arXiv subjects

William T. Emond

Publications and source records attributed to William T. Emond.

17 recordsLinked to original sources

arXiv2025

Explicit finite-time illustration of improper unitary evolution for the Klein--Gordon field in de Sitter space

It is known that quantum field theories in curved spacetime suffer from a number of pathologies, including the inability to relate states on different spatial slices by proper unitary time-evolution operators. In this article, we illustrate this issue by describing the canonical quantisation of a free scalar field in de Sitter space and explicitly demonstrating that the vacuum at a given time slice is unitarily inequivalent to that at any other time. In particular, we find that, if both background and Hamiltonian dynamics are taken into account, this inequivalence holds even for infinitesimally small time steps and not only in the asymptotic time limits.

hep-th↗

arXiv2025

Topological modes, non-locality and the double copy

The double copy connects scattering amplitudes and other objects in gauge and gravity theories. Open conceptual issues include whether non-local information in gravity theories can be generated from the double copy, and how the double copy should be practically implemented in unseen cases. In this paper, we consider topological theories (with and without mass) in 2+1 dimensions, and argue that this makes a useful playground for exploring non-locality. In particular, topological modes of the gauge field arise, themselves associated with non-trivial global behaviour, and it is not clear {\it a priori} how to double copy them. We settle this issue, and clarify the role of BCJ shifts in modifying how topological modes contribute. We show how our conclusions apply to four- and five-point scattering amplitudes in topological gauge / gravity theories, as a by-product obtaining greatly simplified analytic expressions for the four-point amplitudes.

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arXiv2022

Mini-twistors and the Cotton Double Copy

The double copy relates quantities in gauge, gravity and related theories. A well-known procedure for relating exact classical solutions is the Weyl double copy in four spacetime dimensions, and a three-dimensional analogue of this -- the Cotton double copy -- has recently been found for topologically massive gauge theory and gravity. In this paper, we use twistor methods to provide a derivation of the position-space Cotton double copy, where this is seen to arise from combining appropriate data in so-called minitwistor space. Our methods rely on a massive generalisation of the Penrose transform linking spacetime fields with cohomology classes in minitwistor space. We identify the relevant transform from the twistor literature, but also show that it naturally arises from considering scattering amplitudes in momentum space. We show that the Cotton double copy in position space is only valid for type N solutions, but that a simple twistor space double copy is possible for non-type N solutions, where we use anyons to illustrate our arguments.

hep-th↗

arXiv2022

Shrouded black holes in Einstein-Gauss-Bonnet gravity

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like potential. For a proper choice of sign, the non-minimal coupling to gravity leads to symmetry restoration near the black hole horizon, prompting the development of the scalar wall in its vicinity. The wall thickness depends on the bare mass of the scalar and can be much smaller than the Schwarzschild radius. In a weakly coupled regime, the quadratic coupling to the Gauss-Bonnet invariant effectively becomes linear, and no walls are formed. We find approximate analytical solutions for the scalar field in the test field regime, and obtain numerically static black hole solutions within this setup. We discuss cosmological implications of the model and show that it is fully consistent with the existence of an inflationary stage, unlike the spontaneous scalarization scenario assuming the opposite sign of the non-minimal coupling to gravity. Our model predicts the speed of gravitational waves to be extremely close to unity, - in a comfortable agreement with the observation of the GW170817 event and its electromagnetic counterpart.

gr-qc↗

arXiv2022

Scattering Amplitudes and The Cotton Double Copy

We construct classical curvature spinors in topologically massive gauge theory and topologically massive gravity, expressed in terms of massive three-particle amplitudes. We show that when the amplitudes double copy, the curvature spinors satisfy the Cotton double copy, the three-dimensional cousin of the Weyl double copy. Furthermore, we show that under certain circumstances the Cotton double copy can be derived via a dimensional reduction of the Weyl double copy.

hep-th↗

arXiv2022

Gravitational waves from melting cosmic strings

Appearance of cosmic strings in the early Universe is a common manifestation of new physics typically linked to some high energy scale. In this paper, we discuss a different situation, where a model underlying cosmic string formation is approximately scale free. String tension is naturally related to the square of the temperature of the hot primordial plasma in such a setting, and hence decreases with (cosmic) time. With gravitational backreaction neglected, the dynamics of these melting strings in an expanding Universe is equivalent to the dynamics of constant tension strings in a Minkowski spacetime. We provide an estimate for the emission of gravitational waves from string loops. Contrary to the standard case, the resulting spectrum is markedly non-flat and has a characteristic falloff at frequencies below the peak one. The peak frequency is defined by the underlying model and lies in the range accessible by the future detectors for very weak couplings involved.

hep-ph↗

arXiv2021

Anyons and the Double Copy

We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimensions by introducing a non-trivial mixing of the topological graviton and the dilaton. Finally, we show that the celebrated Aharonov-Bohm phase can be derived directly from the constructed on-shell amplitude and that it too enjoys a simple double copy to its gravitational counterpart.

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arXiv2021

Quadratic curvature corrections to stringy effective actions and the absence of de Sitter vacua

We investigate the combined effect of fluxes and higher-order curvature corrections, in the form of the Gauss-Bonnet term, on the existence of de Sitter vacua in a heterotic string inspired framework, compactified on spheres and tori. We first gain some intuition on the effects of these corrections by studying a perturbative expansion in the small Gauss-Bonnet coupling. Then, for choices of potential closer to the string theory predictions, we show that the inclusion of quadratic curvature corrections actually reduces the parametric likelihood of de Sitter solutions.

hep-th↗

arXiv2021

Quantization Conditions and the Double Copy

We formulate Wilson loop observables as products of eikonal Wilson lines given in terms of on-shell scattering amplitudes. Using these, we derive the Dirac-Schwinger-Zwanziger quantization condition and its gravitational (Taub-NUT) double copy, where we find a relativistic generalisation of the usual non-relativistic gravitational quantization condition. We also compute the relativistic Wilson loop for an anyon-anyon system, obtaining a similar relativistic generalisation of the Aharonov-Bohm phase for gravitational anyons.

hep-th↗

arXiv2021

Rotating Black Holes in Cubic Gravity

Using on-shell amplitude methods, we derive a rotating black hole solution in a generic theory of Einstein gravity with additional terms cubic in the Riemann tensor. We give an explicit expression for the metric in Einsteinian Cubic Gravity (ECG) and low energy effective string theory, which correctly reproduces the previously discovered solutions in the zero angular-momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential, and we comment on the relation to the Janis-Newman algorithm. Furthermore, we derive the classical impulse and scattering angle for such a black hole and comment on the phenomenological interest of such quantities.

hep-th↗

arXiv2020

Amplitudes from Coulomb to Kerr-Taub-NUT

Electric-magnetic duality, the Newman-Janis shift, and the double copy all act by elementary operations on three-point amplitudes. At the same time, they generate a network of interesting classical solutions spanning from the Coulomb charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes corresponding to each of these solutions, working to all orders in spin, but to leading perturbative order. We confirm that the amplitudes double-copy when the solutions are related by the classical double copy. Along the way we show that the Kerr-Taub-NUT solution corresponds to a gravitational electric-magnetic duality rotation acting on the Kerr solution, again to all orders in spin, and demonstrate that the asymptotic charges also transform simply under our operations.

hep-th↗

arXiv2020

Unified framework for Early Dark Energy from $α$-attractors

One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift window around the time of recombination and dilutes faster than radiation afterwards. In this paper, we analyze EDE in the framework of $α$-attractor models. As well known, the success in alleviating the Hubble tension crucially depends on the shape of the energy injection. We show how different types of energy injections can be easily obtained, thanks to the freedom in choosing the functional form of the potential inspired by $α$-attractor models. To confirm our intuition we perform an MCMC analysis for three representative cases and find indeed that $H_0$ is significantly larger than in $Λ$CDM like in other EDE models. Unlike axion-driven EDE models with super Planckian decay constant, the curvature of EDE models required by the data is natural in the context of recent theoretical developments in $α$-attractors.

astro-ph.CO↗

arXiv2020

A larger value for $H_0$ by an evolving gravitational constant

We provide further evidence that a massless cosmological scalar field with a non-minimal coupling to the Ricci curvature of the type $M^2_{\rm pl}(1+ξσ^n/M_{\rm pl}^n) $ alleviates the existing tension between local measurements of the Hubble constant and its inference from CMB anisotropies and baryonic acoustic oscillations data in presence of a cosmological constant. In these models, the expansion history is modified compared to $Λ$CDM at early time, mimicking a change in the effective number of relativistic species, and gravity weakens after matter-radiation equality. Compared to $Λ$CDM, a quadratic ($n=2$) coupling increases the Hubble constant when {\em Planck} 2018 (alone or in combination with BAO and SH0ES) measurements data are used in the analysis. Negative values of the coupling, for which the scalar field decreases, seem favored and consistency with Solar System can be naturally achieved for a large portion of the parameter space without the need of any screening mechanism. We show that our results are robust to the choice of $n$, also presenting the analysis for $n=4$.

astro-ph.CO↗

arXiv2020

Black holes in self-tuning cubic Horndeski cosmology

Observations of neutron star mergers in the late Universe have given significant restrictions to the class of viable scalar-tensor theories. In this paper we construct black holes within the "self-tuning" class of this restricted set, whereby the bare cosmological constant is absorbed by the dynamics of the scalar, giving a lower effective cosmological constant. We use analytic expansions at the singularity, black hole and cosmological horizon, and asymptotic region, coupled with numerical solutions, to find well-behaved black holes that asymptote to the self-tuned de Sitter geometry. The geometry differs from standard general relativity black holes near the horizon, and the scalar field velocity provides a hair for the black holes.

gr-qc↗

arXiv2019

Well-Tempered Cosmology

We examine an approach to cosmology, known as Well-Tempering, that allows for a de Sitter phase whose expansion is independent of the cosmological constant. Starting from a generic scalar-tensor theory compatible with the recent gravitational wave observation, we impose the Well-Tempering conditions and derive a system that is capable of tuning away the cosmological constant within a sub-class of Horndeski theory, where the scalar has a canonical kinetic term and a general potential. This scenario improves upon the Fab-Four approach by allowing a standard fluid-cosmology before entering the de Sitter phase, and we present an explicit example of our general solution.

gr-qc↗

arXiv2018

Boltzmann equations for preheating

We derive quantum Boltzmann equations for preheating by means of the density matrix formalism, which account for both the non-adiabatic particle production and the leading collisional processes between the produced particles. In so doing, we illustrate the pivotal role played by pair correlations in mediating the particle production. In addition, by numerically solving the relevant system of Boltzmann equations, we demonstrate that collisional processes lead to a suppression of the growth of the number density even at the very early stages of preheating.

hep-th↗

arXiv2016

Disformally self-tuning gravity

We extend a previous self-tuning analysis of the most general scalar-tensor theory of gravity in four dimensions with second order field equations by considering a generalized coupling to the matter sector. Through allowing a disformal coupling to matter we are able to extend the Fab Four model and construct a new class of theories that are able to tune away the cosmological constant on Friedmann-Lemaitre-Robertson-Walker backgrounds.

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