arXiv subjects

Pedro G. Ferreira

Publications and source records attributed to Pedro G. Ferreira.

At least 19 recordsLinked to original sources

arXiv2026

The Status of Single Scalar Field Dark Energy

We present an assessment of the current observational status of single scalar field models of dark energy. Motivated by recent cosmological measurements -- including baryon acoustic oscillations, Type Ia supernovae, and CMB data -- we examine whether a dynamical scalar field offers a viable explanation for the accelerated expansion of the Universe. Working within an effective field theory (EFT) framework, we argue that cosmological observations are fundamentally limited and can at most constrain a small number of parameters that govern scalar field dynamics. We show that quintessence remains only marginally distinguishable from a cosmological constant, $Λ$, and that more general EFT extensions exhibit modest statistical preference, though such evidence is sensitive to data set selection and prior assumptions. These extended models generically predict fifth forces and modifications to the growth of structure, raising challenges from astrophysical constraints. We compare their predictions with current growth rate measurements, Integrated Sachs-Wolfe (ISW) effect and Solar System constraints. We emphasize that viable screening mechanisms remain theoretically non-trivial and observationally testable. On the other hand, we find that current ISW and growth data remain largely in agreement. Looking ahead to Stage IV surveys we forecast improvements in constraints on the dark energy behaviour; although there will be some tightening of bounds, we argue that the problem of underdetermination will persist. We conclude that while single scalar field dark energy remains a natural and flexible framework, its ultimate viability will hinge on improved low-redshift growth measurements and a clearer understanding of gravitational screening.

astro-ph.CO↗

arXiv2026

Evaluation of Population Initialization Methods for Genetic Programming-based Symbolic Regression

We analyze the effect of optimizing the initial population of genetic programming (GP) for symbolic regression (SR) on the accuracy and complexity of solutions. We compare three well-established random initialization methods as well as initialization with small optimized solutions from exhaustive symbolic regression (ESR) using a GP/SR implementation which is based on the multi-objective evolutionary algorithm NSGA-II. We compare the final Pareto fronts found with each initialization method on twelve synthetic problems of varying complexity and one real-world dataset. We find no significant differences in accuracy or model complexity among the initialization methods. The initial advantage of initialization with ESR disappears after only a few generations. Our results show that, given similar diversity in the initial population, the effect of the initialization method in GP-based symbolic regression on the final Pareto front is negligible.

cs.NE↗

arXiv2026

CMBolic: Symbolic emulators for the Cosmic Microwave Background. I. Lensing

We present the first installment of CMBolic: a suite of symbolic cosmic microwave background (CMB) emulators. In this instance, we emulate the CMB lensing potential power spectrum $C_\ell^{ϕϕ}$ for the widely used extended $Λ$CDM model which simultaneously includes massive neutrinos and evolving dark energy modelled using the Chevallier-Polarski-Linder (CPL) parameterization. We achieve comparable precision to existing neural network emulators, with the added benefit of simpler handling as our emulators are analytic functions of the model parameters and multipole $\ell$. On independent validation spectra evaluated in the range $2\leq \ell \leq 5500$, CMBolic achieves mean absolute fractional errors of $0.27\%$ in the $Λ$CDM subspace and $0.32\%$ across the full extended parameter space. This emulation error is well below even the most optimistic noise forecasts from CMB Stage 4 experiments. We apply CMBolic to cosmological parameter estimation with Bayesian inference using the lensing-only likelihoods from ACT DR6 and Planck. We show excellent agreement between the posteriors obtained by CMBolic and the Boltzmann code CLASS. This demonstrates the practical use of CMBolic on cosmological parameter estimation, reducing the runtime from 2 weeks to under 3 minutes.

astro-ph.CO↗

arXiv2026

Cosmological constraints on Galileon dark energy with broken shift symmetry

Current cosmological data seem to show that dark energy is evolving in time and that it possibly crossed the phantom divide in the past. So far the only theories that lead to such a behavior involve a non-trivial coupling between dark energy, in the form of a scalar field, and the gravitational or matter sector. We show that there is another possibility involving both a non-trivial kinetic sector in a cubic Galileon theory and a scalar field potential that breaks the Galileon shift symmetry, which can lead to a similar phenomenology on large scales. We perform a full Bayesian analysis using the latest cosmological data, including DESI DR2 BAO measurements, type Ia SNe measurements from DESY5, Union3, and Pantheon+, and CMB data from Planck and ACT. We find that it is statistically strongly favored over a Universe dominated by a cosmological constant (with a Bayes factor of $\log B\simeq 6.5$). Yet, as with other non-minimally coupled theories, it has severe ancillary gravitational effects. These can be mitigated to some extent, but as with other viable theories, the penalty is ever more elaborate scalar field models of dark energy.

astro-ph.CO↗

arXiv2026

Guiding Multi-Objective Genetic Programming with Description Length Improves Symbolic Regression Solutions

Symbolic regression with genetic programming (GPSR) may suffer from overfitting and structural bloat, especially when noise is present. In this paper we evaluate description length (DL) and fractional Bayes factor (FBF) criteria as principled, data-efficient alternatives to heuristics for selecting compact expressions that generalise well. We implement DL using a Fisher-information-based parameter encoding and compare it to AIC and BIC across multiple datasets, including noisy synthetic benchmarks and real-world regression problems. We study three search/selection strategies: (i) multi-objective search for accuracy and program length followed by DL/FBF selection; (ii) multi-objective search using DL directly as an objective; and (iii) single-objective optimisation with DL/FBF as the fitness. Across datasets we find that DL/FBF post-selection improves test performance compared to AIC/BIC baseline and that BIC in combination with the same function complexity penalty from DL/FBF produces similar results. In contrast, using DL/FBF directly as a fitness function in single-objective GPSR frequently induces premature convergence to overly simple models. We conclude with practical guidance for using DL/FBF as robust model-selection tools in genetic programming workflows.

cs.NE↗

arXiv2026

Scalar fields around black hole binaries in LIGO-Virgo-KAGRA

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 semi-analytic 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 $\ln \mathrm{B}^{\rm env}_{\rm vac} \approx 3.5$, consistent with a light scalar of mass $\sim10^{-12}\,\mathrm{eV}$.

gr-qc↗

arXiv2026

Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature

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.

physics.soc-ph↗

arXiv2026

Testing cosmic anisotropy with cluster scaling relations

We test claims of large-scale anisotropy in the local expansion rate using cluster scaling relations as distance indicators. Using a Bayesian forward model, we jointly fit the X-ray luminosity--temperature (LT) and thermal Sunyaev-Zel'dovich--temperature (YT) relations, marginalising over the latent cluster distances and modelling selection effects as well as peculiar velocities. The latter are modelled using reconstructions of the local peculiar velocity field where we self-consistently account for possible anisotropic redshift--distance relations via an approximate scheme. This treatment proves crucial to the inferred anisotropy and breaks the degeneracy between anisotropy in scaling relation normalisations and underlying cosmological anisotropy. We apply our method to 312 clusters at $z \lesssim 0.2$, testing dipolar, quadrupolar and general (pixelised) anisotropy models. Bayesian model selection finds no more than weak evidence for any anisotropic model. For dipole models, we obtain upper limits of $δH_0 / H_0 < 3.2\%$ and bulk flow magnitude $< 1300\,\mathrm{km\,s^{-1}}$. Our results contrast with previous claims of statistically significant anisotropy from the same data, which we attribute to our principled forward modelling of both redshifts and scaling relation observables through latent distances and our treatment of the impact of anisotropic redshift--distance relations when modelling the local peculiar velocity field. Our work highlights the importance of accurately modelling peculiar velocities when testing isotropy with distance indicators, and motivates the further development of reconstructions that self-consistently treat large-scale deviations from the Hubble flow.

astro-ph.CO↗

arXiv2026

Apparent Dark-Energy Evolution from Cosmic Inhomogeneities

A mildly inhomogeneous universe with a cosmological constant may look like it contains evolving dark energy. We show that could be the case by modelling the inhomogeneities and their effects in three different ways: as clumped matter surrounded by voids, as back-reaction of small-scale structure on the overall expansion of the Universe, and, finally, as a large-scale curvature inhomogeneity. In all of these cases, the propagation of light is affected, and differs from that in a homogeneous and isotropic universe. The net result is that cosmological observables, such as angular diameter and luminosity distances, become distorted. We find, in all three models, that the inclusion of these effects pushes the distance-redshift relation towards closer agreement with recent data from both supernovae Ia from the Dark Energy Survey, and from baryon acoustic oscillations from the Dark Energy Spectroscopic Instrument. The amount of inhomogeneity in these models might not be enough to explain the entirety of the deviation from a cosmological constant, but is found to be of a similar order of magnitude, hinting that these data may be consistent with a universe dominated by a cosmological constant.

astro-ph.CO↗

arXiv2026

Symbolically regressing dark matter halo profiles using weak lensing

The structure of dark matter haloes is often described by radial density profiles motivated by cosmological simulations. These are typically assumed to have a fixed functional form (e.g. NFW), with some free parameters that can be constrained with observations. However, relying on simulations has the disadvantage that the resulting profiles depend on the dark matter model and the baryonic physics implementation, which are highly uncertain. Instead, we present a method to constrain halo density profiles directly from observations. This is done using a symbolic regression algorithm called Exhaustive Symbolic Regression (ESR). ESR searches for the optimal analytic expression to fit data, combining both accuracy and simplicity. We apply ESR to a sample of 149 galaxy clusters from the HSC-XXL survey to identify which functional forms perform best across the entire sample of clusters. We identify density profiles that statistically outperform NFW under a minimum-description-length criterion. Within the radial range probed by the weak-lensing data ($R \sim 0.3 - 3$ h$^{-1}$ Mpc), the highest-ranked ESR profiles exhibit shallow inner behaviour and a maximum in the density profile. As a practical application, we show how the best-fitting ESR models can be used to obtain enclosed mass estimates. We find masses that are, on average, higher than those derived using NFW, highlighting a source of potential bias when assuming the wrong density profile. These results have important knock-on effects for analyses that utilise clusters, for example cosmological constraints on $σ_8$ and $Ω_m$ from cluster abundance and clustering. Beyond the HSC dataset, the method is readily applicable to any data constraining the dark matter distribution in galaxies and galaxy clusters, such as other weak lensing surveys, galactic rotation curves, or complementary probes.

astro-ph.CO↗

arXiv2025

Introduction to Symbolic Regression in the Physical Sciences

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the Special Issue on Symbolic Regression for the Physical Sciences, motivated by the Royal Society discussion meeting held in April 2025. The contributions collected here span applications from automated equation discovery and emergent-phenomena modelling to the construction of compact emulators for computationally expensive simulations. The introductory review outlines the conceptual foundations of SR, contrasts it with conventional regression approaches, and surveys its main use cases in the physical sciences, including the derivation of effective theories, empirical functional forms and surrogate models. We summarise methodological considerations such as search-space design, operator selection, complexity control, feature selection, and integration with modern AI approaches. We also highlight ongoing challenges, including scalability, robustness to noise, overfitting and computational complexity. Finally we emphasise emerging directions, particularly the incorporation of symmetry constraints, asymptotic behaviour and other theoretical information. Taken together, the papers in this Special Issue illustrate the accelerating progress of SR and its growing relevance across the physical sciences.

cs.LG↗

arXiv2025

A Short Introduction to Cosmology and its Current Status

The current cosmological model, known as the $Λ$-Cold Dark Matter model (or $Λ$CDM for short) is one of the most astonishing accomplishments of contemporary theoretical physics. It is a well-defined mathematical model which depends on very few ingredients and parameters and is able to make a range of predictions and postdictions with astonishing accuracy. It is built out of well-known physics - general relativity, quantum mechanics and atomic physics, statistical mechanics and thermodynamics - and predicts the existence of new, unseen components. Again and again it has been shown to fit new data sets with remarkable precision. Despite these successes, we have yet to understand the unseen components of the Universe and there has been evidence for inconsistencies in the model. In these lectures, we lay the foundations of modern cosmology.

astro-ph.CO↗

arXiv2025

The Cosmological Dipole in Tilted Anisotropic Universes

There is tentative evidence for a mismatch between the rest frames of matter and the cosmic microwave background, the "quasar dipole anomaly". We consider such a dipole in tilted anisotropic models, for a range of scenarios and sources: spatial curvature, cosmic heat flux, large scale electromagnetic fields and a Khronon field. Crucially, we determine the ancillary effects on other cosmological observables in each of these models and we show that, apart from the case of the Khronon field, it is unlikely that one can obtain a dipole with the amplitude that is being observed unless one considers additional exotica.

astro-ph.CO↗

arXiv2025

Constraining dark matter halo profiles with symbolic regression

Dark matter haloes are typically characterised by radial density profiles with fixed forms motivated by simulations (e.g. 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 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.

astro-ph.CO↗

arXiv2025

Skew-spectra: a generalization to spin-$s$

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 data sets like cosmic shear or CMB 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 $Λ$CDM and vary cosmological parameters.

astro-ph.CO↗

arXiv2025

Assessing cosmological evidence for non-minimal coupling

The recent observational evidence of deviations from the $Λ$-Cold Dark Matter ($Λ$CDM) model points towards the presence of evolving dark energy. The simplest possibility consists of a cosmological scalar field $φ$, dubbed quintessence, driving the accelerated expansion. We assess the evidence for the existence of such a scalar field. We find that, if the accelerated expansion is driven by quintessence, the data favour a potential energy $V(φ)$ that is concave, i.e., $m^2=d^2V/dφ^2<0$. Furthermore, and more significantly, the data strongly favour a scalar field that is non-minimally coupled to gravity (Bayes factor $\log(B) = 7.34 \pm 0.6$), leading to time variations in the gravitational constant on cosmological scales, and the existence of fifth forces on smaller scales. The fact that we do not observe such fifth forces implies that either new physics must come into play on non-cosmological scales or that quintessence is an unlikely explanation for the observed cosmic acceleration.

astro-ph.CO↗

arXiv2025

The Spectre of Underdetermination in Modern Cosmology

The scientific status of physical cosmology has been the subject of philosophical debate ever since detailed mathematical models of the Universe emerged from Einstein's general theory of relativity. Such debates have revolved around whether and to what extent cosmology meets established demarcation criteria for a discipline to be scientific, as well as determining how to best characterize cosmology as a science, given the unique challenges and limitations faced by a discipline which aims to study the origin, composition, and fate of the Universe itself. The present article revisits, in light of the dramatic progress in cosmology in recent decades, an earlier debate held in the 1950s between Herman Bondi and Gerald Whitrow regarding the scientific status of cosmology. We analyse cosmology's transition from an emerging science to a cornerstone of modern physics, highlighting its empirical successes in establishing the $Λ$-Cold Dark Matter ($Λ$CDM) model and in its delivery of various successful novel predictions. Despite this remarkable scientific success and progress, we argue that modern cosmology faces a further profound challenge: the permanent underdetermination of the microphysical nature of its exotic energy components: inflation, dark matter, and dark energy. Drawing historical parallels with the role of spectroscopy in revealing the microphysical nature of atomic physics, we argue that the epistemic barriers obstructing us from ascertaining the microphysical nature of these exotic energy components are significant, in turn casting doubt upon whether cosmology can ever transcend these particular epistemic challenges. We conclude by reflecting on the prospects for future breakthroughs and/or non-empirical arguments which could decide this issue conclusively.

physics.hist-ph↗

arXiv2025

syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum

Baryonic physics has a considerable impact on the distribution of matter in our Universe on scales probed by current and future cosmological surveys, acting as a key systematic in such analyses. We seek simple symbolic parametrisations for the impact of baryonic physics on the matter power spectrum for a range of physically motivated models, as a function of wavenumber, redshift, cosmology, and parameters controlling the baryonic feedback. We use symbolic regression to construct analytic approximations for the ratio of the matter power spectrum in the presence of baryons to that without such effects. We obtain separate functions of each of four distinct sub-grid prescriptions of baryonic physics from the CAMELS suite of hydrodynamical simulations (Astrid, IllustrisTNG, SIMBA and Swift-EAGLE) as well as for a baryonification algorithm. We also provide functions which describe the uncertainty on these predictions, due to both the stochastic nature of baryonic physics and the errors on our fits. The error on our approximations to the hydrodynamical simulations is comparable to the sample variance estimated through varying initial conditions, and our baryonification expression has a root mean squared error of better than one percent, although this increases on small scales. These errors are comparable to those of previous numerical emulators for these models. Our expressions are enforced to have the physically correct behaviour on large scales and at high redshift. Due to their analytic form, we are able to directly interpret the impact of varying cosmology and feedback parameters, and we can identify parameters which have little to no effect. Each function is based on a different implementation of baryonic physics, and can therefore be used to discriminate between these models when applied to real data. We provide publicly available code for all symbolic approximations found.

astro-ph.CO↗