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Abstract:

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.

Abstract:

Abstract The galaxy luminosity and stellar mass function (LF, SMF), and halo mass function (HMF), are fundamental quantities in astrophysics and crucial inputs to a range of astrophysical and cosmological analyses. They are typically parametrised by fitting functions that have been chosen ‘by eye’ to match observed or simulated data. We apply symbolic regression—specifically the Exhaustive Symbolic Regression (ESR) algorithm—to automate the search for optimal LF, SMF and HMF functional forms. ESR scores all functions up to a maximum complexity composed of a user-defined basis set of operators using the description length, an approximation to the Bayesian evidence that balances accuracy with complexity. We find many functions that outperform the Schechter and double Schechter functions for the LF and SMF, and that outperform all investigated literature functions (that outperform the Press–Schechter, Warren, Tinker, Sheth–Tormen and Jenkins) for the HMF. By additionally imposing ‘physicality checks’ on functions’ extrapolation and integration properties, we identify the optimal, low-complexity functional forms in terms of accuracy, simplicity and behaviour beyond the data range. As well as providing drop-in replacements for literature LF, SMF and HMF fitting functions, and identifying robust behaviour across well-fitting functions, we present a framework with which symbolic regression may be used to automate the discovery of optimal functions for any astrophysical dataset.

Abstract:

Dark matter dominates the matter content of the Universe, and its properties can be constrained through large-scale structure probes such as the cross-correlation between the unresolved gamma-ray background (UGRB) and weak gravitational lensing. We analysed 15 years of Fermi–LAT data, constructing UGRB intensity maps in ten energy bins (0.5–1000 GeV), and cross-correlated them with KiDS-Legacy shear in six tomographic bins. The measurements were performed using angular power spectra estimated with the pseudo- C ℓ method. No significant cross-correlation was found. Based on this non-detection, we present 95% upper bounds on the weakly interacting massive particle decay rate Γ dec and velocity-averaged annihilation cross-section ⟨ σ ann v ⟩ as functions of mass. We compared our results with bounds from other cosmological tracers and from local probes, and we found them to be complementary, particularly at low masses (GeV/TeV). In addition, using a Euclid -like lensing survey cross-correlated with Fermi–LAT, we forecast approximately two to four times tighter limits, highlighting the potential of forthcoming data to strengthen constraints on dark matter annihilation and decay.

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'.