arXiv subjects

W. J. Handley

Publications and source records attributed to W. J. Handley.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Comprehensive Bayesian re-analysis of the SARAS2 data from the Epoch of Reionization

We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with polychord, spectrally smooth foreground modelling implemented with maxsmooth, detailed systematic modelling and rapid signal emulation with globalemu. Our analysis differs from previous analysis of the SARAS2 data through the use of a full Bayesian framework and separate modelling of the foreground and non-smooth systematics. We use the most up-to-date signal models including Lyman-$α$ and CMB heating parameterised by astrophysical parameters such as star formation efficiency, X-ray heating efficiency, minimal virial circular velocity of star forming galaxies, CMB optical depth and the low energy cutoff of the X-ray spectral energy distribution. We consider models with an excess radio background above the CMB produced via radio emission from early galaxies and parameterised by a radio production efficiency. A non-smooth systematic is identified and modelled as both a frequency damped sinusoid introduced by the electronics and separately from the sky. The latter is modulated by the total efficiency of the antenna and marginally favoured by the data. We consider three different models for the noise in the data. The SARAS2 constraints on individual astrophysical parameters are extremely weak however we identify classes of disfavoured signals. We weakly disfavour standard astrophysical models with high Lyman-$α$ fluxes and weak heating and more confidently disfavour exotic models with high Lyman-$α$ fluxes, low X-ray efficiencies and high radio production efficiencies in early galaxies.

astro-ph.CO↗

arXiv2022

Perturbations and the Future Conformal Boundary

The concordance model of cosmology predicts a universe which finishes in a finite amount of conformal time at a future conformal boundary. We show that for particular cases we study, the background variables and perturbations may be analytically continued beyond this boundary and that the "end of the universe" is not necessarily the end of their physical development. Remarkably, these theoretical considerations of the end of the universe might have observable consequences today: perturbation modes consistent with these boundary conditions have a quantised power spectrum which may be relevant to features seen in the large scale cosmic microwave background. Mathematically these cosmological models may either be interpreted as a palindromic universe mirrored in time, a reflecting boundary condition, or a double cover, but are identical with respect to their observational predictions and stand in contrast to the predictions of conformal cyclic cosmologies.

gr-qc↗

arXiv2022

Improved cosmological fits with quantized primordial power spectra

We observationally examine cosmological models based on primordial power spectra with quantized wavevectors. Introducing a linearly quantized power spectrum with $k_0=3.225\times10^{-4}\mathrm{Mpc}^{-1}$ and spacing $Δk = 2.257 \times 10^{-4} \mathrm{Mpc}^{-1}$ provides a better fit to the Planck 2018 observations than the concordance baseline, with $Δχ^2 = -8.55$. Extending the results of Lasenby et al [1], we show that the requirement for perturbations to remain finite beyond the future conformal boundary in a universe containing dark matter and a cosmological constant results in a linearly quantized primordial power spectrum. It is found that the infrared cutoffs for this future conformal boundary quantized cosmology do not provide cosmic microwave background power spectra compatible with observations, but future theories may predict more observationally consistent quantized spectra.

astro-ph.CO↗

arXiv2021

GLOBALEMU: A novel and robust approach for emulating the sky-averaged 21-cm signal from the cosmic dawn and epoch of reionisation

Emulation of the Global (sky-averaged) 21-cm signal with neural networks has been shown to be an essential tool for physical signal modelling. In this paper we present globalemu, a Global 21-cm signal emulator that uses redshift as a character defining variable alongside a set of astrophysical parameters to estimate the signal brightness temperature. Combined with physically-motivated data pre-processing this makes for a reliable and fast emulator that is relatively insensitive to the network design. globalemu can emulate a high resolution signal in 1.3 ms in comparison to 133 ms, a factor of 102 improvement, when using the existing public state of the art 21cmGEM. We illustrate, with the standard astrophysical models used to train 21cmGEM, that globalemu is almost twice as accurate and for a test set of $\approx1,700$ signals we achieve a mean RMSE of 2.52 mK across the band z=7-28 ($\approx$10 per cent the expected noise of the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH)). The models are parameterised by the star formation efficiency, $f_*$, minimum virial circular velocity, $V_c$, X-ray efficiency, $f_X$, CMB optical depth, $τ$, the slope and low energy cut off of the X-ray spectral energy density, $α$ and $ν_\mathrm{min}$, and the mean free path of ionizing photons, $R_\mathrm{mfp}$. globalemu provides a flexible framework for easily emulating updated simulations of the Global signal and in addition the neutral fraction history. The emulator is pip installable and available at: \url{https://github.com/htjb/globalemu}. globalemu will be used extensively by the REACH collaboration.

astro-ph.CO↗

arXiv2021

Constraining Quantum Initial Conditions before Inflation

We theoretically and observationally investigate different choices of initial conditions for the primordial mode function that are imposed during an epoch preceding inflation. By deriving predictions for the observables resulting from several alternate quantum vacuum prescriptions we show some choices of vacua are theoretically observationally distinguishable from others. Comparing these predictions to the Planck 2018 observations via a Bayesian analysis shows no significant evidence to favour any of the quantum vacuum prescriptions over the others. In addition we consider frozen initial conditions, representing a white-noise initial state at the big-bang singularity. Under certain assumptions the cosmological concordance model and frozen initial conditions are found to produce identical predictions for the cosmic microwave background anisotropies. Frozen initial conditions may thus provide an alternative theoretic paradigm to explain observations that were previously understood in terms of the inflation of a quantum vacuum.

astro-ph.CO↗

arXiv2021

Bayesian noise wave calibration for 21-cm global experiments

Detection of millikelvin-level signals from the 'Cosmic Dawn' requires an unprecedented level of sensitivity and systematic calibration. We report the theory behind a novel calibration algorithm developed from the formalism introduced by the EDGES collaboration for use in 21-cm experiments. Improvements over previous approaches are provided through the incorporation of a Bayesian framework and machine learning techniques such as the use of Bayesian evidence to determine the level of frequency variation of calibration parameters that is supported by the data, the consideration of correlation between calibration parameters when determining their values and the use of a conjugate-prior based approach that results in a fast algorithm for application in the field. In self-consistency tests using empirical data models of varying complexity, our methodology is used to calibrate a 50 $Ω$ ambient-temperature load. The RMS error between the calibration solution and the measured temperature of the load is 8 mK, well within the 1$σ$ noise level. Whilst the methods described here are more applicable to global 21-cm experiments, they can easily be adapted and applied to other applications, including telescopes such as HERA and the SKA.

astro-ph.IM↗

arXiv2021

Rapid numerical solutions for the Mukhanov-Sasaki equation

We develop a novel technique for numerically computing the primordial power spectra of comoving curvature perturbations. By finding suitable analytic approximations for different regions of the mode equations and stitching them together, we reduce the solution of a differential equation to repeated matrix multiplication. This results in a wavenumber-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wavenumbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance initial conditions.

astro-ph.CO↗

arXiv2021

maxsmooth: Rapid Maximally Smooth Function Fitting With Applications in Global 21-cm Cosmology

Maximally Smooth Functions (MSFs) are a form of constrained functions in which there are no inflection points or zero crossings in high order derivatives. Consequently, they have applications to signal recovery in experiments where signals of interest are expected to be non-smooth features masked by larger smooth signals or foregrounds. They can also act as a powerful tool for diagnosing the presence of systematics. The constrained nature of MSFs makes fitting these functions a non-trivial task. We introduce maxsmooth, an open source package that uses quadratic programming to rapidly fit MSFs. We demonstrate the efficiency and reliability of maxsmooth by comparison to commonly used fitting routines and show that we can reduce the fitting time by approximately two orders of magnitude. We introduce and implement with maxsmooth Partially Smooth Functions, which are useful for describing elements of non-smooth structure in foregrounds. This work has been motivated by the problem of foreground modelling in 21-cm cosmology. We discuss applications of maxsmooth to 21-cm cosmology and highlight this with examples using data from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) and the Large-aperture Experiment to Detect the Dark Ages (LEDA) experiments. We demonstrate the presence of a sinusoidal systematic in the EDGES data with a log-evidence difference of $86.19\pm0.12$ when compared to a pure foreground fit. MSFs are applied to data from LEDA for the first time in this paper and we identify the presence of sinusoidal systematics. maxsmooth is pip installable and available for download at: https://github.com/htjb/maxsmooth

astro-ph.CO↗

arXiv2021

Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I. Cases with curvature-free constraints

It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background.

gr-qc↗

arXiv2020

Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy

The ten-parameter, quadratic Poincaré gauge theory of gravity is a plausible alternative to general relativity. We show that the rich background cosmology of the gauge theory is described by a non-canonical bi-scalar-tensor theory in the Jordan frame: the `metrical analogue'. This provides a unified framework for future investigation by the broader community. For many parameter choices, the non-canonical term reduces to a Cuscuton field of the form $\smash{\sqrt{|X^{ϕϕ}|}}$. The Einstein-Cartan-Kibble-Sciama theory maps to a pure quadratic Cuscuton, whereas the teleparallel theory maps to the Einstein-Hilbert Lagrangian. We apply the metrical analogue to novel unitary and power-counting-renormalisable cases of Poincaré gauge theory. These theories support the concordance $Λ$CDM background cosmology up to an optional, effective dark radiation component, we explain this behaviour in terms of a stalled Cuscuton. We also obtain two dark energy solutions from one of these cases: accelerated expansion from a negative bare cosmological constant whose magnitude is screened, and emergent dark energy to replace vanishing bare cosmological constant in $Λ$CDM.

gr-qc↗

arXiv2020

Addressing $H_0$ tension with emergent dark radiation in unitary gravity

We propose a one-parameter extension to $Λ$CDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early universe redshifts away as hot dark matter, then quintessence, tracking the dominant equation-of-state parameter and leaving a falsifiable torsion field in the current epoch. This picture results from a new Poincaré gauge theory (PGT), one of the most promising among the latest batch of 58 PGTs found to be both power-counting renormalisable and free from ghosts and tachyons. We systematically categorise the cosmologies of 33 of these PGTs, as special cases of the most general parity-preserving, Ostrogradsky-stable PGT with a purely Yang-Mills action. The theory we consider contains two propagating massless gravitons, which may be $J^P=2^+$ (long-range gravitation and gravitational waves). A conspiracy among the coupling constants eliminates the spatial curvature $k\in\{\pm 1,0\}$ from the field equations. We show that this `$k$-screening' is not restricted to conformal gravity theories. The flat Friedmann equations are then emergent, with potentially tension-resolving freedom at the early scale-invariant epoch that reliably gives way to an attractor-like state of modern $Λ$CDM evolution. We compare with related theories and promising special cases, such as $k$-screened theories with negative-definite effective $k$, and more traditional theories with effective $Λ$ and a $J^P=0^-$ massive graviton (dark matter candidate). As a bonus, we analyse similarly constrained actions in the new extended Weyl gauge theory (eWGT). We show that in cosmology, PGT and eWGT span exactly the same classical phenomenology up to a linear map between their coupling constants, hinting at a deeper relationship between the two.

gr-qc↗

arXiv2020

Dense output for highly oscillatory numerical solutions

We present a method to construct a continuous extension (otherwise known as dense output) for a numerical routine in the special case of the numerical solution being a scalar-valued function exhibiting rapid oscillations. Such cases call for numerical routines that make use of the known global behaviour of the solution, one example being methods using asymptotic expansions to forecast the solution at each step of the independent variable. An example is oscode, numerical routine which uses the Wentzel-Kramers-Brillouin (WKB) approximation when the solution oscillates rapidly and otherwise behaves as a Runge-Kutta (RK) solver. Polynomial interpolation is not suitable for producing the solution at an arbitrary point mid-step, since efficient numerical methods based on the WKB approximation will step through multiple oscillations in a single step. Instead we construct the continuous solution by extending the numerical quadrature used in computing a WKB approximation of the solution with no additional evaluations of the differential equation or terms within, and provide an error estimate on this dense output. Finally, we draw attention to previous work on the continuous extension of Runge-Kutta formulae, and construct an extension to a RK method based on Gauss--Lobatto quadrature nodes, thus describing how to generate dense output from each of the methods underlying oscode.

physics.comp-ph↗

arXiv2020

Quantum initial conditions for inflation and canonical invariance

We investigate the transformation of initial conditions for primordial curvature perturbations under two types of transformations of the associated action: simultaneous redefinition of time and the field to be quantised, and the addition of surface terms. The latter encompasses all canonical transformations, whilst the time- and field-redefinition is a distinct, non-canonical transformation since the initial and destination systems use different times. Actions related to each other via such transformations yield identical equations of motion and preserve the commutator structure. They further preserve the time-evolution of expectation values of quantum operators unless the vacuum state also changes under the transformation. These properties suggest that it is of interest to investigate vacuum prescriptions that also remain unchanged under canonical transformations. We find that initial conditions derived via minimising the vacuum expectation value of the Hamiltonian and those obtained using the Danielsson vacuum prescription are not invariant under these transformations, whereas those obtained by minimising the local energy density are. We derive the range of physically distinct initial conditions obtainable by Hamiltonian diagonalisation, and illustrate their effect on the scalar primordial power spectrum and the Cosmic Microwave Background under the just enough inflation model. We also generalise the analogy between the dynamics of a quantum scalar field on a curved, time-dependent spacetime and the gauge-invariant curvature perturbation. We argue that the invariance of the vacuum prescription obtained by minimising the renormalised stress--energy tensor should make it the preferred procedure for setting initial conditions for primordial perturbations. All other procedures reviewed in this work yield ambiguous initial conditions, which is problematic both in theory and practice.

gr-qc↗

arXiv2019

An efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems

We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions. The method is based on a Runge-Kutta-like stepping procedure that makes use of the Wentzel-Kramers-Brillouin (WKB) approximation to skip regions of integration where the characteristic frequency varies slowly. In regions where this is not the case, the method is able to switch to a made-to-measure Runge-Kutta integrator that minimises the total number of function evaluations. We demonstrate the effectiveness of the method with example solutions of the Airy equation and an equation exhibiting a burst of oscillations, discussing the error properties of the method in detail. We then show the method applied to physical systems. First, the one-dimensional, time-independent Schrödinger equation is solved as part of a shooting method to search for the energy eigenvalues for a potential with quartic anharmonicity. Then, the method is used to solve the Mukhanov-Sasaki equation describing the evolution of cosmological perturbations, and the primordial power spectrum of the perturbations is computed in different cosmological scenarios. We compare the performance of our solver in calculating a primordial power spectrum of scalar perturbations to that of BINGO, an efficient code specifically designed for such applications.

physics.comp-ph↗

arXiv2018

Constraining the kinetically dominated Universe

We present cosmological constraints from Planck 2015 data for a universe that is kinetically dominated at very early times. We perform a Markov chain Monte Carlo analysis to estimate parameters and use nested sampling to determine the evidence for a model comparison of the single-field quadratic and Starobinsky inflationary models with the standard $Λ$CDM cosmology. In particular we investigate how different amounts of inflation before and after horizon exit affect the primordial power spectrum and subsequently the power spectrum of the cosmic microwave background. We find that the model using kinetically dominated initial conditions for inflation performs similarly well in terms of Bayesian evidence as a model directly starting out in the slow-roll phase, despite having an additional parameter. The data show a slight preference for a cutoff at large scales in the primordial and temperature power spectra.

astro-ph.CO↗

arXiv2018

A case for kinetically dominated initial conditions for inflation

We make a case for setting initial conditions for inflation at the Planck epoch in the kinetically dominated regime. For inflationary potentials with a plateau or a hill, i.e. potentials that are bounded from above within a certain region of interest, we cannot claim complete ignorance of the energy distribution between kinetic and potential energy, and equipartition of energy at the Planck epoch becomes questionable. We analyse different classes of potentials in phase-space and quantify the fraction of the Planck surface that is kinetically dominated. For the small amplitudes of the potentials as suggested by current data, the Planck surface lies in the region of kinetic dominance for almost all values of interest of the inflaton field.

astro-ph.CO↗

arXiv2018

Kinetic Initial Conditions for Inflation

We consider the classical evolution of the inflaton field $ϕ(t)$ and the Hubble parameter $H(t)$ in homogeneous and isotropic single-field inflation models. Under an extremely broad assumption, we show that the universe generically emerges from an initial singularity in a non-inflating state where the kinetic energy of the inflaton dominates its potential energy, $\dotϕ^2 \gg V(ϕ)$. In this kinetically-dominated regime, the dynamical equations admit simple analytic solutions for $ϕ(t)$ and $H(t)$, which are independent of the form of $V(ϕ)$. In such models, these analytic solutions thus provide a simple way of setting the initial conditions from which to start the (usually numerical) integration of the coupled equations of motion for $ϕ(t)$ and $H(t)$. We illustrate this procedure by applying it to spatially-flat models with polynomial and exponential potentials, and determine the background evolution in each case; generically $H(t)$ and $|ϕ(t)|$ as well as their time derivatives decrease during kinetic dominance until $\dotϕ^2\sim V(ϕ)$, marking the onset of a brief period of fast-roll inflation prior to a slow roll phase. We also calculate the approximate spectrum of scalar perturbations produced in each model and show that it exhibits a generic damping of power on large scales. This may be relevant to the apparent low-$\ell$ falloff in the CMB power spectrum.

astro-ph.CO↗

arXiv2017

Constraining the dark energy equation of state using Bayes theorem and the Kullback-Leibler divergence

Data-driven model-independent reconstructions of the dark energy equation of state $w(z)$ are presented using Planck 2015 era CMB, BAO, SNIa and Lyman-$α$ data. These reconstructions identify the $w(z)$ behaviour supported by the data and show a bifurcation of the equation of state posterior in the range $1.5{<}z{<}3$. Although the concordance $Λ$CDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as `phantom dark energy') is identified within the $1.5 σ$ confidence intervals of the posterior distribution. To identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback--Leibler divergence. This formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lyman-$α$ datasets. Further, SNIa and BAO constrain most strongly around redshift range $0.1-0.5$, whilst the Lyman-$α$ data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the $Λ$CDM model was favoured at more than $2$ log-units in Bayes factors over all the models tested despite the weakly preferred $w(z)$ structure in the data.

astro-ph.CO↗