arXiv subjects

Michael P. Hobson

Publications and source records attributed to Michael P. Hobson.

At least 19 recordsLinked to original sources

arXiv2024

Quantum initial conditions for curved inflating universes

We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of nonadiabaticity with spatial curvature. We construct a novel curvature perturbation that is canonically normalized in the sense of its equation of motion and is unique up to a single scalar parameter. With this construction it becomes possible to set initial conditions invariant under canonical transformations, overcoming known ambiguities in the literature. This corrected quantization has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantization procedures in curved cosmologies filled with a scalar field.

gr-qc↗

arXiv2022

Towards fast machine-learning-assisted Bayesian posterior inference of microseismic event location and source mechanism

Bayesian inference applied to microseismic activity monitoring allows the accurate location of microseismic events from recorded seismograms and the estimation of the associated uncertainties. However, the forward modelling of these microseismic events, which is necessary to perform Bayesian source inversion, can be prohibitively expensive in terms of computational resources. A viable solution is to train a surrogate model based on machine learning techniques, to emulate the forward model and thus accelerate Bayesian inference. In this paper, we substantially enhance previous work, which considered only sources with isotropic moment tensors. We train a machine learning algorithm on the power spectrum of the recorded pressure wave and show that the trained emulator allows complete and fast event locations for $\textit{any}$ source mechanism. Moreover, we show that our approach is computationally inexpensive, as it can be run in less than 1 hour on a commercial laptop, while yielding accurate results using less than $10^4$ training seismograms. We additionally demonstrate how the trained emulators can be used to identify the source mechanism through the estimation of the Bayesian evidence. Finally, we demonstrate that our approach is robust to real noise as measured in field data. This work lays the foundations for efficient, accurate future joint determinations of event location and moment tensor, and associated uncertainties, which are ultimately key for accurately characterising human-induced and natural earthquakes, and for enhanced quantitative seismic hazard assessments.

physics.geo-ph↗

arXiv2022

Finite inflation in curved space

We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of non-zero curvature today would significantly limit the total number of e-folds of the scale factor during inflation, rendering just-enough inflation scenarios with a kinetically dominated or fast-roll stage prior to slow-roll inflation more likely. Finite inflation leads to oscillations and a cutoff towards large scales in the primordial power spectrum and curvature pushes them into the CMB observable window. Using nested sampling, we carry out Bayesian parameter estimations and model comparisons taking into account constraints from reheating and horizon considerations. We confirm the preference of CMB data for closed universes with Bayesian odds of over $100:1$ and with a posterior on the curvature density parameter of $Ω_{K,0}=-0.051\pm0.017$ for a curvature extension of LCDM and $Ω_{K,0}=-0.031\pm0.014$ for Starobinsky inflation. Model comparisons of various inflation models give similar results as for flat universes with the Starobinsky model outperforming most other models.

astro-ph.CO↗

arXiv2021

Ghost and tachyon free Weyl gauge theories: a systematic approach

We investigate the particle content of parity-preserving Weyl gauge theories of gravity (WGT$^+$) about a Minkowski background. Within a subset of the full theory, we use a systematic method previously presented in [arXiv:1812.02675] to determine 862 critical cases for which the parameter values in the action lead to additional gauge invariances. We find that 168 of these cases are free of ghosts and tachyons, provided the parameters satisfy certain conditions that we also determine. We further identify 40 of these cases that are also power-counting renormalizable and determine the corresponding conditions on the parameters. Of these theories, 11 have only massless tordion propagating particles, 23 have only a massive tordion propagating mode, and 6 have both. We also repeat our analysis for WGT$^+$ with vanishing torsion or curvature, respectively. We compare our findings with the very few previous results in the literature.

gr-qc↗

arXiv2021

Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_ν$: Effects of uniform vs logarithmic priors

We review the effect that the choice of a uniform or logarithmic prior has on the Bayesian evidence and hence on Bayesian model comparisons when data provide only a one-sided bound on a parameter. We investigate two particular examples: the tensor-to-scalar ratio $r$ of primordial perturbations and the mass of individual neutrinos $m_ν$, using the cosmic microwave background temperature and polarisation data from Planck 2018 and the NuFIT 5.0 data from neutrino oscillation experiments. We argue that the Kullback-Leibler divergence, also called the relative entropy, mathematically quantifies the Occam penalty. We further show how the Bayesian evidence stays invariant upon changing the lower prior bound of an upper constrained parameter. While a uniform prior on the tensor-to-scalar ratio disfavours the $r$-extension compared to the base LCDM model with odds of about 1:20, switching to a logarithmic prior renders both models essentially equally likely. LCDM with a single massive neutrino is favoured over an extension with variable neutrino masses with odds of 20:1 in case of a uniform prior on the lightest neutrino mass, which decreases to roughly 2:1 for a logarithmic prior. For both prior options we get only a very slight preference for the normal over the inverted neutrino hierarchy with Bayesian odds of about 3:2 at most.

astro-ph.CO↗

arXiv2020

Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories

We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT$^+$) that are also power-counting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, eight have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of nonpropagating modes in determining whether a theory is PCR.

gr-qc↗

arXiv2020

Physical modelling of galaxy clusters detected by Planck

We present a comparison of mass estimates for $54$ galaxy cluster candidates from the second Planck catalogue (PSZ2) of Sunyaev-Zel'dovich sources. We compare the mass values obtained with data taken from the Arcminute Microkelvin Imager (AMI) radio interferometer system and from the Planck satellite. The former of these uses a Bayesian analysis pipeline that parameterises a cluster in terms of its physical quantities, and models the dark matter & baryonic components of a cluster using NFW and GNFW profiles respectively. Our mass estimates derived from Planck data are obtained from the results of the Bayesian detection algorithm PowellSnakes (PwS), are based on the methodology detailed in the PSZ2 paper, and produce two sets of mass estimates; one estimate is calculated directly from the angular radius $θ$ - integrated Comptonisation parameter $Y$ posterior distributions, and the other uses a `slicing function' to provide information on $θ$ based on X-ray measurements and previous Planck mission samples. We find that for $37$ of the clusters, the AMI mass estimates are lower than both values obtained from Planck data. However the AMI and slicing function estimates are within one combined standard deviation of each other for $31$ clusters. We also generate cluster simulations based on the slicing-function mass estimates, and analyse them in the same way as we did the real AMI data. We find that inclusion in the simulations of radio-source confusion & CMB noise and measurable radio-sources causes AMI mass estimates to be systematically low.

astro-ph.CO↗

arXiv2020

Sunyaev--Zel'dovich profile fitting with joint AMI-Planck analysis

We develop a Bayesian method of analysing Sunyaev-Zel'dovich measurements of galaxy clusters obtained from the Arcminute Microkelvin Imager (AMI) radio interferometer system and from the Planck satellite, using a joint likelihood function for the data from both instruments. Our method is applicable to any combination of Planck data with interferometric data from one or more arrays. We apply the analysis to simulated clusters and find that when the cluster pressure profile is known a-priori, the joint dataset provides precise and accurate constraints on the cluster parameters, removing the need for external information to reduce the parameter degeneracy. When the pressure profile deviates from that assumed for the fit, the constraints become biased. Allowing the pressure profile shape parameters to vary in the analysis allows an unbiased recovery of the integrated cluster signal and produces constraints on some shape parameters, depending on the angular size of the cluster. When applied to real data from Planck-detected cluster PSZ2 G063.80+11.42, our method resolves the discrepancy between the AMI and Planck $Y$-estimates and usefully constrains the gas pressure profile shape parameters at intermediate and large radii.

astro-ph.CO↗

arXiv2020

Comparison of physical and observational galaxy cluster modelling

We present a comparison between three cluster models applied to data obtained by the Arcminute Microkelvin Imager radio interferometer system. The physical model (PM) parameterises a cluster in terms of its physical quantities to model the dark matter and baryonic components of the cluster using NFW and GNFW profiles respectively. The observational models (OM I and OM II) model only the gas content of the cluster. The two OMs vary only in the priors they use in Bayesian inference: OM I has a joint prior on angular radius $θ$ and integrated Comptonisation $Y$, derived from simulations, while OM II uses separable priors on $θ$ and $Y$ which are based on calculations of the physical model. For the comparison we consider a sample of $54$ clusters which are a subsample of the second Planck catalogue of Sunyaev-Zel'dovich sources. We first compare the $Y$ estimates of the three models, and find that the PM generally yields lower estimates relative to the OMs. We then compute the Earth Mover's Distance between the $θ$ - $Y$ posterior distributions obtained from each model for each cluster, and find that the two models which are most discrepant are PM and OM I. Finally, we compare the Bayesian evidence values obtained from each model for each cluster. OM I generally provides the best fit to the data but not at a statistically significant level, according to the Jeffreys scale. The highest evidence ratio obtained is actually in favour of the PM over OM I.

astro-ph.CO↗

arXiv2019

Bayesian inflationary reconstructions from Planck 2018 data

We present three non-parametric Bayesian primordial reconstructions using Planck 2018 polarization data: linear spline primordial power spectrum reconstructions, cubic spline inflationary potential reconstructions and sharp-featured primordial power spectrum reconstructions. All three methods conditionally show hints of an oscillatory feature in the primordial power spectrum in the multipole range $\ell\sim20$ to $\ell\sim50$, which is to some extent preserved upon marginalization. We find no evidence for deviations from a pure power law across a broad observable window ($50\lesssim\ell\lesssim2000$), but find that parameterizations are preferred which are able to account for lack of resolution at large angular scales due to cosmic variance, and at small angular scales due to Planck instrument noise. Furthermore, the late-time cosmological parameters are unperturbed by these extensions to the primordial power spectrum. This work is intended to provide a background and give more details of the Bayesian primordial reconstruction work found in the Planck 2018 papers.

astro-ph.CO↗

arXiv2019

Ghost and tachyon free Poincaré gauge theories: a systematic approach

A systematic method is presented for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity for it to contain no ghost or tachyon particles. The technique naturally accommodates critical cases in which the parameter values lead to additional gauge invariances. The method is implemented as a computer program, and is used here to investigate the particle content of parity-conserving Poincaré gauge theory, which we compare with previous results in the literature. We find 450 critical cases that are free of ghosts and tachyons, and we further identify 10 of these that are also power-counting renormalizable, of which four have only massless tordion propagating particles and the remaining six have only a massive tordion propagating mode.

gr-qc↗

arXiv2018

Bayesian power spectrum estimation at the Epoch of Reionization

We introduce a new method for performing robust Bayesian estimation of the three-dimensional spatial power spectrum at the Epoch of Reionization (EoR), from interferometric observations. The versatility of this technique allows us to present two approaches. First, when the observations span only a small number of independent spatial frequencies ($k$-modes) we sample directly from the spherical power spectrum coefficients that describe the EoR signal realisation. Second, when the number of $k$-modes to be included in the model becomes large, we sample from the joint probability density of the spherical power spectrum and the signal coefficients, using Hamiltonian Monte Carlo methods to explore this high dimensional ($\sim$ 20000) space efficiently. This approach has been successfully applied to simulated observations that include astrophysically realistic foregrounds in a companion publication (Sims et al. 2016). Here we focus on explaining the methodology in detail, and use simple foreground models to both demonstrate its efficacy, and highlight salient features. In particular, we show that including an arbitrary flat spectrum continuum foreground that is $10^8$ times greater in power than the EoR signal has no detectable impact on our parameter estimates of the EoR power spectrum recovered from the data.

astro-ph.IM↗

arXiv2018

Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.

gr-qc↗

arXiv2018

An alternative approach to modelling a cosmic void and its effect on the cosmic microwave background

We apply our tetrad-based approach for constructing spherically-symmetric solutions in general relativity to modelling a void, and compare it with the standard Lemaître-Tolman-Bondi (LTB) formalism. In particular, we construct models for the void observed in the direction of Draco in the WISE-2MASS galaxy survey, and a corresponding cosmic microwave background (CMB) temperature decrement in the Planck data in the same direction. We find that the present-day density and velocity profiles of the void are not well constrained by the existing data, so that void models produced from the two approaches can differ substantially while remaining broadly consistent with the observations. We highlight the importance of considering the velocity as well as the density profile in constraining voids.

astro-ph.CO↗

arXiv2017

AMI-CL J0300+2613: a Galactic anomalous-microwave-emission ring masquerading as a galaxy cluster

The Arcminute Microkelvin Imager (AMI) carried out a blind survey for galaxy clusters via their Sunyaev-Zel'dovich effect decrements between 2008 and 2011. The first detection, known as AMI-CL J0300+2613, has been reobserved with AMI equipped with a new digital correlator with high dynamic range. The combination of the new AMI data and more recent high-resolution sub-mm and infra-red maps now shows the feature in fact to be a ring of positive dust-correlated Galactic emission, which is likely to be anomalous microwave emission (AME). If so, this is the first completely blind detection of AME at arcminute scales.

astro-ph.GA↗

arXiv2017

AMI SZ observation of galaxy-cluster merger CIZA J2242+5301: perpendicular flows of gas and dark matter

AMI observations towards CIZA J2242+5301, in comparison with observations of weak gravitational lensing and X-ray emission from the literature, are used to investigate the behaviour of non-baryonic dark matter (NBDM) and gas during the merger. Analysis of the Sunyaev-Zel'dovich (SZ) signal indicates the presence of high pressure gas elongated perpendicularly to the X-ray and weak-lensing morphologies which, given the merger-axis constraints in the literature, implies that high pressure gas is pushed out into a linear structure during core passing. Simulations in the literature closely matching the inferred merger scenario show the formation of gas density and temperature structures perpendicular to the merger axis. These SZ observations are challenging for modified gravity theories in which NBDM is not the dominant contributor to galaxy-cluster gravity.

astro-ph.CO↗

arXiv2017

Free-form modelling of galaxy clusters: a Bayesian and data-driven approach

A new method is presented for modelling the physical properties of galaxy clusters. Our technique moves away from the traditional approach of assuming specific parameterised functional forms for the variation of physical quantities within the cluster, and instead allows for a 'free-form' reconstruction, but one for which the level of complexity is determined automatically by the observational data and may depend on position within the cluster. This is achieved by representing each independent cluster property as some interpolating or approximating function that is specified by a set of control points, or 'nodes', for which the number of nodes, together with their positions and amplitudes, are allowed to vary and are inferred in a Bayesian manner from the data. We illustrate our nodal approach in the case of a spherical cluster by modelling the electron pressure profile Pe(r) in analyses both of simulated Sunyaev-Zel'dovich (SZ) data from the Arcminute MicroKelvin Imager (AMI) and of real AMI observations of the cluster MACS J0744+3927 in the CLASH sample. We demonstrate that one may indeed determine the complexity supported by the data in the reconstructed Pe(r), and that one may constrain two very important quantities in such an analysis: the cluster total volume integrated Comptonisation parameter (Ytot) and the extent of the gas distribution in the cluster (rmax). The approach is also well-suited to detecting clusters in blind SZ surveys.

astro-ph.CO↗

arXiv2017

Fast GPU-Based Seismogram Simulation from Microseismic Events in Marine Environments Using Heterogeneous Velocity Models

A novel approach is presented for fast generation of synthetic seismograms due to microseismic events, using heterogeneous marine velocity models. The partial differential equations (PDEs) for the 3D elastic wave equation have been numerically solved using the Fourier domain pseudo-spectral method which is parallelizable on the graphics processing unit (GPU) cards, thus making it faster compared to traditional CPU based computing platforms. Due to computationally expensive forward simulation of large geological models, several combinations of individual synthetic seismic traces are used for specified microseismic event locations, in order to simulate the effect of realistic microseismic activity patterns in the subsurface. We here explore the patterns generated by few hundreds of microseismic events with different source mechanisms using various combinations, both in event amplitudes and origin times, using the simulated pressure and three component particle velocity fields via 1D, 2D and 3D seismic visualizations.

physics.geo-ph↗