Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions, parallaxes, and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in their apparent positions, a phenomenon known as astrometric deflection. The precision and scale of astrometric datasets make them well suited for searching for a stochastic gravitational-wave background, whose signature appears in the two-point correlation function of the deflection field across the sky. In space-based astrometry, the ultimate sensitivity of such measurements is reduced by systematic uncertainties in the satellite's absolute attitude reconstruction, which constrain the accuracy of absolute astrometry. These orientation errors can be mitigated by focusing on relative angular separation between pairs of stars, which effectively cancel out common-mode orientation noise. In this work, we compute the astrometric response and the overlap reduction functions for this differential approach, correcting previous expressions presented in the literature. We use a Fisher matrix analysis to compare the sensitivity of differential astrometry to that of conventional absolute astrometry. Our analysis shows that while the differential method is theoretically sound, its sensitivity is limited for closely spaced star pairs. Pairs with large angular separations provide competitive sensitivity, but, when considered in connection with Gaia, it is unclear whether the differential strategy would be effective, since instrumental systematics are not expected to remain correlated on such scales. Finally, we demonstrate that combining astrometric data with observations from pulsar-timing arrays leads to slight improvements in sensitivity at frequencies greater than or similar to 10-7Hz.

Existing expressions in the literature appear to indicate that Doppler boosting, due to our proper motion with respect to the isotropic frame of the universe, can amplify stochastic gravitational wave backgrounds whose energy spectra exhibit strong scale dependence, for example, those generated by large scalar perturbations in models of primordial black holes or by astrophysical populations with broken power-law behaviour. It has been suggested that this enhancement could increase the signal-to-noise ratio of such backgrounds in pulsar timing measurements, as well as in ground- and space-based observatories. We show that the reported enhancement is an artefact of a Taylor expansion of the boosted signal, typically performed in the literature under the assumption of a small boosting parameter. This approximation fails to reproduce the correct result for signals with strong scale dependence. When Doppler boosting is treated exactly, the apparent amplification disappears. Using representative spectra, we demonstrate that Doppler motion induces only blue- and red-shifting by the expected amount; it does not lead to additional amplification or introduce new spectral features. The exact expression for the kinematic boost can and should be easily applied in analysing such backgrounds.

We propose the Locally Pumped Dark Energy (LPDE) mechanism in which cosmic acceleration is triggered by the emergence of non-linear dark matter structure. In an effective-field-theory description, coarse-graining over the density contrast profile, whose short-wavelength modes grow during halo formation, induces a shift in the local equilibrium point of a second, sufficiently heavy scalar field χ. At early times, the pump mechanism is negligible and χ remains fixed at the origin, contributing no DE. As structures form, the equilibrium value of χ is locally displaced within halos, generating a vacuum energy whose global contribution, in a mean-field picture, is controlled by the halo volume filling factor. If the χ field is sufficiently heavy, with a Compton wavelength limited by halo scales, its response is localised, and spatial gradients are exponentially suppressed on large scales. After volume-averaging over the halo population, the resulting contribution on large scales behaves as a homogeneous DE component. Using the halo mass function of a fiducial ΛCDM cosmology, we show that vacuum-energy domination generically emerges at z∼𝒪(1), naturally correlating cosmic acceleration with structure formation. For reference, we present an explicit realisation of such a mechanism and show that, by naturally featuring a transient acceleration epoch, it can be in excellent agreement with the most recent cosmological data, including the Dark Energy Spectroscopic Instrument (DESI).

We present a unified spin-weighted harmonic framework that delivers analytic, diagonal expressions for the overlap (correlation) functions of three low frequency gravitational wave observables-pulsar timing redshifts, astrometric deflections, and time-dependent image distortions (“shimmering”). Writing each response in spin-s spherical harmonics and rotating to a basis in which the wave tensor has definite helicity, we obtain compact closed-form series for every auto- and cross-correlation, recovering the Hellings-Downs curve as the s=0 limit and deriving its astrometric (s=± 1) and shimmering (s=± 2) analogues. The formalism naturally extends to non-standard scalar-breathing, longitudinal, and vector polarisation modes, clarifying when higher-spin observables are (and are not) sourced and providing a complete set of harmonic spectra C_ℓ ready for parameter estimation pipelines. These results supply the common theoretical language needed to combine upcoming pulsar timing, Gaia-class astrometric, and high resolution imaging data sets, enabling coherent, multi probe searches for stochastic gravitational wave backgrounds, tests of general relativity and its alternatives across the nano- to micro-hertz gravitational wave band.

Simulation-Based Inference (SBI) offers a principled and flexible framework for conducting Bayesian inference in any situation where forward simulations are feasible. However, validating the accuracy and reliability of the inferred posteriors remains a persistent challenge. In this work, we point out a simple diagnostic approach rooted in ensemble learning methods to assess the internal consistency of SBI outputs that does not require access to the true posterior. By training multiple neural estimators under identical conditions and evaluating their pairwise Kullback-Leibler (KL) divergences, we define a consistency criterion that quantifies agreement across the ensemble. We highlight two core use cases for this framework: a) for generating a robust estimate of the systematic uncertainty in parameter reconstruction associated with the training procedure, and b) for detecting possible model misspecification when using trained estimators on real data. We also demonstrate the relationship between significant KL divergences and issues such as insufficient convergence due to, e.g., too low a simulation budget, or intrinsic variance in the training process. Overall, this ensemble-based diagnostic framework provides a lightweight, scalable, and model-agnostic tool for enhancing the trustworthiness of SBI in scientific applications.

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.

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study).

Using data from the first flight of Spider and from the Planck High Frequency Instrument, we probe the properties of polarized emission from interstellar dust in the Spider observing region. Component-separation algorithms operating in both the spatial and harmonic domains are applied to probe their consistency and to quantify modeling errors associated with their assumptions. Analyses of diffuse Galactic dust emission spanning the full Spider region demonstrate (i) a spectral energy distribution that is broadly consistent with a modified-blackbody (MBB) model with a spectral index of β d = 1.45 ± 0.05 (1.47 ± 0.06) for E ( B )-mode polarization, slightly lower than that reported by Planck for the full sky; (ii) an angular power spectrum broadly consistent with a power law; and (iii) no significant detection of line-of-sight polarization decorrelation. Tests of several modeling uncertainties find only a modest impact (∼10% in σ r ) on Spider ’s sensitivity to the cosmological tensor-to-scalar ratio. The size of the Spider region further allows for a statistically meaningful analysis of the variation in foreground properties within it. Assuming a fixed dust temperature T d = 19.6 K, an analysis of two independent subregions of that field results in inferred values of β d = 1.52 ± 0.06 and β d = 1.09 ± 0.09, which are inconsistent at the 3.9 σ level. Furthermore, a joint analysis of Spider and Planck 217 and 353 GHz data within one subregion is inconsistent with a simple MBB at more than 3 σ , assuming a common morphology of polarized dust emission over the full range of frequencies. This evidence of variation may inform the component-separation approaches of future cosmic microwave background polarization experiments.

We introduce a novel approach for detecting gravitational waves through their influence on the shape of resolved astronomical objects. This method, complementary to pulsar timing arrays and astrometric techniques, explores the time-dependent distortions caused by gravitational waves on the shapes of celestial bodies, such as galaxies or any resolved extended object. By developing a formalism based on that adopted in the analysis of weak lensing effects, we derive the response functions for gravitational wave-induced distortions and compute their angular correlation functions. Our results highlight the sensitivity of these distortions to the lowest frequencies of the gravitational wave spectrum and demonstrate how they produce distinct angular correlation signatures, including null and polarisation-sensitive correlations. These findings pave the way for future high-resolution surveys to exploit this novel observable, potentially offering new insights into the stochastic gravitational wave background and cosmological models.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

We employ the formalism developed in [1] and [2] to study the prospect of detecting an anisotropic Stochastic Gravitational Wave Background (SGWB) with the Laser Interferometer Space Antenna (LISA) alone, and combined with the proposed space -based interferometer Taiji. Previous analyses have been performed in the frequency domain only. Here, we study the detectability of the individual coefficients of the expansion of the SGWB in spherical harmonics, by taking into account the specific motion of the satellites. This requires the use of time -dependent response functions, which we include in our analysis to obtain an optimal estimate of the anisotropic signal. We focus on two applications. Firstly, the reconstruction of the anisotropic galactic signal without assuming any prior knowledge of its spatial distribution. We find that both LISA and LISA with Taiji cannot put tight constraints on the harmonic coefficients for realistic models of the galactic SGWB. We then focus on the discrimination between a galactic signal of known morphology but unknown overall amplitude and an isotropic extragalactic SGWB component of astrophysical origin. In this case, we find that the two surveys can confirm, at a confidence level greater than or similar to 3 sigma, the existence of both the galactic and extragalactic background if both have amplitudes as predicted in standard models. We also find that, in the LISA -only case, the analysis in the frequency domain (under the assumption of a time average of data taken homogeneously across the year) provides a nearly identical determination of the two amplitudes as compared to the optimal analysis.

The subtle influence of gravitational waves on the apparent positioning of celestial bodies offers novel observational windows [1-4]. We calculate the expected astrometric signal induced by an isotropic Stochastic Gravitational Wave Background (SGWB) in the short distance limit. Our focus is on the resultant proper motion of Solar System objects, a signal on the same time scales addressed by Pulsar Timing Arrays (PTA). We derive the corresponding astrometric deflection patterns, finding that they manifest as distinctive dipole and quadrupole correlations or, in some cases, may not be present. Our analysis encompasses both Einsteinian and non-Einsteinian polarisations. We estimate the upper limits for the amplitude of SGWBs that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. We find that for SGWBs with negative spectral indices, such as that generated by Super Massive Black Hole Binaries (SMBHB), the constraints from these observations could rival those from PTAs. With the Gaia satellite and the Vera C. Rubin Observatory poised to track an extensive sample of asteroids - ranging from O (10 5 ) to O (10 6 ), we highlight the significant future potential for similar surveys to contribute to our understanding of the SGWB.

SPIDER is a balloon-borne instrument designed to map the cosmic microwave background at degree-angular scales in the presence of Galactic foregrounds. SPIDER has mapped a large sky area in the Southern Hemisphere using more than 2000 transition-edge sensors (TESs) during two NASA Long Duration Balloon flights above the Antarctic continent. During its first flight in January 2015, SPIDER observed in the 95 GHz and 150 GHz frequency bands, setting constraints on the B-mode signature of primordial gravitational waves. Its second flight in the 2022-23 season added new receivers at 280 GHz, each using an array of TESs coupled to the sky through feedhorns formed from stacks of silicon wafers. These receivers are optimized to produce deep maps of polarized Galactic dust emission over a large sky area, providing a unique data set with lasting value to the field. In this work, we describe the instrument's performance during SPIDER's second flight.

We build an analytical framework to study the observability of anisotropies and a net chiral polarization of the Stochastic Gravitational Wave Background (SGWB) with a generic network of ground-based detectors. We apply this formalism to perform a Fisher forecast of the performance of a network consisting of the current interferometers (LIGO, Virgo and KAGRA) and planned third-generation ones, such as the Einstein Telescope and Cosmic Explorer. Our results yield limits on the observability of anisotropic modes, spanning across noise- and signal-dominated regimes. We find that if the isotropic component of the SGWB has an amplitude close to the current limit, third-generation interferometers with an observation time of 10 years can measure multipoles (in a spherical harmonic expansion) up to ℓ = 8 with 𝒪(10 -3 – 10 -2 ) accuracy relative to the isotropic component, and an 𝒪(10 -3 ) amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

For any given network of detectors, and for any given integration time, even in the idealized limit of negligible instrumental noise, the intrinsic time variation of the isotropic component of the stochastic gravitational wave background (SGWB) induces a limit on how accurately the anisotropies in the SGWB can be measured. We show here how this sample limit can be calculated and apply this to three separate configurations of ground-based detectors placed at existing and planned sites. Our results show that in the idealized, best-case scenario, individual multipoles of the anisotropies at ℓ≤8 can only be measured to ∼10^{-5}-10^{-4} level over five years of observation as a fraction of the isotropic component. As the sensitivity improves as the square root of the observation time, this poses a very serious challenge for measuring the anisotropies of SGWB of cosmological origin, even in the case of idealized detectors with arbitrarily low instrumental noise.

We introduce a unified formalism to describe both timing and astrometric perturbations induced on astrophysical point sources by gravitational waves using a complex spin field on the sphere. This allows the use of spin-weighted spherical harmonics to analyse “astrochronometric” observables. This approach simplifies the interpretation and simulation of anisotropies induced in the observables by gravitational waves. It also allows a simplified derivation of angular cross-spectra of the observables and their relationship with generalised Hellings-Downs correlation functions. The spin-weighted formalism also allows an explicit connection between correlation components and the spin of gravitational wave polarisations and any presence of chirality. We also calculate expected signal-to-noise ratios for observables to compare the utility of timing and deflection observables.

Detection of a stochastic background of gravitational waves is likely to occur in the next few years. Beyond searches for the isotropic component of SGWBs, there have been various mapping methods proposed to target anisotropic backgrounds. Some of these methods have been applied to data taken by the Laser Interferometer Gravitational-wave Observatories (LIGO) and Virgo. Specifically, these directional searches have focused on mapping the intensity of the signal on the sky via maximum likelihood solutions. We compare this intensity mapping approach to a previously proposed, but never employed, amplitude-phase mapping method to understand whether this latter approach may be employed in future searches. We build up our understanding of the differences between these two approaches by analysing simple toy models of time-stream data, and run mock-data mapping tests for the two methods. We find that the amplitude-phase method is only applicable to the case of a background which is phase-coherent on large scales or, at the very least, has an intrinsic coherence scale that is larger than that of the detector. Otherwise, the amplitude-phase mapping method leads to a loss of overall information, with respect to both phase and amplitude. Since we do not expect these phase-coherent properties to hold for any of the gravitational-wave background signals we hope to detect in the near future, we conclude that intensity mapping is the preferred method for such backgrounds.

Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo- C ℓ based, MASTER -style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F ℓ , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, J ℓ ℓ ′ , which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment.

Experiments deploying large arrays of transition-edge sensors (TESs) often require a robust method to monitor gain variations with minimal loss of observing time. We propose a sensitive and non-intrusive method for monitoring variations in TES responsivity using small square waves applied to the TES bias. We construct an estimator for a TES's small-signal power response from its electrical response that is exact in the limit of strong electrothermal feedback. We discuss the application and validation of this method using flight data from SPIDER, a balloon-borne telescope that observes the polarization of the cosmic microwave background with more than 2000 TESs. This method may prove useful for future balloon- and space-based instruments, where observing time and ground control bandwidth are limited.

The stochastic gravitational wave background (SGWB) contains a wealth of information on astrophysical and cosmological processes. A major challenge of upcoming years will be to extract the information contained in this background and to disentangle the contributions of different sources. In this paper we provide the formalism to extract, from the correlation of three signals in the Laser Interferometer Space Antenna (LISA), information about the tensor three-point function, which characterizes the non-Gaussian properties of the SGWB. This observable can be crucial to discriminate whether a SGWB has a primordial or astrophysical origin. Compared to the two-point function, the SGWB three-point function has a richer dependence on the gravitational wave momenta and chiralities. It can be used therefore as a powerful discriminator between different models. For the first time we provide the response functions of LISA to a general SGWB three-point function. As examples, we study in full detail the cases of an equilateral and squeezed SGWB bispectra, and provide the explicit form of the response functions, ready to be convoluted with any theoretical prediction of the bispectrum to obtain the observable signal. We further derive the optimal estimator to compute the signal-to-noise ratio. Our formalism covers general shapes of non-Gaussianity, and can be extended straightaway to other detector geometries. Finally, we provide a short overview of models of the early universe that can give rise to a non-Gaussian SGWB.