Beecroft Institute for Particle Astrophysics and 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:

There is now clear evidence, from a variety of studies, that galactic bars contribute to and/or accelerate processes that quench galaxies. However, bars have a variety of strengths and pattern speeds, and previous work has suggested that slow and strong bars impact their hosts the most. In this paper, we continue to investigate the impact of bar strength and bar speed on host galaxy evolution in a sample of barred galaxies identified via classifications from Galaxy Zoo. We perform a comprehensive assessment of star formation tracers spanning a variety of time-scales, based on spatially resolved spectroscopic information from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. Specifically, we examine the radial distributions of EW [H ], H , H , and Dn4000; spectral data that trace star formation on current, intermediate, and much longer time-scales. We investigate how these star formation tracers vary with respect to each other in diagnostic evolutionary planes for eight categories of barred galaxies (combinations of star forming or quenching; strong and weak; fast and slow). We continue to find that slow-strong bars drive the quenching of their hosts the most by triggering active star formation throughout the barred region; however, we note some additional complexity: we observe that stronger bars boost star formation at the bar centre while slower bars have increased star formation along the bar. This work adds to the growing evidence that galactic bars have both global and local impacts on their host galaxies.

Abstract:

We test whether (Formula presented.) symmetric teleparallel gravity theories can solve the Hubble tension consistently with DESI DR2 BAO. We consider three (Formula presented.) functional forms: logarithmic, exponential, and hyperbolic tangent. We extend these models by allowing a cosmological constant, and compare to phenomenological models with a flexible exponential, hyperbolic secant, and polynomial decay addition to the standard (Formula presented.) CDM (Formula presented.). We test these models against DESI DR2 BAO, CMB (Planck 2018 + SPT-3G + ACT DR6), local (Formula presented.), and Cosmic Chronometer data. The logarithmic and hyperbolic tangent (Formula presented.) models do not provide an adequate solution, but the exponential model does. Furthermore, it slightly reduces the (Formula presented.) parameter space tension between CMB and BAO datasets to (Formula presented.), down from (Formula presented.) for (Formula presented.) CDM. Although (Formula presented.) CDM faces only (Formula presented.) tension in DESI data space, the (Formula presented.) higher tension in parameter space suggests a real anomaly. The models assisted by the cosmological constant perform slightly better still, at the cost of undermined theoretical motivation. They also perform poorly once local (Formula presented.) measurements are included. The phenomenological models fit all data reasonably well, yet the best-fitting models predict isotropically averaged BAO distances exceeding the DESI DR2 measurements at all redshifts. This highlights the difficulties of finding a theoretically motivated solution to the Hubble tension while remaining consistent with BAO data.

Abstract:

Symbolic regression (SR) is the machine learning (ML) method for learning functions from data. After a brief overview of the SR landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown (and probably significant) probability of failing to find any given good function, and they suffer from ambiguity and poorly justified assumptions in their function-selection procedure. To address these, I propose an exhaustive search and model selection by the minimum description length (MDL) principle, which allows accuracy and complexity to be directly traded off by measuring each in units of information. I showcase the resulting publicly available Exhaustive Symbolic Regression (ESR) algorithm on three open problems in astrophysics: the expansion history of the universe, the effective behaviour of gravity in galaxies and the potential of the inflaton field. In each case, the algorithm identifies many functions superior to the literature standards. This general-purpose methodology should find widespread utility in science and beyond. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.