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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, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, 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., Comment: Summary of the second Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at Imperial College London: https://indico.cern.ch/event/1369392/

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., Comment: 12 pages, 2 figures

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., Comment: Submitted to SPIE Astronomical Telescopes + Instrumentation 2024, JATIS

Using data from the first flight of SPIDER and from Planck HFI, 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 spanning the full SPIDER region demonstrate that i) the spectral energy distribution of diffuse Galactic dust emission is broadly consistent with a modified-blackbody (MBB) model with a spectral index of $\beta_\mathrm{d}=1.45\pm0.05$ $(1.47\pm0.06)$ for $E$ ($B$)-mode polarization, slightly lower than that reported by Planck for the full sky; ii) its angular power spectrum is broadly consistent with a power law; and iii) there is no significant detection of line-of-sight decorrelation of the astrophysical polarization. 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 $T_\mathrm{d}=19.6$ K, an analysis of two independent sub-regions of that field results in inferred values of $\beta_\mathrm{d}=1.52\pm0.06$ and $\beta_\mathrm{d}=1.09\pm0.09$, which are inconsistent at the $3.9\,\sigma$ level. Furthermore, a joint analysis of SPIDER and Planck 217 and 353 GHz data within a subset of the SPIDER region is inconsistent with a simple MBB at more than $3\,\sigma$, assuming a common morphology of polarized dust emission over the full range of frequencies. These modeling uncertainties have a small--but non-negligible--impact on limits on the cosmological tensor-to-scalar ratio derived from the \spider dataset. The fidelity of the component separation approaches of future CMB polarization experiments may thus have a significant impact on their constraining power., Comment: 21 pages, 15 figures

We employ the formalism developed in \cite{Mentasti:2023gmg} and \cite{Bartolo_2022} 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 $\gtrsim 3\sigma$, 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. 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 a scale-invariant SGWB that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. 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., Comment: 5 pages, 1 figure

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., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

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 $\ell = 8$ with ${\cal O }\left( 10^{-3} - 10^{-2} \right)$ accuracy relative to the isotropic component, and an ${\cal O }\left( 10^{-3} \right)$ amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude., Comment: 40 pages, 7 figures, prepared for submission to JCAP

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 $\ell \leq 8$ can only be measured to $\sim 10^{-5} - 10^{-4}$ level over 5 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 the measurement of the anisotropies of SGWB of cosmological origin, even in the case of idealised detectors with arbitrarily low instrumental noise., Comment: 5 pages, 2 figures

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

We investigate the sensitivity of the Laser Interferometer Space Antenna (LISA) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We first discuss the main astrophysical and cosmological sources of SGWB which are characterized by anisotropies in the GW energy density, and we build a Signal-to-Noise estimator to quantify the sensitivity of LISA to different multipoles. We then perform a Fisher matrix analysis of the prospects of detectability of anisotropic features with LISA for individual multipoles, focusing on a SGWB with a power-law frequency profile. We compute the noise angular spectrum taking into account the specific scan strategy of the LISA detector. We analyze the case of the kinematic dipole and quadrupole generated by Doppler boosting an isotropic SGWB. We find that $\beta\, \Omega_{\rm GW}\sim 2\times 10^{-11}$ is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor $\sim 10^3 \,\beta$ relative to that of the dipole. The characterization of the anisotropies, both from a theoretical perspective and from a map-making point of view, allows us to extract information that can be used to understand the origin of the SGWB, and to discriminate among distinct superimposed SGWB sources., Comment: 48 page + appendices, 13 figures

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., Comment: 15 pages, 7 figures, 4 tables

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., Comment: 7 pages, 3 figures; Proceedings of the 19th International Workshop on Low Temperature Detectors (LTD19); Minor updates to match published version

Modern 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-$C_\ell$ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, $F_{\ell}$, 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, $J_{\ell\ell'}$, 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., Comment: 14 pages, 7 figures; updated to match published version

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., Comment: 15 pages, 4 figures

We present the XFaster analysis package. XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-$C_\ell$ based methods, the algorithm described here requires a minimal number of simulations, and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data, and also used as part of the Planck analysis. Here, we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the SPIDER instrument. The package includes extensions for self-consistently estimating null spectra and for estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations, and its application to the SPIDER data set., Comment: 18 pages, 11 figures

We present the first linear polarization measurements from the 2015 long-duration balloon flight of SPIDER, an experiment designed to map the polarization of the cosmic microwave background (CMB) on degree angular scales. Results from these measurements include maps and angular power spectra from observations of 4.8% of the sky at 95 and 150 GHz, along with the results of internal consistency tests on these data. While the polarized CMB anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is also detected with high significance; Galactic synchrotron emission is found to be negligible in the SPIDER bands. We employ two independent foreground-removal techniques in order to explore the sensitivity of the cosmological result to the assumptions made by each. The primary method uses a dust template derived from Planck data to subtract the Galactic dust signal. A second approach, employing a joint analysis of SPIDER and Planck data in the harmonic domain, assumes a modified-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the template amplitude and $r$ parameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio from Feldman-Cousins and Bayesian constructions, finding $r<0.11$ and $r<0.19$, respectively. Roughly half the uncertainty in $r$ derives from noise associated with the template subtraction. New data at 280 GHz from SPIDER's second flight will complement the Planck polarization maps, providing powerful measurements of the polarized Galactic dust emission., Comment: 29 pages, 13 figures

In this work we describe upgrades to the Spider balloon-borne telescope in preparation for its second flight, currently planned for December 2021. The Spider instrument is optimized to search for a primordial B-mode polarization signature in the cosmic microwave background at degree angular scales. During its first flight in 2015, Spider mapped ~10% of the sky at 95 and 150 GHz. The payload for the second Antarctic flight will incorporate three new 280 GHz receivers alongside three refurbished 95- and 150 GHz receivers from Spider's first flight. In this work we discuss the design and characterization of these new receivers, which employ over 1500 feedhorn-coupled transition-edge sensors. We describe pre-flight laboratory measurements of detector properties, and the optical performance of completed receivers. These receivers will map a wide area of the sky at 280 GHz, providing new information on polarized Galactic dust emission that will help to separate it from the cosmological signal., Comment: 13 pages, 8 figures; as published in the conference proceedings for SPIE Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy X (2020)

Given the recent advances in gravitational-wave detection technologies, the detection and characterisation of gravitational-wave backgrounds (GWBs) with the Laser Interferometer Space Antenna (LISA) is a real possibility. To assess the abilities of the LISA satellite network to reconstruct anisotropies of different angular scales and in different directions on the sky, we develop a map-maker based on an optimal quadratic estimator. The resulting maps are maximum likelihood representations of the GWB intensity on the sky integrated over a broad range of frequencies. We test the algorithm by reconstructing known input maps with different input distributions and over different frequency ranges. We find that, in an optimal scenario of well understood noise and high frequency, high SNR signals, the maximum scales LISA may probe are $\ell_{\rm max} \lesssim 15$. The map-maker also allows to test the directional dependence of LISA noise, providing insight on the directional sky sensitivity we may expect., Comment: Corresponding author: Arianna I. Renzini, as a part of their PhD thesis. 13 pages, 9 figures

Timely estimation of the current value for COVID-19 reproduction factor $R$ has become a key aim of efforts to inform management strategies. $R$ is an important metric used by policy-makers in setting mitigation levels and is also important for accurate modelling of epidemic progression. This brief paper introduces a method for estimating $R$ from biased case testing data. Using testing data, rather than hospitalisation or death data, provides a much earlier metric along the symptomatic progression scale. This can be hugely important when fighting the exponential nature of an epidemic. We develop a practical estimator and apply it to Scottish case testing data to infer a current (20 May 2020) $R$ value of $0.74$ with $95\%$ confidence interval $[0.48 - 0.86]$.

We construct a model for the angular power spectrum of the instrumental noise in interferometer networks mapping gravitational wave backgrounds (GWBs) as a function of detector noise properties, network configuration and scan strategy. We use the model to calculate the noise power spectrum for current and future ground-based experiments, as well as for planned space missions. We present our results in a language similar to that used in cosmic microwave background and intensity mapping experiments, and connect the formalism with the sensitivity curves that are common lore in GWB analyses. Our formalism is implemented in a lightweight python module that we make publicly available at https://github.com/damonge/schNell., Comment: Comments welcome. Code available at https://github.com/damonge/schNell

Metric perturbations affect the phase of gravitational waves as they propagate through the inhomogeneous universe. This effect causes Stochastic Gravitational Wave Backgrounds (SGWBs) to lose any phase coherence that may have been present at emission or horizon entry. We show that, for a standard cosmological model, this implies complete loss of coherence above frequencies $f \sim 10^{-12}$ Hz. The result is that any attempts to map SGWBs using phase-coherent methods have no foreseeable applications. Incoherent methods that solve directly for the intensity of the SGWBs are the only methods that can reconstruct the angular dependence of any SGWB., Comment: 6 pages, 3 figures. v2: typos corrected

Signals from millisecond pulsars travel to us on geodesics along the line-of-sight that are affected by the space--time metric. The exact path-geometry and redshifting along the geodesics determine the observed Time-of-Arrival (ToA) of the pulses. The metric is determined by the distribution of dark matter, gas, and stars in the galaxy and, in the final stages of travel, by the distribution of solar system bodies. The inhomogeneous distribution of stellar masses can have a small but significant statistical effect on the ToAs through the perturbation of geodesics. This will result in additional noise in ToA observations that may affect Pulsar Timing Array (PTA) constraints on gravitational waves at very low frequencies. We employ a simple model for the stellar distribution in our galaxy to estimate the scale of both static and dynamic sources of what we term generically "geodesic noise". We find that geodesic noise has a standard deviation of ${\cal O}(10)$ ns for typical lines-of-sight. This suggests geodesic noise is relevant for estimates of PTA sensitivity and may limit future efforts for detection of gravitational waves by PTAs., Comment: 4 pages, 2 figures, 1 table

Future mm-wave and sub-mm space missions will employ large arrays of multiplexed Transition Edge Sensor (TES) bolometers. Such instruments must contend with the high flux of cosmic rays beyond our atmosphere that induce "glitches" in bolometer data, which posed a challenge to data analysis from the Planck bolometers. Future instruments will face the additional challenges of shared substrate wafers and multiplexed readout wiring. In this work we explore the susceptibility of modern TES arrays to the cosmic ray environment of space using two data sets: the 2015 long-duration balloon flight of the SPIDER cosmic microwave background polarimeter, and a laboratory exposure of SPIDER flight hardware to radioactive sources. We find manageable glitch rates and short glitch durations, leading to minimal effect on SPIDER analysis. We constrain energy propagation within the substrate through a study of multi-detector coincidences, and give a preliminary look at pulse shapes in laboratory data., Comment: 9 pages, 6 figures, Proceedings of the 18th International Workshop on Low Temperature Detectors

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to confidently detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties and distances that is complementary to the information in any associated electromagnetic emission and that is very hard to obtain in any other way. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model., Comment: 26 pages, 2 figures. White paper submitted to ESA's Voyage 2050 call on behalf of the LISA Consortium 2050 Task Force

We integrate the entire, publicly available, Advanced LIGO (ALIGO) data set to obtain maximum-likelihood constraint maps of the Stochastic Gravitational-Wave Background (SGWB). From these we derive limits on the energy density of the stochastic background $\Omega_{\rm GW}$, and its anisotropy. We find 95% confident limits $\Omega_{\rm GW} < 5.2\times 10^{-8}$ at $50$ Hz for a spectral index $\alpha=2/3$ consistent with a stochastic background due to inspiral events and $\Omega_{\rm GW} < 3.2\times 10^{-7}$ for a scale (frequency) invariant spectrum. We also report upper limits on the angular power spectra $C_\ell$ for three broadband integrations of the data. Finally we present an estimate where we integrate the data into ten separate spectral bins as a first attempt to carry out a model-independent estimate the SGWB and its anisotropies., Comment: 9 pages, 8 figures

The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile that promises to provide breakthrough discoveries in fundamental physics, cosmology, and astrophysics. Supported by the Simons Foundation, the Heising-Simons Foundation, and with contributions from collaborating institutions, SO will see first light in 2021 and start a five year survey in 2022. SO has 287 collaborators from 12 countries and 53 institutions, including 85 students and 90 postdocs. The SO experiment in its currently funded form ('SO-Nominal') consists of three 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT). Optimized for minimizing systematic errors in polarization measurements at large angular scales, the SATs will perform a deep, degree-scale survey of 10% of the sky to search for the signature of primordial gravitational waves. The LAT will survey 40% of the sky with arc-minute resolution. These observations will measure (or limit) the sum of neutrino masses, search for light relics, measure the early behavior of Dark Energy, and refine our understanding of the intergalactic medium, clusters and the role of feedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution of the Planck satellite, and roughly an order of magnitude increase in mapping speed over currently operating ("Stage 3") experiments, SO will measure the CMB temperature and polarization fluctuations to exquisite precision in six frequency bands from 27 to 280 GHz. SO will rapidly advance CMB science while informing the design of future observatories such as CMB-S4., Comment: Astro2020 Decadal Project Whitepaper. arXiv admin note: text overlap with arXiv:1808.07445

We integrate the publicly available O1 LIGO time-domain data to obtain maximum-likelihood constraints on the Gravitational Wave Background (GWB) arising from stochastic, persistent signals. Our method produces sky-maps of the strain intensity $I$ as a function of direction on the sky at a reference frequency $f_0$. The data is integrated assuming a set of fixed power-law spectra for the signal. The maps provide upper limits on the amplitude of the GWB density $\Omega_{\rm GW}(f_0)$ and any anisotropy around the background. We find 95\% confidence upper limits of $\Omega_{\rm GW} < 4.8\times 10^{-7}$ at $f_0=50$ Hz with similar constraints on a dipole modulation for the inspiral-dominated stochastic background case., Comment: 5 pages, 3 figures, 3 tables

Given the recent detection of gravitational waves from individual sources it is almost a certainty that some form of background of gravitational waves will be detected in future. The most promising candidate for such a detection are backgrounds made up of incoherent superposition of the signal of unresolved astrophysical or, backgrounds sourced by earlier cosmological events. Such backgrounds will also contain anisotropies about an average value. The information contained in the background level and any anisotropies will be extremely valuable as an astrophysical and cosmological probe. As such, the ability to reconstruct sky maps of the signal will become important as the sensitivity increases. We build and test a pixel--based, maximum--likelihood Gravitational Wave Background (GWB) map-maker that uses the cross-correlation of sets of generalised baselines as input. The resulting maps are a representation of the GWB power, or strain "intensity" on the sky. We test the algorithm by reconstructing known input maps with different baseline configurations. We also apply the map-maker to a subset of the Advance LIGO data., Comment: 13 pages

The so-called "trans-Planckian" problem of inflation may be evaded by positing that modes come into existence only when they became "cis-Planckian" by virtue of expansion. However, this would imply that for any mode a new random realization would have to be drawn every $N$ wavelengths, with $N$ typically of order 1000 (but it could be larger or smaller). Such a re-drawing of realizations leads to a heteroskodastic distribution if the region under observation contains several such independent domains. This has no effect on the sampled power spectrum for a scale-invariant raw spectrum, but at very small scales it leads to a spectral index bias towards scale-invariance and smooths oscillations in the spectrum. The domain structure would also "unsqueeze" some of the propagating waves, i.e., dismantle their standing wave character. By describing standing waves as travelling waves of the same amplitude moving in opposite directions we determine the observational effects of unsqueezing. We find that it would erase the Doppler peaks in the CMB, but only on very small angular scales, where the primordial signal may not be readily accessible. The standing waves in a primordial gravitational wave background would also be turned into travelling waves. This unsqueezing of the gravitational wave background may constitute a detectable phenomenon.

SPIDER is a balloon-borne instrument designed to map the polarization of the millimeter-wave sky at large angular scales. SPIDER targets the B-mode signature of primordial gravitational waves in the cosmic microwave background (CMB), with a focus on mapping a large sky area with high fidelity at multiple frequencies. SPIDER's first longduration balloon (LDB) flight in January 2015 deployed a total of 2400 antenna-coupled Transition Edge Sensors (TESs) at 90 GHz and 150 GHz. In this work we review the design and in-flight performance of the SPIDER instrument, with a particular focus on the measured performance of the detectors and instrument in a space-like loading and radiation environment. SPIDER's second flight in December 2018 will incorporate payload upgrades and new receivers to map the sky at 285 GHz, providing valuable information for cleaning polarized dust emission from CMB maps., Comment: 10 pages, 7 figures, LTD17 Conference

We describe the construction and characterization of the 280 GHz bolometric focal plane units (FPUs) to be deployed on the second flight of the balloon-borne SPIDER instrument. These FPUs are vital to SPIDER's primary science goal of detecting or placing an upper limit on the amplitude of the primordial gravitational wave signature in the cosmic microwave background (CMB) by constraining the B-mode contamination in the CMB from Galactic dust emission. Each 280 GHz focal plane contains a 16 x 16 grid of corrugated silicon feedhorns coupled to an array of aluminum-manganese transition-edge sensor (TES) bolometers fabricated on 150 mm diameter substrates. In total, the three 280 GHz FPUs contain 1,530 polarization sensitive bolometers (765 spatial pixels) optimized for the low loading environment in flight and read out by time-division SQUID multiplexing. In this paper we describe the mechanical, thermal, and magnetic shielding architecture of the focal planes and present cryogenic measurements which characterize yield and the uniformity of several bolometer parameters. The assembled FPUs have high yields, with one array as high as 95% including defects from wiring and readout. We demonstrate high uniformity in device parameters, finding the median saturation power for each TES array to be ~3 pW at 300 mK with a less than 6% variation across each array at one standard deviation. These focal planes will be deployed alongside the 95 and 150 GHz telescopes in the SPIDER-2 instrument, slated to fly from McMurdo Station in Antarctica in December 2018.

Einstein's theory of General Relativity implies that energy, i.e. matter, curves space-time and thus deforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in the case of the Schwarzschild metric, and has been accurately described in the past; however, lensing in the Kerr space-time has received less attention in the literature despite potential practical observational applications. In particular, lensing in such space is not expressible as the gradient of a scalar potential and as such is a source of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiable lensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools of weak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presence of angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-like foreground object on a distribution of background of sources. We verify that the new unique lensing signature is orders of magnitude below current observational bounds for a range of lens configurations., Comment: 16 pages, 11 figures

We present a new upper limit on CMB circular polarization from the 2015 flight of SPIDER, a balloon-borne telescope designed to search for $B$-mode linear polarization from cosmic inflation. Although the level of circular polarization in the CMB is predicted to be very small, experimental limits provide a valuable test of the underlying models. By exploiting the non-zero circular-to-linear polarization coupling of the HWP polarization modulators, data from SPIDER's 2015 Antarctic flight provide a constraint on Stokes $V$ at 95 and 150 GHz from $33<\ell<307$. No other limits exist over this full range of angular scales, and SPIDER improves upon the previous limit by several orders of magnitude, providing 95% C.L. constraints on $\ell (\ell+1)C_{\ell}^{VV}/(2\pi)$ ranging from 141 $\mu K ^2$ to 255 $\mu K ^2$ at 150 GHz for a thermal CMB spectrum. As linear CMB polarization experiments become increasingly sensitive, the techniques described in this paper can be applied to obtain even stronger constraints on circular polarization., Comment: 9 pages, 4 figures, 5 tables - Updated to version accepted for publication in ApJ, modified acknowledgements

In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to calculate the anisotropies in gravitational wave backgrounds resulting from astrophysical and cosmological sources. Our formalism yields expressions for the angular power spectrum of the anisotropies. We show how the anisotropies are sourced by intrinsic, Doppler, Sachs-Wolfe, and Integrated Sachs-Wolfe terms in analogy with Cosmic Microwave Background photons.

Correlations of polarization components in the coordinate frame are a natural basis for searches of parity-violating modes in the Cosmic Microwave Background (CMB). This fact can be exploited to build estimators of parity-violating modes that are {\sl local} and robust with respect to partial-sky coverage or inhomogeneous weighting. As an example application of a method based on these ideas we develop a peak stacking tool that isolates the signature of parity-violating modes. We apply the tool to {\sl Planck} maps and obtain a constraint on the monopole of the polarization rotation angle $\alpha < 0.72$ degrees at $95\%$ We also demonstrate how the tool can be used as a local method for reconstructing maps of direction dependent rotation $\alpha(\hat {n})$., Comment: 9 pages, 5 figures

We describe the cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the Cosmic Microwave Background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015. The mechanisms operate at liquid helium temperature in flight. A three-point contact design keeps the mechanical bearings relatively small but allows for a large (305 mm) diameter clear aperture. A worm gear driven by a cryogenic stepper motor allows for precise positioning and prevents undesired rotation when the motors are depowered. A custom-built optical encoder system monitors the bearing angle to an absolute accuracy of +/- 0.1 degrees. The system performed well in Spider during its successful 16 day flight., Comment: 11 pages, 7 figures, Published in Review of Scientific Instruments. v2 includes reviewer changes and longer literature review