Symbolic emulators for cosmology: accelerating cosmological analyses without sacrificing precision

Area of Science:

• Cosmology
• Computational Physics
• Symbolic Regression

Background:

• Emulators are vital in cosmology for rapid predictions of complex physical models, overcoming computational limits of direct simulations.
• Symbolic emulators offer a faster alternative to numerical methods with comparable accuracy, but were previously restricted to narrow parameter ranges.

Purpose of the Study:

• To expand the applicability of symbolic emulators to broader parameter spaces relevant for current cosmological analyses.
• To introduce accurate approximations for hypergeometric functions crucial for ΛCDM model predictions.
• To demonstrate the practical utility of symbolic emulators in real-world cosmological data analysis.

Main Methods:

• Developed symbolic emulators covering extended prior ranges for cosmological parameters.
• Introduced novel approximations for hypergeometric functions, achieving high accuracy (better than 0.001% and 0.05%) for comoving distance and linear growth factor.
• Integrated symbolic emulators into a 3x2 point analysis framework similar to the Dark Energy Survey Year 1 (DES-Y1) data.

Main Results:

• Symbolic emulators now cover the parameter space relevant for contemporary cosmological studies.
• Approximations for hypergeometric functions ensure high fidelity across specified redshift and matter density ranges (Ωm∈[0.1,0.5]).
• Cosmological constraints derived using symbolic emulators in a DES-Y1-like analysis are consistent with those from traditional numerical methods.

Conclusions:

• Symbolic emulators provide significant speed and memory improvements for cosmological inference.
• These enhanced emulators are practical for scalable, likelihood-based inference, facilitating efficient exploration of cosmological parameter space.
• The study highlights the potential of symbolic regression in advancing physical sciences research.