arXiv subjects

Marc Lilley

Publications and source records attributed to Marc Lilley.

At least 19 recordsLinked to original sources

arXiv2024

Optimal design of interpolation methods for time-delay interferometry

Time-delay interferometry (TDI) suppresses laser frequency noise by forming linear combinations of time-shifted interferometric measurements. The time-shift operation is implemented by interpolating discretely sampled data. To enable in-band laser noise reduction by eight to nine orders of magnitude, interpolation has to be performed with high accuracy. Optimizing the design of those interpolation methods is the focus of this work. Previous research that studied constant time-shifts suggested Lagrange interpolation as the interpolation method for TDI. Its transfer function performs well at low frequency but requires a high number of coefficients. Furthermore, when applied in TDI we observed prominent time-domain features when a time-varying shift scanned over a pure integer sample shift. To limit this effect we identify an additional requirement for the interpolation kernel: when considering time-varying shifts the interpolation kernel must be sufficiently smooth to avoid unwanted time-domain transitions that produce glitch-like features in power spectral density estimates. The Lagrange interpolation kernel exhibits a discontinuous first derivative by construction, which is insufficient for the application to LISA or other space-based GW observatories. As a solution we propose a novel design method for interpolation kernels that respect a predefined requirement on in-band interpolation residuals and that possess continuous derivatives up to a prescribed order. Using this method we show that an interpolation kernel with 22 coefficients is sufficient to respect LISA's picometre-requirement and to allow for a continuous first derivative which suppresses the magnitude of the time-domain transition adequately. The reduction from 42 (Lagrange interpolation) to 22 coefficients enables us to save computational cost and increases robustness against artefacts in the data.

astro-ph.IM↗

arXiv2023

Dynamical simulations of colliding superconducting strings

We study the collisions of elastic superconducting strings, also referred to as current-carrying strings, formed in a $U_{\rm local}(1) \times U_{\rm global}(1)$ field-theory model, using three-dimensional numerical field-theoretic simulations. The breaking of $U_{\rm local}(1)$ leads to string formation via the Higgs mechanism, while the scalar field of the second $U_{\rm global}(1)$ carries the current, which condenses onto the string. We construct straight and static superconducting string solutions numerically and identify the regions in which they exist in the model parameter space. We then perform dynamical simulations for colliding superconducting strings with various collision angles and collision velocities. We explore the kinematic parameter space for six sets of model parameters characterising the coupling between the two scalar fields and the current on the string. The final states of the strings (after the collision) are reported diagrammatically. We classify them into four categories: (i) regular intercommutation, (ii) double intercommutation, (iii) bound state, and (iv) expanding string solution. We find that the outcome of the collision process is the regular intercommutation of the colliding strings in most of the kinematic parameter space while they form bound states for small velocities and small angles. We also find that the strings undergo two successive intercommutations and, therefore, pass through one other in a small region corresponding to relatively small angles and velocities of order c/2. The string structure breaks down when there is a relatively large coupling between the two scalar fields, even if each string is stable before the occurrence of the collision.

hep-ph↗

arXiv2023

Laser noise residuals in LISA from onboard processing and time-delay interferometry

Time-delay interferometry (TDI) is a crucial step in the on-ground data processing pipeline of the Laser Interferometer Space Antenna (LISA), as it reduces otherwise overwhelming laser noise and allows for the detection of gravitational waves. This being said, several laser noise couplings have been identified that limit the performance of TDI. First, on-board processing, which is used to decimate the sampling rate from tens of MHz down to a few Hz, requires careful design of the anti-aliasing filters to mitigate folding of laser noise power into the observation band. Furthermore, the flatness of those filters is important to limit the effect of the flexing-filtering coupling. Secondly, the post-processing delays applied in TDI are subject to ranging and interpolation errors. All of these effects are partially described in the literature. In this paper, we present them in a unified framework and give a more complete description of aliased laser noise and the coupling of interpolation errors. Furthermore, for the first time, we discuss the impact of laser locking on laser noise residuals in the final TDI output. To verify the validity of the analytic PSD models we derive, we run numerical simulations using LISA Instrument and calculate second-generation TDI variables with PyTDI. We consider a setup with six independent lasers and with locked lasers (locking configuration N1-12). We find that laser locking indeed affects the laser noise residual in the TDI combination as it introduces correlations among the six lasers inducing slight modulations of the PSD compared to the case of six independent lasers. This implies further studies on laser noise residuals should consider the various locking configurations to produce accurate results.

astro-ph.IM↗

arXiv2023

End-to-end simulation and analysis pipeline for LISA

The data produced by the future space-based millihertz gravitational-wave detector LISA will require nontrivial pre-processing, which might affect the science results. It is crucial to demonstrate the feasibility of such processing algorithms and assess their performance and impact on the science. We are building an end-to-end pipeline that includes state-of-the-art simulations and noise reduction algorithms. The simulations must include a detailed model of the full measurement chain, capturing the main features that affect the instrument performance and processing algorithms. In particular, we include in these simulations, for the first time, proper relativistic treatment of reference frames with realistic numerically-optimized orbits; a model for onboard clocks and clock synchronization measurements; proper modeling of total laser frequencies, including laser locking, frequency planning and Doppler shifts; and a better treatment of onboard processing. Using these simulated data, we show that our pipeline is able to reduce the most critical noises and form synchronized observables. By injecting signals from a verification binary, we demonstrate that good parameter estimation can be obtained on this more realistic setup, extending existing results from previous LISA Data Challenges.

astro-ph.IM↗

arXiv2023

Stochastic gravitational wave background reconstruction for a non-equilateral and unequal-noise LISA constellation

We explore the impact of choosing different sets of Time-Delay Interferometry (TDI) variables for detecting and reconstructing Stochastic Gravitational Wave Background (SGWB) signals and estimating the instrumental noise in LISA. Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations.

gr-qc↗

arXiv2022

Accurate CMB covariance matrices: exact calculation and approximations

Accurate covariance matrices are required for a reliable estimation of cosmological parameters from pseudo-power spectrum estimators. In this work, we focus on the analytical calculation of covariance matrices. We consider the case of observations of the Cosmic Microwave Background in temperature and polarization on a small footprint such as in the SPT-3G experiment, which observes 4% of the sky. Power spectra evaluated on small footprints are expected to have large correlations between modes, and these need to be accurately modelled. We present, for the first time, an algorithm that allows an efficient (but computationally expensive) exact calculation of analytic covariance matrices. Using it as our reference, we test the accuracy of existing fast approximations of the covariance matrix. We find that, when the power spectrum is binned in wide bandpowers, current approaches are correct up to the 5% level on the SPT-3G small sky footprint. Furthermore, we propose a new approximation which improves over the previous ones reaching a precision of 1% in the wide bandpowers case and generally more than 4 times more accurate than current approaches. Finally, we derive the covariance matrices for mask-corrected power spectra estimated by the PolSpice code. In particular, we include, in the case of a small sky fraction, the effect of the apodization of the large scale modes. While we considered the specific case of the CMB, our results are applicable to any other cosmological probe which requires the calculation of pseudo-power spectrum covariance matrices.

astro-ph.CO↗

arXiv2022

Time delay interferometry without clock synchronisation

Time-delay interferometry (TDI) is a data processing technique for LISA designed to suppress the otherwise overwhelming laser noise by several orders of magnitude. It is widely believed that TDI can only be applied once all phase or frequency measurements from each spacecraft have been synchronized to a common time frame. We demonstrate analytically, using as an example the commonly-used Michelson combination X, that TDI can be computed using the raw, unsynchronized data, thereby avoiding the need for an initial synchronization processing step and significantly simplifying the initial noise reduction pipeline. Furthermore, the raw data is free of any potential artifacts introduced by clock synchronization and reference frame transformation algorithms, which allows to operate directly on the MHz beatnotes. As a consequence, in-band clock noise is directly suppressed as part of TDI, in contrast to the approach previously proposed in the literature (in which large trends in the beatnotes are removed before the main laser-noise reduction step, and clock noise is suppressed in an extra processing step). We validate our algorithm with full-scale numerical simulations that use LISA Instrument and PyTDI and show that we reach the same performance levels as the previously proposed methods, ultimately limited by the clock sideband stability.

gr-qc↗

arXiv2020

Effect of filters on the time-delay interferometry residual laser noise for LISA

The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. Laser frequency noise enters the interferometric measurements and dominates the expected gravitational signals by many orders of magnitude. Time-delay interferometry (TDI) is a technique that reduces this laser noise by synthesizing virtual equal-arm interferometric measurements. Laboratory experiments and numerical simulations have confirmed that this reduction is sufficient to meet the scientific goals of the mission in proof-of-concept setups. In this paper, we show that the on-board antialiasing filters play an important role in TDI's performance when the flexing of the constellation is accounted for. This coupling was neglected in previous studies. To reach an optimal reduction level, filters with vanishing group delays must be used on board or synthesized off-line. We propose a theoretical model of the residual laser noise including this flexing-filtering coupling. We also use two independent simulators to produce realistic measurement signals and compute the corresponding TDI Michelson variables. We show that our theoretical model agrees with the simulated data with exquisite precision. Using these two complementary approaches, we confirm TDI's ability to reduce laser frequency noise in a more realistic mission setup. The theoretical model provides insight on filter design and implementation.

astro-ph.IM↗

arXiv2019

Assessing the detectability of a Stochastic Gravitational Wave Background with LISA, using an excess of power approach

The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space. It is scheduled to fly in the early 2030's. LISA design predicts sensitivity levels that enable the detection a Stochastic Gravitational Wave Background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes Factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.

astro-ph.IM↗

arXiv2017

Y-junction intercommutations of current carrying strings

Under certain conditions the collision and intercommutation of two cosmic strings can result in the formation of a third string, with the three strings then remaining connected at Y-junctions. The kinematics and dynamics of collisions of this type have been the subject of analytical and numerical analyses in the special case in which the strings are Nambu-Goto. Cosmic strings, however, may well carry currents, in which case their dynamics is not given by the Nambu-Goto action. Our aim is to extend the kinematic analysis to more general kinds of string model. We focus in particular on the collision of strings described by conservative elastic string models, characteristic of current carrying strings, and which are expected to form in a cosmological context. As opposed to Nambu-Goto strings collisions, we show that in this case the collision cannot lead to the formation of a third elastic string: if dynamically such a string forms then the joining string must be described by a more general equation of state. This process will be studied numerically in a forthcoming publication.

astro-ph.CO↗

arXiv2016

CMB-S4 Science Book, First Edition

This book lays out the scientific goals to be addressed by the next-generation ground-based cosmic microwave background experiment, CMB-S4, envisioned to consist of dedicated telescopes at the South Pole, the high Chilean Atacama plateau and possibly a northern hemisphere site, all equipped with new superconducting cameras. CMB-S4 will dramatically advance cosmological studies by crossing critical thresholds in the search for the B-mode polarization signature of primordial gravitational waves, in the determination of the number and masses of the neutrinos, in the search for evidence of new light relics, in constraining the nature of dark energy, and in testing general relativity on large scales.

astro-ph.CO↗

arXiv2015

Bouncing alternatives to inflation

Although the inflationary paradigm is the most widely accepted explanation for the current cosmological observations, it does not necessarily correspond to what actually happened in the early stages of our Universe. To decide on this issue, two paths can be followed: first, all the possible predictions it makes must be derived thoroughly and compared with available data, and second, all imaginable alternatives must be ruled out. Leaving the first task to all other contributors of this volume, we concentrate here on the second option, focusing on the bouncing alternatives and their consequences.

astro-ph.CO↗

arXiv2015

Non-Gaussianity excess problem in classical bouncing cosmologies

The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian perturbations at the end of the contracting phase, we find that the bounce acts as a source such that the resulting value for the post-bounce $f_{\mathrm{NL}}$ may largely exceed all current limits, to the point of potentially casting doubts on the validity of the perturbative expansion. We conjecture that if one can assume that the non-Gaussianity production depends only on the bouncing behavior of the scale factor and not on the specifics of the model examined, then many realistic models in which a nonsingular classical bounce takes place could exhibit a generic non-Gaussianity excess problem that would need to be addressed for each case.

gr-qc↗

arXiv2014

Production of non-gaussianities in a bouncing phase

We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.

gr-qc↗

arXiv2011

Observational signatures of a non-singular bouncing cosmology

We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmological perturbations during the contracting, bouncing and inflationary phases. We derive an expression for the Mukhanov-Sasaki perturbation variable at the onset of the inflationary phase that follows the bounce. Rather than being in the Bunch-Davies vacuum, it is found to be in an excited state that depends on the time scale of the bounce. We then show that this induces oscillations superimposed on the nearly scale-invariant primordial spectra for scalar and tensor perturbations. We discuss the effects of these oscillations in the cosmic microwave background and in the matter power spectrum. We propose a new way to indirectly measure the spatial curvature energy density parameter in the context of this model.

gr-qc↗

arXiv2010

Nonabelian Bosonic Currents in Cosmic Strings

A nonabelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current-carrier belongs to a two dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an abelian current-carrying string, or the three currents are all lightlike, travelling in the same direction (only left or right movers). The third, genuinely nonabelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.

hep-th↗

arXiv2009

Coupled currents in cosmic strings

We first examine the microstructure of a cosmic string endowed with two simple Abelian currents. This microstructure depends on two state parameters. We then provide the macroscopic description of such a string and show that it depends on an additional Lorentz-invariant state parameter that relates the two currents. We find that in most of the parameter space, the two-current string is essentially equivalent to the single current-carrying string, i.e., only one field condenses onto the defect. In the regions where two currents are present, we find that as far as stability is concerned, one can approximate the dynamics with good accuracy using an analytic model based on either a logarithmic (on the electric side, i.e., for timelike currents) or a rational (on the magnetic side, i.e., for spacelike currents) worldsheet Lagrangian.

hep-ph↗

arXiv2008

A classical bounce: constraints and consequences

We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background spacetime with positively curved spatial sections. By means of a phase space analysis, we give the conditions under which an initially contracting phase can be followed by a bounce and an inflationary phase lasting long enough (i.e., at least 60-70 e-folds) to suppress spatial curvature in today's observable universe. We find that, quite generically, this realization requires some amount of fine-tuning of the initial conditions. We study the effect of this background evolution on scalar perturbations by propagating an initial power-law power spectrum through the contracting phase, the bounce and the inflationary phase. We find that it is drastically modified, both spectrally (k-mode mixing) and in amplitude. It also acquires, at leading order, an oscillatory component, which, once evolved through the radiation and matter dominated eras, happens to be compatible with the WMAP data.

gr-qc↗