## Publications

141 results found

Mentasti G, Contaldi CR, Peloso M, 2023, Intrinsic limits on the detection of the anisotropies of the stochastic gravitational wave background, *Physical Review Letters*, Vol: 131, ISSN: 0031-9007

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.

Auclair P, Bacon D, Baker T,
et al., 2023, Cosmology with the Laser Interferometer Space Antenna, *Living Reviews in Relativity*, Vol: 26, ISSN: 1433-8351

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.

Mentasti G, Contaldi CR, Peloso M, 2023, Prospects for detecting anisotropies and polarization of the stochastic gravitational wave background with ground-based detectors, *Journal of Cosmology and Astroparticle Physics*, Vol: 2023, Pages: 053-053, ISSN: 1475-7516

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 Script O(10-3 – 10-2) accuracy relative to the isotropic component, and an Script O(10-3) amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

Filippini JP, Gambrel AE, Rahlin AS,
et al., 2022, In-Flight Gain Monitoring of SPIDER's Transition-Edge Sensor Arrays, *JOURNAL OF LOW TEMPERATURE PHYSICS*, Vol: 209, Pages: 649-657, ISSN: 0022-2291

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- Citations: 1

Bartolo N, Bertacca D, Caldwell R,
et al., 2022, Probing anisotropies of the Stochastic Gravitational Wave Background with LISA, *Journal of Cosmology and Astroparticle Physics*, Vol: 2022, ISSN: 1475-7516

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 β ΩGW ∼ 2 × 10-11 is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor ∼ 103 β 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.

Auclair P, Bacon D, Baker T, et al., 2022, Cosmology with the Laser Interferometer Space Antenna, Publisher: ArXiv

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

Leung JS-Y, Hartley J, Nagy JM,
et al., 2022, A Simulation-based Method for Correcting Mode Coupling in CMB Angular Power Spectra, *ASTROPHYSICAL JOURNAL*, Vol: 928, ISSN: 0004-637X

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- Citations: 2

Collaboration SPIDER, Ade PAR, Amiri M,
et al., 2022, A constraint on primordial B-modes from the first flight of the spider balloon-borne telescope, *The Astrophysical Journal: an international review of astronomy and astronomical physics*, Vol: 927, Pages: 1-26, ISSN: 0004-637X

We present the first linear polarization measurements from the 2015long-duration balloon flight of SPIDER, an experiment designed to map thepolarization of the cosmic microwave background (CMB) on degree angular scales.Results from these measurements include maps and angular power spectra fromobservations of 4.8% of the sky at 95 and 150 GHz, along with the results ofinternal consistency tests on these data. While the polarized CMB anisotropyfrom primordial density perturbations is the dominant signal in this region ofsky, Galactic dust emission is also detected with high significance; Galacticsynchrotron emission is found to be negligible in the SPIDER bands. We employtwo independent foreground-removal techniques in order to explore thesensitivity of the cosmological result to the assumptions made by each. Theprimary method uses a dust template derived from Planck data to subtract theGalactic dust signal. A second approach, employing a joint analysis of SPIDERand Planck data in the harmonic domain, assumes a modified-blackbody model forthe spectral energy distribution of the dust with no constraint on its spatialmorphology. Using a likelihood that jointly samples the template amplitude and$r$ parameter space, we derive 95% upper limits on the primordialtensor-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 280GHz from SPIDER's second flight will complement the Planck polarization maps,providing powerful measurements of the polarized Galactic dust emission.

Golat S, Contaldi CR, 2022, All-sky analysis of astrochronometric signals induced by gravitational waves, *Physical Review D*, Vol: 105, Pages: 1-15, ISSN: 2470-0010

We introduce a unified spin-weighted 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 analyze “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 generalized Hellings-Downs correlation functions. The spin-weighted formalism also allows an explicit connection between correlation components and the spin of gravitational wave polarizations and any presence of chirality. We also calculate expected signal-to-noise ratios for observables to compare the utility of timing and deflection observables.

Renzini A, Romano JD, Contaldi CR,
et al., 2022, Comparison of maximum-likelihood mapping methods for gravitational-wave backgrounds, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 105, Pages: 1-12, ISSN: 1550-2368

Detection of a stochastic background of gravitational waves is likely to occur in the next few years. Beyond searches for the isotropic component of a stochastic gravitational-wave background, 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 Observatory (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 analyzing simple toy models of time-stream data, and we 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 the resolution of the detector. Otherwise, the amplitude-phase mapping method leads to an overall loss of 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.

Gambrel AE, Rahlin AS, Song X,
et al., 2021, The XFaster power spectrum and likelihood estimator for the analysis of cosmic microwave background maps, *The Astrophysical Journal: an international review of astronomy and astronomical physics*, Vol: 922, Pages: 1-17, ISSN: 0004-637X

We present the XFaster analysis package, a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. It 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-Cℓ–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 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.

Golat S, Contaldi CR, 2021, Geodesic noise and gravitational wave observations by pulsar timing arrays, *Physics Letters B: Nuclear Physics and Particle Physics*, Vol: 818, Pages: 1-4, ISSN: 0370-2693

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 (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.

Shaw EC, Ade PAR, Akers S, et al., 2020, Design and pre-flight performance of SPIDER 280 GHz receivers, SPIE ASTRONOMICAL TELESCOPES + INSTRUMENTATION, Publisher: SPIE, Pages: 1-1

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.

Margalit A, Contaldi CR, Pieroni M, 2020, Phase decoherence of gravitational wave backgrounds, *Physical Reveiw D*

Metric perturbations affect the phase of gravitational waves as theypropagate through the inhomogeneous universe. This effect causes StochasticGravitational Wave Backgrounds (SGWBs) to lose any phase coherence that mayhave been present at emission or horizon entry. We show that, for a standardcosmological model, this implies complete loss of coherence above frequencies$f \sim 10^{-12}$ Hz. The result is that any attempts to map SGWBs usingphase-coherent methods have no foreseeable applications. Incoherent methodsthat solve directly for the intensity of the SGWBs are the only methods thatcan reconstruct the angular dependence of any SGWB.

Contaldi CR, Pieroni M, Renzini A,
et al., 2020, Maximum likelihood map making with the Laser Interferometer Space Antenna, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 102, Pages: 043502 – 1-043502 – 13, ISSN: 1550-2368

Given the recent advances in gravitational-wave detection technologies, the detection and characterization 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 ℓmax≲15. The map-maker also allows to test the directional dependence of LISA noise, providing insight on the directional sky sensitivity we may expect.

Alonso D, Contaldi CR, Cusin G,
et al., 2020, Noise angular power spectrum of gravitational wave background experiments, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 101, Pages: 124048 – 1-124048 – 17, ISSN: 1550-2368

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.

Contaldi CR, 2020, COVID-19: nowcasting reproduction factors using biased case testing data, Publisher: arXiv

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 animportant metric used by policy-makers in setting mitigation levels and is alsoimportant for accurate modelling of epidemic progression. This brief paperintroduces a method for estimating $R$ from biased case testing data. Usingtesting data, rather than hospitalisation or death data, provides a muchearlier metric along the symptomatic progression scale. This can be hugelyimportant when fighting the exponential nature of an epidemic. We develop apractical estimator and apply it to Scottish case testing data to infer acurrent (20 May 2020) $R$ value of $0.74$ with $95\%$ confidence interval$[0.48 - 0.86]$.

Osherson B, Filippini JP, Fu J,
et al., 2020, Particle response of antenna-coupled TES arrays: results from SPIDER and the laboratory, *Journal of Low Temperature Physics*, Vol: 199, Pages: 1127-1136, ISSN: 0022-2291

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.

Renzini A, Contaldi CR, 2019, Improved limits on a stochastic gravitational-wave background and its anisotropies from Advanced LIGO O1 and O2 runs, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 100, Pages: 063527-1-063527-9, ISSN: 1550-2368

We integrate the entire, publicly available, Advanced LIGO dataset 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 ΩGW and its anisotropy. We find 95% confident limits ΩGW<5.2×10−8 at 50 Hz for a spectral index α=2/3 consistent with a stochastic background due to inspiral events and ΩGW<3.2×10−7 for a scale (frequency) invariant spectrum. We also report upper limits on the angular power spectra Cℓ for three broadband integrations of the data. Finally, we present an estimate in which we integrate the data into ten separate spectral bins as a first attempt to carry out a model-independent estimate of the SGWB and its anisotropies.

Baker J, Baker T, Carbone C, et al., 2019, High angular resolution gravitational wave astronomy, Publisher: arXiv

Since the very beginning of astronomy the location of objects on the sky hasbeen a fundamental observational quantity that has been taken for granted.While precise two dimensional positional information is easy to obtain forobservations in the electromagnetic spectrum, the positional accuracy ofcurrent and near future gravitational wave detectors is limited to between tensand hundreds of square degrees, which makes it extremely challenging toidentify the host galaxies of gravitational wave events or to confidentlydetect any electromagnetic counterparts. Gravitational wave observationsprovide information on source properties and distances that is complementary tothe information in any associated electromagnetic emission and that is veryhard to obtain in any other way. Observing systems with multiple messengersthus has scientific potential much greater than the sum of its parts. Agravitational wave detector with higher angular resolution would significantlyincrease the prospects for finding the hosts of gravitational wave sources andtriggering a multi-messenger follow-up campaign. An observatory with arcminuteprecision or better could be realised within the Voyage 2050 programme bycreating a large baseline interferometer array in space and would havetransformative scientific potential. Precise positional information of standardsirens would enable precision measurements of cosmological parameters and offernew insights on structure formation; a high angular resolution gravitationalwave observatory would allow the detection of a stochastic background andresolution of the anisotropies within it; it would also allow the study ofaccretion processes around black holes; and it would have tremendous potentialfor tests of modified gravity and the discovery of physics beyond the StandardModel.

Collaboration TSO, Abitbol MH, Adachi S, et al., 2019, The Simons observatory: Astro2020 decadal project whitepaper, Publisher: arXiv

The Simons Observatory (SO) is a ground-based cosmic microwave background(CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile thatpromises to provide breakthrough discoveries in fundamental physics, cosmology,and astrophysics. Supported by the Simons Foundation, the Heising-SimonsFoundation, and with contributions from collaborating institutions, SO will seefirst light in 2021 and start a five year survey in 2022. SO has 287collaborators from 12 countries and 53 institutions, including 85 students and90 postdocs. The SO experiment in its currently funded form ('SO-Nominal') consists ofthree 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large ApertureTelescope (LAT). Optimized for minimizing systematic errors in polarizationmeasurements at large angular scales, the SATs will perform a deep,degree-scale survey of 10% of the sky to search for the signature of primordialgravitational waves. The LAT will survey 40% of the sky with arc-minuteresolution. These observations will measure (or limit) the sum of neutrinomasses, search for light relics, measure the early behavior of Dark Energy, andrefine our understanding of the intergalactic medium, clusters and the role offeedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution ofthe Planck satellite, and roughly an order of magnitude increase in mappingspeed over currently operating ("Stage 3") experiments, SO will measure the CMBtemperature and polarization fluctuations to exquisite precision in sixfrequency bands from 27 to 280 GHz. SO will rapidly advance CMB science whileinforming the design of future observatories such as CMB-S4.

Renzini AI, Contaldi CR, 2019, Gravitational wave background sky maps from advanced LIGO O1 data, *PHYSICAL REVIEW LETTERS*

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 f0. 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 ΩGW(f0) and any anisotropy around the background. We find 95\% confidence upper limits of ΩGW<4.8×10−7 at f0=50 Hz with similar constraints on a dipole modulation for the inspiral-dominated stochastic background case.

Bergman AS, Ade PAR, Akers S,
et al., 2018, 280 GHz Focal Plane Unit Design and Characterization for the SPIDER-2 Suborbital Polarimeter, *JOURNAL OF LOW TEMPERATURE PHYSICS*, Vol: 193, Pages: 1075-1084, ISSN: 0022-2291

Renzini AI, Contaldi CR, 2018, Mapping incoherent gravitational wave backgrounds, *Monthly Notices of the Royal Astronomical Society*, Vol: 481, Pages: 4650-4661, ISSN: 0035-8711

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 is 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 generalized 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 Advanced Laser Interferometer Gravitational Wave observatory data.

Gualtieri R, Filippini JP, Ade PAR,
et al., 2018, SPIDER: CMB polarimetry from the edge of space, *Journal of Low Temperature Physics*, Vol: 193, Pages: 1112-1121, ISSN: 0022-2291

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 long-duration 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.

Bartolo N, Domcke V, Figueroa DG,
et al., 2018, Probing non-Gaussian stochastic gravitational wave backgrounds with LISA, *Journal of Cosmology and Astroparticle Physics*, Vol: 2018, ISSN: 1475-7516

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.

Contaldi CR, Magueijo J, 2018, Unsqueezing of standing waves due to inflationary domain structure, *Physical Review D*, Vol: 98, ISSN: 2470-0010

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 redrawing 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 toward 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 traveling 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 cosmic microwave background, but only on very small angular scales, in which the primordial signal may not be readily accessible. The standing waves in a primordial gravitational wave background would also be turned into traveling waves. This unsqueezing of the gravitational wave background may constitute a detectable phenomenon.

Nagy JM, Ade PAR, Amiri M,
et al., 2017, A New Limit on CMB Circular Polarization from SPIDER, *Astrophysical Journal*, Vol: 844, ISSN: 0004-637X

We present a new upper limit on cosmic microwave background (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 nonzero circular-to-linear polarization coupling of the half-wave plate polarization modulators, data from Spider's 2015 Antarctic flight provide a constraint on Stokes V at 95 and 150 GHz in the range $33\lt {\ell }\lt 307$. No other limits exist over this full range of angular scales, and Spider improves on 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 to 255 μK2 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.

Renzini AI, Contaldi CR, Heavens A, 2017, Mapping weak lensing distortions in the Kerr metric, *Physical Review D*, Vol: 95, ISSN: 2470-0010

Einstein’s theory of General Relativity implies that energy, i.e., matter, curves space-time and thusdeforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in thecase of the Schwarzschild metric and has been accurately described in the past; however, lensing in the Kerrspace-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 asource of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiablelensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools ofweak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presenceof angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-likeforeground object on a distribution of background of sources. We verify that the new unique lensingsignature is orders of magnitude below current observational bounds for a range of lens configurations.

Contaldi CR, 2017, Anisotropies of gravitational wave backgrounds: a line of sight approach, *Physics Letters B*, Vol: 771, Pages: 9-12, ISSN: 0370-2693

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.

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