Professor Pedro Ferreira

Abstract:

Light scalar particles arise naturally in many extensions of the standard model and are compelling dark-matter candidates. Gravitational interactions near black holes can trigger the growth of dense scalar configurations that, if sustained during inspiral, alter binary dynamics and imprint signatures on gravitational-wave signals. Detecting such effects would provide a novel probe of fundamental physics and dark matter. Here, we develop a semianalytic waveform model for binaries in scalar environments, validate it against numerical relativity simulations, and apply it in a Bayesian analysis of the LIGO-Virgo-KAGRA catalog. We obtain physically meaningful upper limits on scalar densities around most compact binaries. For GW190728 and GW190814, vacuum lies outside the 95% credible region. When including superradiance priors, GW190728 shows tentative evidence for a scalar environment with a Bayes factor of \(\ln \mathcal{B}_{\text{env}}^{\text{vac}} \approx 3.5\), consistent with a light scalar of mass ∼10^-12  eV.

Abstract:

Dark matter haloes are typically characterized by radial density profiles with fixed forms motivated by simulations (e.g. Navarro-Frenk-White [NFW]). However, simulation predictions depend on uncertain dark matter physics and baryonic modelling. Here, we present a method to constrain halo density profiles directly from observations using Exhaustive Symbolic Regression (ESR), a technique that searches the space of analytic expressions for the function that best balances accuracy and simplicity for a given dataset. We test the approach on mock weak lensing excess surface density (ESD) data of synthetic clusters with NFW profiles. Motivated by real data, we assign each ESD data point a constant fractional uncertainty and vary this uncertainty and the number of clusters to probe how data precision and sample size affect model selection. For fractional errors around 5%, ESR recovers the NFW profile even from samples as small as approximately 20 clusters. At higher uncertainties representative of current surveys, simpler functions are favoured over NFW, though it remains competitive. This preference arises because weak lensing errors are smallest in the outskirts, causing the fits to be dominated by the outer profile. ESR therefore provides a robust, simulation-independent framework both for testing mass models and determining which features of a halo's density profile are genuinely constrained by the data. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Physics seeks to uncover the laws of Nature and express them through mathematical equations . Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical expressions. While principles such as dimensional analysis have long guided the formulation of physical models, the exploration of more subtle statistical patterns within the equations of physics remains an open question. Here, by analysing four corpora of physics equations and applying advanced implicit-likelihood techniques, we find that the frequency of mathematical operators follows an exponential decay law, in contrast to Zipf's power law for word frequencies in natural languages. This reveals a statistical meta-law of physics, possibly reflecting a combination of communication efficiency and constraints imposed by Nature itself. The meta-law offers practical benefits for symbolic regression by drastically narrowing down the space of physically plausible expressions. More broadly, it may inform the development of language models that can generate coherent mathematical representations, advancing the automation of physical law discovery. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Skew spectra allow us to extract non-Gaussian information by taking the square of a map and finding the power spectrum of this new map with the original map. This allows us to use much of the infrastructure of power spectra and avoid the intricacies of estimating three point statistics. In this paper we present the first extension of skew spectra to arbitrary spin- $s$ fields, as a means to extract non-Gaussian information efficiently from cosmological datasets like cosmic shear or cosmic microwave background polarization. We apply the formalism to weak lensing in the context of large scale structure, and discuss different ways of combining fields to build skew spectra, all while avoiding the problems associated with mass mapping. We provide plots of these new statistics for $\mathrm{\Lambda }$ cold dark matter and vary cosmological parameters.