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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

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

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

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

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

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.

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

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

The bispectrum of single-field inflationary trajectories in which the speed of sound of the inflationary trajectories $c_s$ is constant but not equal to the speed of light $c=1$ is explored. The trajectories are generated as random realisations of the Hubble Slow-Roll (HSR) hierarchy and the bispectra are calculated using numerical techniques that extends previous work. This method allows for out-of-slow-roll models with non-trivial time dependence and arbitrarily low $c_s$. The ensembles obtained using this method yield distributions for the shape and scale-dependence of the bispectrum and their relations with the standard inflationary parameters such as scalar spectral tilt $n_s$ and tensor-to-scalar ratio $r$. The distributions demonstrate the squeezed-limit consistency relations for arbitrary single-field inflationary models.

The simplest interpretation of the Bicep2 result is that the scalar primordial power spectrum is slightly suppressed at large scales. These models result in a large tensor-to-scalar ratio $r$. In this work we show that the type of inflationary trajectory favoured by Bicep2 also leads to a larger non-Gaussian signal at large scales, roughly an order of magnitude larger than a standard slow-roll trajectory., Comment: 5 pages, 4 figures

The recent BICEP2 detection of, what is claimed to be primordial $B$-modes, opens up the possibility of constraining not only the energy scale of inflation but also the detailed acceleration history that occurred during inflation. In turn this can be used to determine the shape of the inflaton potential $V(\phi)$ for the first time - if a single, scalar inflaton is assumed to be driving the acceleration. We carry out a Monte Carlo exploration of inflationary trajectories given the current data. Using this method we obtain a posterior distribution of possible acceleration profiles $\epsilon(N)$ as a function of $e$-fold $N$ and derived posterior distributions of the primordial power spectrum $P(k)$ and potential $V(\phi)$. We find that the BICEP2 result, in combination with Planck measurements of total intensity Cosmic Microwave Background (CMB) anisotropies, induces a significant feature in the scalar primordial spectrum at scales $k\sim 10^{-3}$ Mpc$^{-1}$. This is in agreement with a previous detection of a suppression in the scalar power., Comment: 10 pages, 6 figures

We present the technology and control methods developed for the pointing system of the SPIDER experiment. SPIDER is a balloon-borne polarimeter designed to detect the imprint of primordial gravitational waves in the polarization of the Cosmic Microwave Background radiation. We describe the two main components of the telescope's azimuth drive: the reaction wheel and the motorized pivot. A 13 kHz PI control loop runs on a digital signal processor, with feedback from fibre optic rate gyroscopes. This system can control azimuthal speed with < 0.02 deg/s RMS error. To control elevation, SPIDER uses stepper-motor-driven linear actuators to rotate the cryostat, which houses the optical instruments, relative to the outer frame. With the velocity in each axis controlled in this way, higher-level control loops on the onboard flight computers can implement the pointing and scanning observation modes required for the experiment. We have accomplished the non-trivial task of scanning a 5000 lb payload sinusoidally in azimuth at a peak acceleration of 0.8 deg/s$^2$, and a peak speed of 6 deg/s. We can do so while reliably achieving sub-arcminute pointing control accuracy., Comment: 20 pages, 12 figures, Presented at SPIE Ground-based and Airborne Telescopes V, June 23, 2014. To be published in Proceedings of SPIE Volume 9145

The BICEP2 collaboration has reported a strong B mode signal in the CMB polarization, which is well fit by a tensor-to-scalar ratio of r ~ 0.2. This is greater than the upper limit r < 0.11 obtained from the temperature anisotropies under the assumption of a constant scalar spectral index n_s. This discrepancy can be reduced once the statistical error and the contamination from polarized dust are accounted for. If however a large value for r will be confirmed, it will need to be reconciled with the temperature anisotropies data. The most advocated explanation involves a variation of n_s with scales (denoted as running) that has a magnitude significantly greater than the generic slow roll predictions. We instead study the possibility that the large scale temperature anisotropies are not enhanced because of a suppression of the scalar power at large scales. Such a situation can be achieved for instance by a sudden change of the speed of the inflaton (by about 14 %), and we show that it fits the temperature anisotropies and polarization data considerably better than a constant running (its chi^2 improves by ~ 7.5 over that of the constant running, at the cost of one more parameter). We also consider the possibility that the large scale temperature fluctuations are suppressed by an anti-correlation between tensor and scalar modes. Unfortunately, while such effect does affect the temperature fluctuations at large scales, it does not affect the temperature power spectrum and cannot, therefore, help in reconciling a large value of r with the limits from temperature fluctuations., Comment: Published version. 14 pages, 5 figures

We use the Hamilton--Jacobi formalism to constrain the space of possible single field, inflationary Hubble flow trajectories when compared to the WMAP and Planck satellites Cosmic Microwave Background (CMB) results. This method yields posteriors on the space of Hubble Slow Roll (HSR) parameters that uniquely determine the history of the Hubble parameter during the inflating epoch. The trajectories are used to numerically determine the observable primordial power spectrum and bispectra that can then be compared to observations. Our analysis is used to infer the most likely shape of the inflaton potential $V(\phi)$ and also yields a prediction for, $f_{\rm NL}$, the dimensionless amplitude of the non-Gaussian bispectrum., Comment: 11 pages, 12 figures

We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single--field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation allows generally shape and scale dependent bispectra, or dimensionless $f_{NL}$, in the out-of-slow-roll regime. The distributions of $f_{NL}$ for various shapes and HSR proposals are shown as an example of how this procedure can be used within the context of Monte Carlo exploration of inflationary trajectories. We also show how allowing out-of-slow-roll behaviour can lead to a bispectrum that is relatively large for equilateral shapes., Comment: 13 pages, 7 figures

The Hamilton-Jacobi (HJ) approach for exploring inflationary trajectories is employed in the generation of generalised inflationary non-Gaussian signals arising from single field inflation. Scale dependent solutions for $f_{NL}$ are determined via the numerical integration of the three--point function in the curvature perturbation. This allows the full exploration of single field inflationary dynamics in the out-of-slow-roll regime and opens up the possibility of using future observations of non-Gaussianity to constraint the inflationary potential using model-independent methods. The distribution of `equilateral' $f_{NL}$ arising from single field inflation with both canonical and non-canonical kinetic terms are show as an example of the application of this procedure.

Model-independent parametrisations for examining departures from General Relativity have been increasingly studied over the past few years. Various observables have been used to constrain the parameters and forecasts for future surveys have been carried out. In one such forecast, galaxy cluster counts were used to constrain the parameters. Here, we carry out a limited set of $N$-body simulations, with a modified Poisson equation, to examine the accuracy of existing mass functions for modified gravity cosmologies. As well as altering the gravitational calculation, we include the effect of a screening scale to ensure consistency of the theory with solar system tests. Our results suggest that if a screening scale exists its effect can be taken into account in the cluster count calculation through its effect on the linear matter power spectrum. If this is done, the accuracy of the standard mass function formalism in modified gravity theories with reasonably small departures from General Relativity, as tested in this work, is comparable to the standard case., Comment: 7 pages, 3 figures

The CERN-OPERA experiment claims to have measured a one-way speed of neutrinos that is apparently faster than the speed of light c. One-way speed measurements such as these inevitably require a convention for the synchronisation of clocks in non-inertial frames since the Earth is rotating. We argue that the effect of the synchronisation convention is not properly taken into account in the OPERA analysis and may well invalidate their interpretation of superluminal neutrino velocity., Comment: 3 pages, added reference and expanded some comments

Model-independent parametrisations of modified gravity have attracted a lot of attention over the past few years and numerous combinations of experiments and observables have been suggested to constrain the parameters used in these models. Galaxy clusters have been mentioned, but not looked at as extensively in the literature as some other probes. Here we look at adding galaxy clusters into the mix of observables and examine how they could improve the constraints on the modified gravity parameters. In particular, we forecast the constraints from combining Planck satellite Cosmic Microwave Background (CMB) measurements and Sunyaev-Zeldovich (SZ) cluster catalogue with a DES-like weak lensing survey. We find that cluster counts significantly improve the constraints over those derived using CMB and WL. We then look at surveys further into the future, to see how much better it may be feasible to make the constraints., Comment: 14 pages, 8 figures, Updated to match version published in JCAP

We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) modifications alone do not result in suitable curvature perturbations whilst Scalar-Tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes., Comment: 9 pages

Spider is a balloon-borne array of six telescopes that will observe the Cosmic Microwave Background. The 2624 antenna-coupled bolometers in the instrument will make a polarization map of the CMB with approximately one-half degree resolution at 145 GHz. Polarization modulation is achieved via a cryogenic sapphire half-wave plate (HWP) skyward of the primary optic. We have measured millimeter-wave transmission spectra of the sapphire at room and cryogenic temperatures. The spectra are consistent with our physical optics model, and the data gives excellent measurements of the indices of A-cut sapphire. We have also taken preliminary spectra of the integrated HWP, optical system, and detectors in the prototype Spider receiver. We calculate the variation in response of the HWP between observing the CMB and foreground spectra, and estimate that it should not limit the Spider constraints on inflation.

A model of Lorentz invariant random fluctuations in photon polarization is presented. The effects are frequency dependent and affect the polarization of photons as they propagate through space. We test for this effect by confronting the model with the latest measurements of polarization of Cosmic Microwave Background (CMB) photons., Comment: 4 pages, 1 figure

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters., Comment: 23 pages, 9 figures

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models, and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill-defined at the quantum level in the high energy/sub horizon regime (and create serious problems for finding a well behaved UV completion); (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without vev in a FRW geometry, and of a vector with vev plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular., Comment: 44 pages, 11 figures

Vector perturbations sourced by topological defects can generate rotations in the lensing of background galaxies. This is a potential smoking gun for the existence of defects since rotation generates a curl-like component in the weak lensing signal which is not generated by standard density perturbations at linear order. This rotation signal is calculated as generated by cosmic strings. Future large scale weak lensing surveys should be able to detect this signal even for string tensions an order of magnitude lower than current constraints.

We develop a method to reconstruct the primordial power spectrum, P(k), using both temperature and polarisation data from the joint analysis of a number of Cosmic Microwave Background (CMB) observations. The method is an extension of the Richardson-Lucy algorithm, first applied in this context by Shafieloo & Souradeep. We show how the inclusion of polarisation measurements can decrease the uncertainty in the reconstructed power spectrum. In particular, the polarisation data can constrain oscillations in the spectrum more effectively than total intensity only measurements. We apply the estimator to a compilation of current CMB results. The reconstructed spectrum is consistent with the best-fit power spectrum although we find evidence for a `dip' in the power on scales k ~ 0.002 Mpc^-1. This feature appears to be associated with the WMAP power in the region 18 < l < 26 which is consistently below best--fit models. We also forecast the reconstruction for a simulated, Planck-like survey including sample variance limited polarisation data., Comment: 8 pages, 5 figures, comments welcome

How did the universe evolve? The fine angular scale (l>1000) temperature and polarization anisotropies in the CMB are a Rosetta stone for understanding the evolution of the universe. Through detailed measurements one may address everything from the physics of the birth of the universe to the history of star formation and the process by which galaxies formed. One may in addition track the evolution of the dark energy and discover the net neutrino mass. We are at the dawn of a new era in which hundreds of square degrees of sky can be mapped with arcminute resolution and sensitivities measured in microKelvin. Acquiring these data requires the use of special purpose telescopes such as the Atacama Cosmology Telescope (ACT), located in Chile, and the South Pole Telescope (SPT). These new telescopes are outfitted with a new generation of custom mm-wave kilo-pixel arrays. Additional instruments are in the planning stages., Comment: Science White Paper submitted to the US Astro2010 Decadal Survey. Full list of 177 author available at http://cmbpol.uchicago.edu

We prove that the anisotropic inflationary background of the Ackerman-Carroll-Wise model, characterized by a fixed-norm vector field, is unstable. We found the instability by explicitly solving the linearized equations for the most general set of perturbations around this background, and by noticing that the solutions diverge close to horizon crossing. This happens because one perturbation becomes a ghost at that moment. A simplified computation, with only the perturbations of the vector field included, shows the same instability, clarifying the origin of the problem. We then discuss several other models, with a particular emphasis on the case of a nonminimal coupling to the curvature, in which vector fields are used either to support an anisotropic expansion, or to generate cosmological perturbations on an isotropic background. In many cases, the mass term of the vector needs to have the ``wrong'' sign; we show that, as a consequence, the longitudinal vector mode is a ghost (a field with negative kinetic term, and negative energy; not simply a tachyon). We comment on problems that arise at the quantum level. In particular, the presence of a ghost can be a serious difficulty for the UV completion that such models require in the sub-horizon regime., Comment: 22 pages, 4 figures

Models with vector fields acquiring a non-vanishing vacuum expectation value along one spatial direction have been proposed to sustain a prolonged stage of anisotropic accelerated expansion. Such models have been used for realizations of early time inflation, with a possible relation to the large scale CMB anomalies, or of the late time dark energy. We show that, quite generally, the concrete realizations proposed so far are plagued by instabilities (either ghosts, or unstable growth of the linearized perturbations) which can be ultimately related to the longitudinal vector polarization present in them. Phenomenological results based on these models are therefore unreliable.