Publications

You can find the complete list of my works on Google Scholar and Inspire.

Preprints

Emergence of phantom cold dark matter from spacetime diffusion, J. Oppenheim, EP and A. Pontzen, 2024

Abstract: A way to reconcile general relativity and quantum field theory without quantising the geometry is to demand the metric evolve stochastically. In this article, we explore the consequences of such a proposal at early cosmological times. We find the stochastic evolution results in the spatial metric diffusing away from its deterministic value, generating phantom cold dark matter (CDM). It is produced primarily at the end of the inflationary phase of the Universe's evolution, with a statistical distribution that depends on the specifics of the early-times cosmological model. We find the energy density of this phantom cold dark matter is positive on average, a necessary condition to reproduce the cosmological phenomenology of CDM, although further work is required to calculate its mean density and spatial distribution. If the density is cosmologically significant, phantom dark matter acts on the geometry in a way that is indistinguishable from conventional CDM. As such, it has the potential to reproduce phenomenology such as structure formation, lensing, and galactic rotation curves. We conclude by discussing the possibility of testing hybrid theories of gravity by combining measurements of the Cosmic Microwave Background with tabletop experiments.

Three-dimensional Quantum Black Holes: a Primer, EP, J. Pedraza and A. Svesko, 2024

Abstract: We review constructions of three-dimensional `quantum' black holes. Such spacetimes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large−c quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction. Notably, such quantum-corrected black holes are much larger than the Planck length. We describe the geometry and horizon thermodynamics of a host of asymptotically (anti-) de Sitter and flat quantum black holes. A summary of higher-dimensional extensions is given. We survey multiple applications of quantum black holes and braneworld holography.

Stochastic Dark Matter: Covariant Brownian Motion from Planckian Discreteness, E. Albertini, A. Nasiri, EP, 2024

Abstract: Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is the granularity of spacetime, which suggests that free particles would deviate from classical geodesics by following a covariant Brownian motion. This notion is further supported by swerves models in causal set theory, a discrete approach to quantum gravity. At an effective level, such deviations are described by a stochastic correction to the geodesic equation. We show that the form of this correction is strictly restricted by covariance and the mass-shell condition. Under minimal coupling to curvature, the resulting covariant Brownian motion is unique. The process is equivalently described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space. When applied to dark matter particles, covariant Brownian motion results in spontaneous warming at late times, suppressing the matter power spectrum at small scales in a time-dependent manner. Using bounds on the diffusion rate from CMB and growth history measurements of Sigma8, we show that the model offers a resolution to the S8 tension. Future studies on the model's behavior at non-linear cosmological scales will provide further constraints and, therefore, critical tests for the viability of stochastic dark matter.

Published works

Quantum Kerr-de Sitter Black Holes in Three Dimensions, EP and A. Svesko, JHEP, 2023, 127 (2023)

Abstract: We use braneworld holography to construct a three-dimensional quantum-corrected Kerr-de Sitter black hole, exactly accounting for semi-classical backreaction effects due to a holographic conformal field theory. By contrast, classically there are no de Sitter black holes in three-dimensions, only geometries with a single cosmological horizon. The quantum Kerr black hole shares many qualitative features with the classical four-dimensional Kerr-de Sitter solution. Of note, backreaction induces inner and outer black hole horizons which hide a ring singularity. Moreover, the quantum-corrected geometry has extremal, Nariai, and ultracold limits, which appear as fibered products of a circle and two-dimensional anti-de Sitter, de Sitter, and Minkowski space, respectively. The thermodynamics of the classical bulk black hole, described by the rotating four-dimensional anti-de Sitter C-metric, has an interpretation on the brane as thermodynamics of the quantum black hole, obeying a semi-classical first law where the Bekenstein-Hawking area entropy is replaced by the generalized entropy. For purposes of comparison, we derive the renormalized quantum stress-tensor due to a free conformally coupled scalar field in the classical Kerr-de Sitter conical geometry and perturbatively solve for its backreaction.

Path Integral Monte Carlo Methods for Option Pricing, P. Capuozzo, EP, T. Schettini Gherardini and D.D. Vvedensky, Physica A 581, 126231 (2021)

Abstract: The Markov chain Monte Carlo (MCMC) method, in conjunction with the Metropolis–Hastings algorithm, is used to simulate the path integral for the Black–Scholes–Merton model of option pricing. After a brief derivation of the path integral solution of this model, we develop the MCMC method by discretizing the path integral on a time lattice and evaluating this discretized form for various scenarios. Particular attention is paid to the existence of autocorrelations, their decay with the number of sweeps, and the resulting estimate of the corresponding errors. After testing our approach against closed-form solutions, we demonstrate the utility and flexibility of our method with applications to non-Gaussian models.

Non Invasive Amelioration of Essential Tremor via Phase Locked Disruption of its Temporal Coherence, S.R. Schreglmann et al., Nat Commun 12, 363 (2021)

Abstract: Aberrant neural oscillations hallmark numerous brain disorders. Here, we first report a method to track the phase of neural oscillations in real-time via endpoint-corrected Hilbert transform (ecHT) that mitigates the characteristic Gibbs distortion. We then used ecHT to show that the aberrant neural oscillation that hallmarks essential tremor (ET) syndrome, the most common adult movement disorder, can be transiently suppressed via transcranial electrical stimulation of the cerebellum phase-locked to the tremor. The tremor suppression is sustained shortly after the end of the stimulation and can be phenomenologically predicted. Finally, we use feature-based statistical-learning and neurophysiological-modelling to show that the suppression of ET is mechanistically attributed to a disruption of the temporal coherence of the aberrant oscillations in the olivocerebellar loop, thus establishing its causal role. The suppression of aberrant neural oscillation via phase-locked driven disruption of temporal coherence may in the future represent a powerful neuromodulatory strategy to treat brain disorders.

Master thesis (supervised by Professor Toby Wiseman)

Numerical Investigations of the Free Energy for a Scalar Field Theory on Deformed Spheres, EP (2021)

Abstract: Casimir energy is object of growing interest in physics, mainly due to recent techno- logical advances in condensed matter theory that might allow the study of quantum field theories in controlled lab conditions, but also for its possible applications in the gravity sector. Recent results seem to suggest that a (2 + 1)-dimensional non- interacting scalar field has its Casimir energy maximised, at least locally, by the round sphere with respect to arbitrarily big axisymmetric deformations. After re- viewing the theoretical background surrounding the topic of Casimir energy, we generalise such results, by extending the analysis to a more general family of dis- tortions. We deploy spectral numerical methods to calculate the Casimir energy of a free scalar field living on a R × Σ static spacetime, where Σ is a spatial manifold with S2 topology. We investigate the free energy for various geometries Σ, finding that the scalar disfavours the spherical configuration. We further systematically ex- plore the effect that non-minimal coupling to the background geometry has on the free energy, having it received little attention in previous works. We find that this extra contribution manifests itself as a secondary peak in the heat kernel profile, and observe the system to transition to a curvature dominated regime around the ξ = 1/6 value for the coupling. Suggestively, this is also the value of the coupling for which the massless scalar becomes conformally invariant. The effects of non-zero temperature and mass on the computed free energy are also considered.

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