines: pessimistic case with large parameter degeneracies. Possible signals from SMBHBs~\cite{Ellis:2023owy}, cosmic strings and FOPTs are also shown.
GUEST 10-year sensitivity. \textbf{Left:} monochromatic GWs (SNR $=1$) for the conservative (``with arcs'') and best-case (``no arc'') analyses. \textbf{Right:} SGWB sensitivity (ideal analysis) compared to SMBHBs consistent with NANOGrav~\cite{NANOGrav:2023gor,Ellis:2023owy}, phase transitions and cosmic strings. The continuous line is the power-law integrated sensitivity~\cite{Thrane:2013oya}; the peaks are resonances. From~\cite{Blas:2026xol}.
Caption GUEST 10-year sensitivity. \textbf{Left:} monochromatic GWs (SNR $=1$) for the conservative (``with arcs'') and best-case (``no arc'') analyses. \textbf{Right:} SGWB sensitivity (ideal analysis) compared to SMBHBs consistent with NANOGrav~\cite{NANOGrav:2023gor,Ellis:2023owy}, phase transitions and cosmic strings. The continuous line is the power-law integrated sensitivity~\cite{Thrane:2013oya}; the peaks are resonances. From~\cite{Blas:2026xol}.
GUEST 10-year sensitivity. \textbf{Left:} monochromatic GWs (SNR $=1$) for the conservative (``with arcs'') and best-case (``no arc'') analyses. \textbf{Right:} SGWB sensitivity (ideal analysis) compared to SMBHBs consistent with NANOGrav~\cite{NANOGrav:2023gor,Ellis:2023owy}, phase transitions and cosmic strings. The continuous line is the power-law integrated sensitivity~\cite{Thrane:2013oya}; the peaks are resonances. From~\cite{Blas:2026xol}.
Caption GUEST 10-year sensitivity. \textbf{Left:} monochromatic GWs (SNR $=1$) for the conservative (``with arcs'') and best-case (``no arc'') analyses. \textbf{Right:} SGWB sensitivity (ideal analysis) compared to SMBHBs consistent with NANOGrav~\cite{NANOGrav:2023gor,Ellis:2023owy}, phase transitions and cosmic strings. The continuous line is the power-law integrated sensitivity~\cite{Thrane:2013oya}; the peaks are resonances. From~\cite{Blas:2026xol}.
\textbf{Left:} GUEST reach for ULDM in the $(m_{\rm DM},\beta\rho_{\rm DM}/\rho_\odot)$ plane, where $\beta=1$ is the universal gravitational coupling, compared to PTAs, Cassini and LISA. \textbf{Right:} constraints on a Yukawa fifth force of strength $\alpha$ and range $\lambda$, and the region opened by GUEST. From~\cite{Blas:2026xol}.
Caption \textbf{Left:} GUEST reach for ULDM in the $(m_{\rm DM},\beta\rho_{\rm DM}/\rho_\odot)$ plane, where $\beta=1$ is the universal gravitational coupling, compared to PTAs, Cassini and LISA. \textbf{Right:} constraints on a Yukawa fifth force of strength $\alpha$ and range $\lambda$, and the region opened by GUEST. From~\cite{Blas:2026xol}.
\textbf{Left:} GUEST reach for ULDM in the $(m_{\rm DM},\beta\rho_{\rm DM}/\rho_\odot)$ plane, where $\beta=1$ is the universal gravitational coupling, compared to PTAs, Cassini and LISA. \textbf{Right:} constraints on a Yukawa fifth force of strength $\alpha$ and range $\lambda$, and the region opened by GUEST. From~\cite{Blas:2026xol}.
Caption \textbf{Left:} GUEST reach for ULDM in the $(m_{\rm DM},\beta\rho_{\rm DM}/\rho_\odot)$ plane, where $\beta=1$ is the universal gravitational coupling, compared to PTAs, Cassini and LISA. \textbf{Right:} constraints on a Yukawa fifth force of strength $\alpha$ and range $\lambda$, and the region opened by GUEST. From~\cite{Blas:2026xol}.
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