TY - JOUR

T1 - A precise symbolic emulator of the linear matter power spectrum

AU - Bartlett, Deaglan J.

AU - Kammerer, Lukas

AU - Kronberger, Gabriel

AU - Desmond, Harry

AU - Ferreira, Pedro G.

AU - Wandelt, Benjamin D.

AU - Burlacu, Bogdan

AU - Alonso, David

AU - Zennaro, Matteo

N1 - Publisher Copyright:
© The Authors 2024.

PY - 2024/6/1

Y1 - 2024/6/1

N2 - Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert As to σ8 given the other cosmological parameters. Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ8. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 × 10−3−9 hMpc−1 and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than camb and 36 times faster than the neural network based matter power spectrum emulator bacco. We also provide a simple analytic approximation for σ8 with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain As as a function of σ8 and the other cosmological parameters, if preferred. Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

AB - Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert As to σ8 given the other cosmological parameters. Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ8. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 × 10−3−9 hMpc−1 and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than camb and 36 times faster than the neural network based matter power spectrum emulator bacco. We also provide a simple analytic approximation for σ8 with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain As as a function of σ8 and the other cosmological parameters, if preferred. Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

KW - cosmological parameters

KW - cosmology: theory

KW - large-scale structure of Universe

KW - methods: numerical

UR - http://www.scopus.com/inward/record.url?scp=85195633703&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/202348811

DO - 10.1051/0004-6361/202348811

M3 - Article

AN - SCOPUS:85195633703

SN - 0004-6361

VL - 686

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A209

ER -