arXiv subjects

E. P. S. Shellard

Publications and source records attributed to E. P. S. Shellard.

At least 19 recordsLinked to original sources

arXiv2026

Evolution of Cosmic String Loops under Gravitational Backreaction

Nambu-Goto cosmic string loops generically develop cusps, points where the string momentarily reaches the speed of light. These cusps produce strong gravitational wave bursts with a characteristic strain spectrum $\tilde{h}(\omega)\propto (G\mu)\,\omega^{-4/3}$, making them prime targets for gravitational wave searches, where $\mu$ is the string mass per unit length. However, this picture is modified when one accounts for gravitational backreaction. Using a convenient gauge, we reformulate the Nambu-Goto equations of motion for a loop moving in its own dynamically sourced gravitational field, enabling the first continuous numerical evolution of loops under this backreaction. A key finding is that locally cusps survive backreaction. Nevertheless, the gravitational waveform calculated in this formalism is significantly modified, weakening the cusp burst and introducing a high-frequency cutoff at $f_c\propto(G\mu)^{-3/2}$. This suppression above $f_c$ reduces the expected signal-to-noise ratio in current and near-future detectors relative to unperturbed waveform predictions.

gr-qc↗

arXiv2026

Primordial non-Gaussianity constraints on dissipative inflation

Dissipative effects appear in many early-Universe scenarios, yet their universal observational signatures and systematic confrontation with data remain largely unexplored. We employ the Open Effective Field Theory of Inflation (Open EFToI) to consistently incorporate dissipative and stochastic effects while preserving scale invariance. Dissipation enhances specific interaction channels of the Goldstone mode, generating distinctive primordial non-Gaussian signatures, beyond those generically produced by standard EFToI. In the weak-dissipation regime, this includes folded bispectrum shapes observationally more favoured than both the equilateral and orthogonal templates. Using the Modal bispectrum pipeline with the Planck CMB data, we obtain the likelihood and derive the first model-independent bounds on early-Universe dissipation. We find a marginalised upper bound on the dissipation scale $\gamma \leq 384\,H$ and a lower bound on the sound speed $c_s \geq 0.38$ at $95\%$ confidence level. The maximum likelihood for best-fit models reveals a degeneracy between $\gamma$ and $c_s$. These results open a model-independent window for probing departures from minimal inflation and discriminating between early-Universe scenarios with stochastic noise and dissipative effects.

astro-ph.CO↗

arXiv2025

Searching for Cosmological Collider in the Planck CMB Data II: collider templates and Modal analysis

Signatures of massive particles during inflation are highly informative targets for cosmological experiments. With recent progress on both theoretical and observational frontiers, we have reached the point where these novel signals of primordial non-Gaussianities (PNG) can be systematically tested with increasingly precise data. In this paper, we present the results of improved CMB data analysis for cosmological collider signals using Planck CMB data. To set the stage, we first construct a set of simplified but characteristic collider templates which are accurate over a broad range of particle masses, spins and sound speeds. In order to break degeneracies with single-field PNG, we propose an orthogonalization scheme such that the collider templates are uncorrelated with the highly constrained equilateral and orthogonal shapes. On this basis, we deploy the Modal bispectrum estimator for the Planck analysis and perform a systematic scan of parameters to search for the most significant collider signal. The maximum signal-to-noise ratio is found to be $2.35\sigma$ for massive spin-0 exchange after taking into account the look-elsewhere effect. In addition, we cross-validate the Modal analysis with the CMB-BEST pipeline, which demonstrates the consistency of results across the benchmark examples of collider templates. Given the low signal-to-noise ratio regime we find at the current stage of PNG observations, we believe the orthogonalization procedure provides an optimized strategy for future tests of the cosmological collider with the ability to rule out single field inflation.

astro-ph.CO↗

arXiv2025

A Modal Approach to Constrain Inflation through Numerical Bispectra

Constraining inflationary models with high precision bispectra across broad parameter ranges is a challenging task, requiring intensive computations at all stages, first, predicting the primordial inflation bispectrum from quantum field theory, secondly, projecting this forward with transfer functions to the late universe and, finally, comparing with the bispectrum extracted from the observational data and matching mock catalogues. Here, the longstanding separable \texttt{Modal} pipeline for constraining primordial bispectrum templates using WMAP and Planck CMB data has been supplemented by the more recently developed \texttt{Primodal} code to accurately calculate bispectra numerically from inflation models, showing great potential for enhanced computational efficiency; \texttt{Primodal} exploits the in-in separability of the tree-level in-in formalism, together with a separable mode-expansion technique to bypass the need for point-by-point bispectrum calculations. Building upon this progress, we propose a bispectrum pipeline that systematically explores the parameter space of inflationary Lagrangians, numerically computing the tree-level bispectrum (and power spectrum) for each scenario and comparing with the \texttt{Modal} bispectrum decompositions obtained from the Planck 2018 data. Our pipeline identifies and excludes disfavored scenarios through this analysis, providing direct constraints on the parameter space, the sound speed and other quantities from the surviving observationally viable scenarios. This is preparatory work for a planned analysis using much higher-resolution CMB data from the Simons Observatory. To validate our pipeline, we perform a proof-of-concept analysis of the IR DBI inflation model, obtaining constraints of $c_s \geq 0.073$ for the sound speed and $\beta \leq 0.39$ for the parameter space, demonstrating the pipeline's accuracy and effectiveness.

astro-ph.CO↗

arXiv2025

How Significant are Cosmological Collider Signals in the Planck Data?

The search for primordial non-Gaussianities (PNG) is theoretically well motivated but remains observationally challenging. Tight constraints with low significance for the standard non-Gaussian shapes suggest that detection may lie beyond the reach of near-future experiments. However, tests of PNG are highly template-dependent. From a theory perspective, a whole new family of bispectrum shapes arise in the cosmological collider program, with distinct signatures of heavy particles during inflation. In this work, we provide a class of simplified collider templates for these particles that encompasses a broader range of masses, sound speeds, and interactions. We propose that, given the current state of observations, the most effective strategy to search for PNG signals is through orthogonalizing the collider templates, such that they are uncorrelated with the tightly constrained single field predictions. Using the Modal pipeline and Planck CMB data, we perform a systematic parameter scan of the collider templates with the most significant result reaching $2.4\sigma$ for spin-0, after taking into account the look-elsewhere effect; indicative results for spin-1 and spin-2 peak near 2$\sigma$. These results indicate that, with refined collider templates and improved data analysis strategies, there are credible prospects with forthcoming observations to detect PNG and also rule out single field inflation.

astro-ph.CO↗

arXiv2024

Searching for Cosmological Collider in the Planck CMB Data

In this paper, we present the first comprehensive CMB data analysis of cosmological collider physics. New heavy particles during inflation can leave imprints in the primordial correlators which are observable in today's cosmological surveys. This remarkable detection channel provides an unsurpassed opportunity to probe new physics at extremely high energies. Here we initiate the search for these relic signals in the cosmic microwave background (CMB) data from the Planck legacy release. On the theory side, guided by recent progress from the cosmological bootstrap, we first propose a family of analytic bispectrum templates that incorporate the distinctive signatures of cosmological collider physics. Our consideration includes the oscillatory signals in the squeezed limit, the angular dependence from spinning fields, and several new shapes from nontrivial sound speed effects. On the observational side, we apply the recently developed pipeline, CMB Bispectrum Estimator (CMB-BEST), to efficiently analyze the three-point statistics and search directly for these new templates in the Planck 2018 temperature and polarization data. We report stringent CMB constraints on these new templates. Furthermore, we perform parameter scans to search for the best-fit values with maximum significance. For a benchmark example of collider templates, we find $f_{NL}=-91\pm40$ at the $68\%$ confidence level. After accounting for the look-elsewhere effect, the biggest adjusted significance we get is $1.8σ$. In general, we find no significant evidence of cosmological collider signals in the Planck data. However, this innovative analysis demonstrates the potential for discovering new heavy particles during inflation in forthcoming cosmological surveys.

astro-ph.CO↗

arXiv2024

Cosmic Microwave Background Signatures from Current-carrying Cosmic Strings

We continue our studies of the evolution and cosmological consequences of current-carrying cosmic string networks, described by a charge-velocity-dependent one scale (CVOS) model. We present a detailed calculation of the effects of these networks on the cosmic microwave background (CMB), in the context of this model, and specifically discuss how such current-carrying strings may be distinguished from their uncharged (Nambu-Goto) counterparts by current or forthcoming CMB data. We find that, under the CVOS hypothesis, the constraints on current-carrying strings should not differ much from those of their structureless counterparts in that the impact on the CMB can at most be reduced by a factor of ~25%. Nevertheless, the presence of a current and charge affects the distribution of power among scalar, vector and tensor modes, and also its distribution between small and large scales. It should therefore be possible for future high-sensitivity CMB experiments to distinguish between the two types of strings.

astro-ph.CO↗

arXiv2024

Stochastic Inflation in General Relativity

We provide a formulation of Stochastic Inflation in full general relativity that goes beyond the slow-roll and separate universe approximations. We show how gauge invariant Langevin source terms can be obtained for the complete set of Einstein equations in their ADM formulation by providing a recipe for coarse-graining the spacetime in any small gauge. These stochastic source terms are defined in terms of the only dynamical scalar degree of freedom in single-field inflation and all depend simply on the first two time derivatives of the coarse-graining window function, on the gauge-invariant mode functions that satisfy the Mukhanov-Sasaki evolution equation, and on the slow-roll parameters. It is shown that this reasoning can also be applied to include gravitons as stochastic sources, thus enabling the study of all relevant degrees of freedom of general relativity for inflation. We validate the efficacy of these Langevin dynamics directly using an example in uniform field gauge, obtaining the stochastic e-fold number in the long wavelength limit without the need for a first-passage-time analysis. As well as investigating the most commonly used gauges in cosmological perturbation theory, we also derive stochastic source terms for the coarse-grained BSSN formulation of Einstein's equations, which enables a well-posed implementation for 3+1 numerical relativity simulations.

gr-qc↗

arXiv2023

Axion String Source Modelling

In this paper, we perform an investigation into the effect of the string radius of curvature $R_\mathrm{\,Gaussian}$ on the magnitude and relative magnitude of the massive and massless radiation from axion (global) string configurations, motivated by qualitative observations from string network simulations. We construct initial conditions from travelling wave solutions on a global string for two colliding Gaussians, performing parameter scans over amplitude $A$ and standard deviation $σ_\mathrm{d}$. We show that the energy emitted via massless radiation obeys a power law $E_\mathrm{massless} \propto A^γ$, where the coefficient $γ$ depends on the curvature regime. Massive radiation is exponentially suppressed approximately as $E_{\mathrm{massive}} \propto e^{-ζR_\mathrm{\,Gaussian}}$ in the quasi-linear regime $σ_\mathrm{d} \gg δ$ and exhibits power-law decay $E_{\mathrm{massive}} \propto (R_\mathrm{\,Gaussian})^{-γ}$ in the nonlinear regime where $σ_\mathrm{d} \lesssim 2δ$, with different $γ$ in different regimes of $R_\mathrm{\,Gaussian}$. In certain regions of the nonlinear regime, massive particle radiation comprises up to 50% of the total energy emitted. Drawing on a known parallel between axion radiation from global strings and gravitational radiation from Abelian-Higgs strings, this suggests that massive particle radiation channel may become of equal significance to the massless (gravitational) channel for nonlinear burst signals where $R < σ_\mathrm{d}$, unless we are in the regime where additional loops are generated. We also estimate the spectral index $q$ of the axion radiation for different amplitudes, showing that a higher proportion of radiation is emitted in high frequency modes as the curvature increases, bounded by $q \gtrsim 1$ for the configurations studied.

astro-ph.CO↗

arXiv2023

High-resolution CMB bispectrum estimator with flexible modal basis

We present a new independent pipeline for the CMB bispectrum estimation of primordial non-Gaussianity and release a public code for constraining bispectrum shapes of interest based on the Planck 2018 temperature and polarization data. The estimator combines the strengths of the conventional KSW and Modal estimators at the cost of increased computational complexity, which has been made manageable through intensive algorithmic and implementation optimization. We also detail some methodological advances in numerical integration over a tetrapyd - domain where the bispectrum is defined on - via new quadrature rules. The pipeline has been validated both internally and against Planck. As a proof-of-concept example, we constrain some highly oscillatory models that were out of reach in conventional analyses using a targeted basis with a fixed oscillation frequency, and no significant evidence for primordial non-Gaussianity of these shapes is found. The methodology and code developed in this work will be directly applicable to future surveys where we expect a notable boost in sensitivity.

astro-ph.CO↗

arXiv2023

Cosmological evolution of Witten superconducting string networks

We consider the evolution of current-carrying cosmic string networks described by the charge-velocity-dependent one scale (CVOS) model beyond the linear equation of state regime, specifically focusing on the Witten superconducting model. We find that, generically, for almost chiral currents, the network evolution reduces dynamically to that of the linear case, which has been discussed in our previous work. However, the Witten model introduces a maximum critical current which constrains the network scaling behaviour during the radiation era when currents can grow and approach this limit. Unlike the linear model, only if the energy density in the critical current is comparable to the bare string tension will there be substantial backreaction on the network evolution, thus changing the observational predictions of superconducting strings from those expected from a Nambu-Goto network. During the matter era, if there are no external sources, then dynamical effects dilute these network currents and they disappear at late times.

astro-ph.CO↗

arXiv2023

Radiation from Global Topological Strings using Adaptive Mesh Refinement: Massive Modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public code, GRChombo. We perform a quantitative investigation of massive radiation from single sinusoidally displaced string configurations, studying a range of string widths defined by the coupling parameter $λ$ over two orders of magnitude, effectively varying the mass of radiated particles $m_H \sim \sqrtλ$. We perform an in-depth investigation into the effects of AMR on massive radiation emission, including radiation trapping and the refinement required to resolve high frequency modes. We use quantitative diagnostic tools to determine the eigenmode decomposition, showing a complex superposition of high frequency propagating modes with different phase and group velocities. We conclude that massive radiation is generally strongly suppressed relative to the preferred massless channel, with suppression increasing at lower amplitudes and higher $λ$. Only in extreme nonlinear regimes (e.g.\ with relative amplitude $\varepsilon \sim 1.5$ and $λ< 1$) do we observe massive and massless radiation to be emitted at comparable magnitude. We find that massive radiation is emitted in distinct high harmonics of the fundamental frequency of the string, and we demonstrate that, for the sinusoidal configurations studied, massive radiation is exponentially suppressed with $\sqrtλ$ (i.e. the particle mass). Finally, we place these results in the context of axions and gravitational waves produced by cosmological cosmic string networks, and note that AMR provides a significant opportunity to explore higher $λ$ (thin string) regimes whilst using fewer computational resources.

astro-ph.CO↗

arXiv2022

Radiation from Global Topological Strings using Adaptive Mesh Refinement: Methodology and Massless Modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public numerical relativity code, GRChombo. We perform a quantitative investigation of the dynamics of single sinusoidally displaced string configurations, studying a wide range of string energy densities $μ\propto \lnλ$, defined by the string width parameter $λ$ over two orders of magnitude. We investigate the resulting massless (Goldstone boson or axion) radiation signals, using quantitative diagnostic tools to determine the eigenmode decomposition. Given analytic radiation predictions, we compare the oscillating string trajectory with a backreaction model accounting for radiation energy losses, finding excellent agreement. We establish that backreaction decay is accurately characterised by the inverse square of the amplitude being proportional to the inverse tension $μ$ for $3\lesssim λ\lesssim 100$. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate cosmological limit for global strings. We contextualise these results with respect to axions and gravitational waves produced by cosmic string networks.

astro-ph.CO↗

arXiv2021

Charge-velocity-dependent one-scale linear model

We apply a recently developed formalism to study the evolution of a current-carrying string network under the simple but generic assumption of a linear equation of state. We demonstrate that the existence of a scaling solution with non-trivial current depends on the expansion rate of the universe, the initial root mean square current on the string, and the available energy loss mechanisms. We find that the fast expansion rate after radiation-matter equality will tend to rapidly dilute any pre-existing current and the network will evolve towards the standard Nambu-Goto scaling solution (provided there are no external current-generating mechanisms). During the radiation era, current growth is possible provided the initial conditions for the network generate a relatively large current and/or there is significant early string damping. The network can then achieve scaling with a stable non-trivial current, assuming large currents will be regulated by some leakage mechanism. The potential existence of current-carrying string networks in the radiation era, unlike the standard Nambu-Goto networks expected in the matter era, could have interesting phenomenological consequences.

astro-ph.CO↗

arXiv2021

Probing Inflation with Precision Bispectra

Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained. Exploiting the inherent separability of the tree level in-in formalism using expansions in separable basis functions provides a means by which to obviate some of these difficulties. Here, we develop this approach further into a practical and efficient numerical methodology which can be applied to a much wider and more complicated range of bispectrum phenomenology, making an important step forward towards observational pipelines which can directly confront specific models of inflation. We describe a simple augmented Legendre polynomial basis and its advantages, then test the method on single-field inflation models with non-trivial phenomenology, showing that our calculation of these coefficients is fast and accurate to high orders.

astro-ph.CO↗

arXiv2020

Generalised velocity-dependent one-scale model for current-carrying strings

We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string worldsheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or alternatively the string correlation length) and the root mean square (RMS) velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.

astro-ph.CO↗

arXiv2019

Advancing the matter bispectrum estimation of large-scale structure: fast prescriptions for galaxy mock catalogues

We investigate various phenomenological schemes for the rapid generation of 3D mock galaxy catalogues with a given power spectrum and bispectrum. We apply the fast bispectrum estimator \MODALLSS{} to these mock galaxy catalogues and compare to $N$-body simulation data analysed with the halo-finder \texttt{ROCKSTAR} (our benchmark data). We propose an assembly bias model for populating parent halos with subhalos by using a joint lognormal-Gaussian probability distribution for the subhalo occupation number and the halo concentration. This prescription enabled us to recover the benchmark power spectrum from $N$-body simulations to within 1\% and the bispectrum to within 4\% across the entire range of scales of the simulation. A small further boost adding an extra galaxy to all parent halos above the mass threshold $M>2\times10^{14}\,h^{-1} M_\odot$ obtained a better than 1\% fit to both power spectrum and bispectrum in the range $K/3<1.1\,h\,\text{Mpc}^{-1}$, where $K=k_1+k_2+k_3$. This statistical model should be applicable to fast dark matter codes, allowing rapid generation of mock catalogues which simultaneously reproduce the halo power spectrum and bispectrum obtained from $N$-body simulations. We also investigate alternative schemes using the Halo Occupation Distribution (HOD) which depend only on halo mass, but these yield results deficient in both the power spectrum (2\%) and the bispectrum (>4\%) at $k,K/3 \approx 0.2\,h\,\text{Mpc}^{-1}$, with poor scaling for the latter. Efforts to match the power spectrum by modifying the standard four-parameter HOD model result in overboosting the bispectrum (with a 10\% excess). We also characterise the effect of changing the halo profile on the power spectrum and bispectrum.

astro-ph.CO↗

arXiv2019

General modal estimation for cross-bispectra

We describe a fast, optimal estimator for measuring angular bispectra between two correlated weakly non-Gaussian fields ($Y$ and $Z$) from observational datasets, based on a separable modal bispectrum expansion. Our methodology is applicable to (1) any shape of the input theoretical bispectrum templates (factorizable or not), (2) both even and odd $\ell_1 + \ell_2 + \ell_3$ multipole domains and (3) both amplitude ($f_{\rm NL})$ bispectrum estimation and full bispectrum reconstruction, considering either joint estimation of ($YYY$, $ZZZ$, $YYZ$ and $ZZY$) shapes, or independent estimation of auto-bispectra ($YYY$ or $ZZZ$) and cross-bispectra ($YYZ$ or $ZZY$); hence, it has quite high versatility. The methodology described here was implemented and used for the official analysis of temperature and polarization cosmic microwave background maps from the $Planck$ satellite.

astro-ph.CO↗