arXiv subjects

Mark Hindmarsh

Publications and source records attributed to Mark Hindmarsh.

At least 37 records · Page 2Linked to original sources

arXiv2022

Reconstructing physical parameters from template gravitational wave spectra at LISA: first order phase transitions

A gravitational wave background from a first order phase transition in the early universe may be observable at millihertz gravitational wave (GW) detectors such as the Laser Interferometer Space Antenna (LISA). In this paper we introduce and test a method for investigating LISA's sensitivity to gravitational waves from a first order phase transition using parametrised templates as an approximation to a more complete physical model. The motivation for developing the method is to provide a less computationally intensive way to perform Markov Chain Monte Carlo (MCMC) inference on the thermodynamic parameters of a first order phase transition, or on generally computationally intensive models. Starting from a map between the physical parameters and the parameters of an empirical template, we first construct a prior on the empirical parameters that contains the necessary information about the physical parameters; we then use the inverse mapping to reconstruct approximate posteriors on the physical parameters from a fast MCMC on the empirical template. We test the method on a double broken power law approximation to spectra in the sound shell model. The reconstruction method substantially reduces the proposal evaluation time, and despite requiring some precomputing of the mapping, this method is still cost-effective overall. In two test cases, with signal-to-noise $\sim 40$, the method recovers the physical parameters and the spectrum of the injected gravitational wave power spectrum to $95\%$ confidence. In previous Fisher matrix analysis we found the phase boundary speed $v_{\rm w}$ was expected to be the best constrained of the thermodynamic parameters. In this work, for an injected phase transition GW power spectrum with $v_{\rm w} = 0.55$, with a direct sample on the thermodynamic parameters we recover $0.630^{+0.17}_{-0.059}$ and for our reconstructed sample $0.646^{+0.098}_{-0.075}$.

astro-ph.CO↗

arXiv2022

Generation of gravitational waves from freely decaying turbulence

We study the stochastic gravitational wave background (SGWB) produced by freely decaying vortical turbulence in the early Universe. We thoroughly investigate the time correlation of the velocity field, and hence of the anisotropic stresses producing the gravitational waves. With hydrodynamical simulations, we show that the unequal time correlation function (UETC) of the Fourier components of the velocity field is Gaussian in the time difference, as predicted by the "sweeping" decorrelation model. We introduce a decorrelation model that can be extended to wavelengths around the integral scale of the flow. Supplemented with the evolution laws of the kinetic energy and of the integral scale, this provides a new model UETC of the turbulent velocity field consistent with the simulations. We discuss the UETC as a positive definite kernel, and propose to use the Gibbs kernel for the velocity UETC as a natural way to ensure positive definiteness of the SGWB. The SGWB is given by a 4-dimensional integration of the resulting anisotropic stress UETC with the gravitational wave Green's function. We perform this integration using a Monte Carlo algorithm based on importance sampling, and find that the result matches that of the simulations. Furthermore, the SGWB obtained from the numerical integration and from the simulations show close agreement with a model in which the source is constant in time and abruptly turns off after a few eddy turnover times. Based on this assumption, we provide an approximate analytical form for the SGWB spectrum and its scaling with the initial kinetic energy and integral scale. Finally, we use our model and numerical integration algorithm to show that including an initial growth phase for the turbulent flow heavily influences the spectral shape of the SGWB. This highlights the importance of a complete understanding of the turbulence generation mechanism.

astro-ph.CO↗

arXiv2022

Supercooling of the A phase of $^3$He

Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid $^3$He A-B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A-B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase seeds formed upon passage through the superfluid transition. A greater understanding of the physics is essential before the $^3$He can be exploited to model transitions in the early universe.

cond-mat.other↗

arXiv2022

The distribution of loss to future USS pensions due to the UUK cuts of April 2022

We present the first global analysis of the impact of the April 2022 cuts to the future pensions of members of the Universities Superannuation Scheme. For the 196,000 active members, if Consumer Price Inflation (CPI) remains at its historic average of 2.5%, the distribution of the range of cuts peaks between 30%-35%. This peak increases to 40%-45% cuts if CPI averages 3.0%. The global loss across current USS scheme members, in today's money, is calculated to be 16-18 billion GBP, with most of the 71,000 staff under the age of 40 losing between 100k-200k GBP each, for CPI averaging 2.5%-3.0%. A repeated claim made during the formal consultation by the body representing university management (Universities UK) that those earning under 40k GBP would receive a "headline" cut of 12% to their future pension is shown to be a serious underestimate for realistic CPI projections.

econ.GN↗

arXiv2022

Thermal suppression of bubble nucleation at first-order phase transitions in the early Universe

One of the key observables in a gravitational wave power spectrum from a first order phase transition in the early Universe is the mean bubble spacing, which depends on the rate of nucleation of bubbles of the stable phase, as well as the bubble wall speed. When the bubbles expand as deflagrations, it is expected that the heating of the fluid in front of the phase boundary suppresses the nucleation rate. We quantify the effect, showing that it increases the mean bubble separation, and acts to enhance the gravitational wave signal by a factor of up to order 10. The effect is largest for small wall speeds and strong transitions.

gr-qc↗

arXiv2021

Comment on "More Axions from Strings''

We comment on a claim that axion strings show a long-term logarithmic increase in the number of Hubble lengths per Hubble volume [arXiv:2007.04990], thereby violating the standard "scaling" expectation of an O(1) constant. We demonstrate that the string density data presented in [arXiv:2007.04990] are consistent with standard scaling, at a string density consistent with that obtained by us [arXiv:1908.03522, arXiv:2102.07723] and other groups. A transient slow growth in Hubble lengths per Hubble volume towards its constant scaling value is explained by standard network modelling [arXiv:2102.07723].

astro-ph.CO↗

arXiv2021

Effective actions and bubble nucleation from holography

We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality, and its use to determine quasi-equilibrium parameters of first order phase transitions relevant for gravitational wave production. A particularly simple holographic model is introduced, containing only the metric and a free massive scalar field. Despite the simplicity, the model contains a rich phase diagram, including first order phase transitions at non-zero temperature, due to various multi-trace deformations. We obtain the leading terms in the effective action from homogeneous black brane solutions in the gravity dual, and linearised perturbations around them. We then employ the effective action to construct bubble and domain wall solutions in the field theory side and study their properties. In particular, we show how the scaling of the effective action with the effective number of degrees of freedom of the quantum field theory determines the corresponding scaling of gravitational wave parameters.

hep-th↗

arXiv2021

Gravitational Waves at Strong Coupling from an Effective Action

Using a holographic derivation of a quantum effective action for a scalar operator at strong coupling, we compute quasi-equilibrium parameters relevant for the gravitational wave signal from a first order phase transition in a simple dual model. We discuss how the parameters of the phase transition vary with the effective number of degrees of freedom of the dual field theory. Our model can produce an observable signal at LISA if the critical temperature is around a TeV, in a parameter region where the field theory has an approximate conformal symmetry.

hep-th↗

arXiv2021

Observational prospects for phase transitions at LISA: Fisher matrix analysis

A first order phase transition at the electroweak scale would lead to the production of gravitational waves that may be observable at upcoming space-based gravitational wave (GW) detectors such as LISA (Laser Interferometer Space Antenna). As the Standard Model has no phase transition, LISA can be used to search for new physics by searching for a stochastic gravitational wave background. In this work we investigate LISA's sensitivity to the thermodynamic parameters encoded in the stochastic background produced by a phase transition, using the sound shell model to characterise the gravitational wave power spectrum, and the Fisher matrix to estimate uncertainties. We explore a parameter space with transition strengths $α< 0.5$ and phase boundary speeds $0.4 < v_\text{w} < 0.9$, for transitions nucleating at $T_{\text{N}} = 100$ GeV, with mean bubble spacings $0.1$ and $0.01$ of the Hubble length, and sound speed $c/\sqrt{3}$. We show that the power spectrum in the sound shell model can be well approximated by a four-parameter double broken power law, and find that the peak power and frequency can be measured to approximately 10% accuracy for signal-to-noise ratios (SNRs) above 20. Determinations of the underlying thermodynamic parameters are complicated by degeneracies, but in all cases the phase boundary speed will be the best constrained parameter. Turning to the principal components of the Fisher matrix, a signal-to-noise ratio above 20 produces a relative uncertainty less than 3% in the two highest-order principal components, indicating good prospects for combinations of parameters. The highest-order principal component is dominated by the wall speed. These estimates of parameter sensitivity provide a preliminary accuracy target for theoretical calculations of thermodynamic parameters.

astro-ph.CO↗

arXiv2021

Approach to scaling in axion string networks

We study the approach to scaling in axion string networks in the radiation era, through measuring the root-mean-square velocity $v$ as well as the scaled mean string separation $x$. We find good evidence for a fixed point in the phase-space analysis in the variables $(x,v)$, providing a strong indication that standard scaling is taking place. We show that the approach to scaling can be well described by a two parameter velocity-one-scale (VOS) model, and show that the values of the parameters are insensitive to the initial state of the network. The string length has also been commonly expressed in terms of a dimensionless string length density $ζ$, proportional to the number of Hubble lengths of string per Hubble volume. In simulations with initial conditions far from the fixed point $ζ$ is still evolving after half a light-crossing time, which has been interpreted in the literature as a long-term logarithmic growth. We show that all our simulations, even those starting far from the fixed point, are accounted for by a VOS model with an asymptote of $ζ_*=1.20\pm0.09$ (calculated from the string length in the cosmic rest frame) and $v_* = 0.609\pm 0.014$.

astro-ph.CO↗

arXiv2021

Loop decay in Abelian-Higgs string networks

We study the decay of cosmic string loops in the Abelian-Higgs model. We confirm earlier results that loops formed by intersections of infinite strings formed from random-field initial conditions disappear quickly, with lifetime proportional to their initial rest-frame length $\ell_\text{init}$. We study a population with $\ell_\text{init}$ up to $6000$ inverse mass units, and measure the proportionality constant to be $0.14\pm0.04$, independently of the initial lengths. We propose a new method to construct oscillating non-self intersecting loops from initially stationary strings, and show that by contrast these loops have lifetimes scaling approximately as $\ell_\text{init}^2$, in line with previous works on artificially created string configurations. We show that the oscillating strings have mean-square velocity $\bar{v}^2 \simeq 0.500 \pm 0.004$, consistent with the Nambu-Goto value of $1/2$, while the network loops have $\bar{v}^2 \simeq 0.40 \pm 0.04$. We argue that whatever the mechanism behind the network loop decay is, it is non-linear, can only be suppressed by careful tuning of initial conditions, and is much stronger than gravitational radiation. An implication is that one cannot use the Nambu-Goto model to derive robust constraints on the tension of field theory strings. We advocate parametrising the uncertainty as the fraction $f_\text{NG}$ of Nambu-Goto-like loops surviving to radiate gravitationally. None of the 31 large network loops created survived longer than 0.25 of their initial length, so one can estimate that $f_\text{NG}<0.1$ at $95$% confidence level. If the recently reported NANOgrav signal is due to cosmic strings, $f_\text{NG}$ must be greater than $10^{-3}$ in order not to violate bounds from the Cosmic Microwave Background.

astro-ph.CO↗

arXiv2021

Detecting gravitational waves from cosmological phase transitions with LISA: an update

We investigate the potential for observing gravitational waves from cosmological phase transitions with LISA in light of recent theoretical and experimental developments. Our analysis is based on current state-of-the-art simulations of sound waves in the cosmic fluid after the phase transition completes. We discuss the various sources of gravitational radiation, the underlying parameters describing the phase transition and a variety of viable particle physics models in this context, clarifying common misconceptions that appear in the literature and identifying open questions requiring future study. We also present a web-based tool, PTPlot, that allows users to obtain up-to-date detection prospects for a given set of phase transition parameters at LISA.

astro-ph.CO↗

arXiv2021

Gravitational waves from vacuum first order phase transitions II: from thin to thick walls

In a vacuum first-order phase transition, gravitational waves are generated from collision of bubbles of the true vacuum. The spectrum from such collisions takes the form of a broken power law. We consider a toy model for such a phase transition, where the dynamics of the scalar field depends on a single parameter $\overlineλ$, which controls how thin the bubble wall is at nucleation and how close to degenerate the vacua are relative to the barrier. We extend on our previous work by performing a series of simulations with a range of $\overlineλ$. The peak of the gravitational-wave power spectrum varies by up to a factor of $1.3$, which is probably an unobservable effect. We find that the ultraviolet (UV) power law in the gravitational-wave spectrum becomes steeper as $\overlineλ \rightarrow 0$, varying between $k^{-1.4}$ and $k^{-2.2}$ for the $\overlineλ$ considered. This provides some evidence that the form of the underlying effective potential of a vacuum first-order phase transition could be determined from the gravitational-wave spectrum it produces.

astro-ph.CO↗

arXiv2020

Gravitational waves from a holographic phase transition

We investigate first order phase transitions in a holographic setting of five-dimensional Einstein gravity coupled to a scalar field, constructing phase diagrams of the dual field theory at finite temperature. We scan over the two-dimensional parameter space of a simple bottom-up model and map out important quantities for the phase transition: the region where first order phase transitions take place; the latent heat, the transition strength parameter $α$, and the stiffness. We find that $α$ is generically in the range 0.1 to 0.3, and is strongly correlated with the stiffness (the square of the sound speed in a barotropic fluid). Using the LISA Cosmology Working Group gravitational wave power spectrum model corrected for kinetic energy suppression at large $α$ and non-conformal stiffness, we outline the observational prospects at the future space-based detectors LISA and TianQin. A TeV-scale hidden sector with a phase transition described by the model could be observable at both detectors.

hep-th↗

arXiv2020

Vorticity, kinetic energy, and suppressed gravitational wave production in strong first order phase transitions

We have performed the first 3-dimensional simulations of strong first-order thermal phase transitions in the early Universe. For deflagrations, we find that the rotational component of the fluid velocity increases as the transition strength is increased. For detonations, however, the rotational velocity component remains constant and small. We also find that the efficiency with which kinetic energy is transferred to the fluid falls below theoretical expectations as we increase the transition strength. The probable origin of the kinetic energy deficit is the formation of reheated droplets of the metastable phase during the collision, slowing the bubble walls. The rate of increase in the gravitational wave energy density for deflagrations in strong transitions is suppressed compared to that predicted in earlier work. This is largely accounted for by the reduction in kinetic energy. Current modelling therefore substantially overestimates the gravitational wave signal for strong transitions with deflagrations, in the most extreme case by a factor of $10^{3}$. Detonations are less affected.

hep-ph↗

arXiv2020

Irreducible background of gravitational waves from a cosmic defect network: update and comparison of numerical techniques

Cosmological phase transitions in the early Universe may produce relics in the form of a network of cosmic defects. Independently of the order of a phase transition, topology of the defects, and their global or gauge nature, the defects are expected to emit gravitational waves (GWs) as the network energy-momentum tensor adapts itself to maintaining {scaling}. We show that the evolution of any defect network (and for that matter any scaling source) emits a GW background with spectrum $Ω_{\rm GW} \propto f^3$ for $f \ll f_0$, $Ω_{\rm GW} \propto 1/f^2$ for $f_0 \lesssim f \lesssim f_{\rm eq}$, and $Ω_{\rm GW} \propto~const$ (i.e.~exactly scale-invariant) for $f \gg f_{\rm eq}$, where $f_0$ and $ f_{\rm eq}$ denote respectively the frequencies corresponding to the present and matter-radiation equality horizons. This background represents an irreducible emission of GWs from any scaling network of cosmic defects, with its amplitude characterized only by the symmetry breaking scale and the nature of the defects. Using classical lattice simulations we calculate the GW signal emitted by defects created after the breaking of a global symmetry $O(N) \rightarrow O(N-1)$. We obtain the GW spectrum for $N$ between 2 and 20 with two different techniques: integrating over unequal time correlators of the energy momentum tensor, updating our previous work on smaller lattices, and for the first time, comparing the result with the real time evolution of the tensor perturbations sourced by the same defects. Our results validate the equivalence of the two techniques. Using CMB upper bounds on the defects' energy scale, we discuss the difficulty of detecting this GW background in the case of global defects.

astro-ph.CO↗

arXiv2020

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

We present results from large-scale numerical simulations of a first order thermal phase transition in the early universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted $k^{-3}$ behaviour, where $k$ is the wavenumber, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-$k$ decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wavenumber behaviour of the velocity power spectrum is consistent with a causal $k^{3}$, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about $0.05c$, produced from bubbles with a mean separation of about $10^{-2}$ of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

astro-ph.CO↗

arXiv2020

The scaling density of axion strings

In the QCD axion dark matter scenario with post-inflationary Peccei-Quinn symmetry breaking, the number density of axions, and hence the dark matter density, depends on the length of string per unit volume at cosmic time $t$, by convention written $ζ/t^2$. The expectation has been that the dimensionless parameter $ζ$ tends to a constant $ζ_0$, a feature of a string network known as scaling. It has recently been claimed that in larger numerical simulations $ζ$ shows a logarithmic increase with time, while theoretical modelling suggests an inverse logarithmic correction. Either case would result in a large enhancement of the string density at the QCD transition, and a substantial revision to the axion mass required for the axion to constitute all of the dark matter. With a set of new simulations of global strings we compare the standard scaling (constant-$ζ$) model to the logarithmic growth and inverse-logarithmic correction models. In the standard scaling model, by fitting to linear growth in the mean string separation $ξ= t/\sqrtζ$, we find $ζ_0 = 1.19 \pm 0.20$. We conclude that the apparent corrections to $ζ$ are artefacts of the initial conditions, rather than a property of the scaling network. The residuals from the constant-$ζ$ (linear $ξ$) fit also show no evidence for logarithmic growth, restoring confidence that numerical simulations can be simply extrapolated from the Peccei-Quinn symmetry-breaking scale to the QCD scale. Re-analysis of previous work on the axion number density suggests that recent estimates of the axion dark matter mass in the post-inflationary symmetry-breaking scenario we study should be increased by about 50%.

astro-ph.CO↗