Cosmology

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:

In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct numerical simulations. Symbolic emulators have emerged as promising alternatives to numerical approaches, delivering comparable accuracy with significantly faster evaluation times. While previous symbolic emulators were limited to relatively narrow prior ranges, we expand these to cover the parameter space relevant for current cosmological analyses. We introduce approximations to hypergeometric functions used for the Λ cold dark matter (ΛCDM) comoving distance and linear growth factor which are accurate to better than 0.001% and 0.05%, respectively, for all redshifts and for Ωm∈[0.1,0.5]. We show that integrating symbolic emulators into a Dark Energy Survey Year 1 (DES-Y1)-like 3×2 pt analysis produces cosmological constraints consistent with those obtained using standard numerical methods. Our symbolic emulators offer substantial improvements in speed and memory usage, demonstrating their practical potential for scalable, likelihood-based inference. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

The upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will enable astronomers to discover rare and distant astrophysical transients. Host-galaxy association is crucial for selecting the most scientifically interesting transients for follow-up. LSST deep drilling field (DDF) observations will detect distant transients occurring in galaxies below the detection limits of most all-sky catalogs. Here, we investigate the use of preexisting, field-specific catalogs for host identification in the DDFs and a ranking of their usefulness. We have compiled a database of 70 deep catalogs that overlap with the Rubin DDFs and constructed thin catalogs to be homogenized and combined for transient-host matching. A systematic ranking of their utility is discussed and applied based on the inclusion of information such as spectroscopic redshifts and morphological information. Utilizing this data against a Dark Energy Survey sample of supernovae with pre-identified hosts in the XMM-Large Scale Structure and the Extended Chandra Deep Field-South fields, we evaluate different methods for transient-host association in terms of both accuracy and processing speed. We also apply light data-cleaning techniques to identify and remove contaminants within our associations, such as diffraction spikes and blended galaxies where the correct host cannot be determined with confidence. We use a lightweight machine learning approach in the form of extreme gradient boosting to generate confidence scores in our contaminant selections and associated metrics. Finally, we discuss the computational expense of implementation within the LSST transient alert brokers, which will require efficient, fast-paced processing to handle the large stream of survey data.

Abstract:

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR, which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focused on the promising regions in order to be equally performant. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Abstract A key question in extragalactic astronomy is how the star-formation rate density (SFRD) evolves over cosmic time. A powerful way of addressing this question is using radio-continuum observations, where the radio waves are unaffected by dust and are able to reach sufficient resolution to resolve individual galaxies. We present an investigation of the 1.4 GHz radio luminosity functions (RLFs) of star-forming galaxies (SFGs) and Active Galactic Nuclei (AGN) using deep radio continuum observations in the COSMOS and XMM–LSS fields, covering a combined area of ∼4 deg2. These data enable the most accurate measurement of the evolution in the SFRD from mid-frequency radio continuum observations. We model the total RLF as the sum of evolving SFG and AGN components, negating the need for individual source classification. We find that the SFGs have systematically higher space densities at fixed luminosity than found in previous radio studies, but consistent with more recent studies with MeerKAT. We attribute this to the excellent low-surface brightness sensitivity of MeerKAT. We then determine the evolution of the SFRD. Adopting the far-infrared – radio correlation results in a significantly higher SFRD at z > 1, compared to combined UV and far-infrared measurements. However, using more recent relations for the correlation between star-formation rate and radio luminosity, based on full spectral energy distribution modelling, can resolve this apparent discrepancy. Thus radio observations provide a powerful method of determining the total SFRD, in the absence of dust-sensitive far-infrared data.