Evolution of linear matter perturbations with error-bounded bundle physics-informed neural networks

Abstract

We consider the evolution of linear matter perturbations in the context of the standard cosmological model ($\Lambda$CDM) and a phenomenological modified gravity model. We use the physics-informed neural network (PINN) bundle method, which allows to integrate differential systems as an alternative to the traditional numerical method. We apply the PINN bundle method to the equation that describes the matter perturbation evolution, to compare its outcomes with recent data on structure growth, $f{\sigma }_8$. Unlike our previous works, we can calculate a bound on the error of this observable without using the numerical solution of the equation. For this, we use a method developed previously by ourselves to calculate an exact bound on the PINN-based solution using only the outcomes of the network and its residual. On the other hand, the use of an updated data set allows us to obtain more stringent constraints on the plane ${\Omega }_m-{\sigma }_8$ than previous works.

12 pages, 6 figures

References in corpus (31)

• Cosmological Constant - the Weight of the Vacuum
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• Disappearing cosmological constant in f(R) gravity
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• The Temperature of the Cosmic Microwave Background
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z < 1
• Reconstructing the history of structure formation using redshift distortions
• A Lower Growth Rate from Recent Redshift Space Distortion Measurements than Expected from Planck
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Cosmic flows in the nearby universe from Type Ia Supernovae
• The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at $z\sim 1.4$
• Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure
• Tension and constraints on modified gravity parametrizations of $G_{\text{eff}}(z)$ from growth rate and Planck data
• The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue
• The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structures at $0.5<z<1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear bias
• Testing $\Lambda$CDM at the lowest redshifts with SN Ia and galaxy velocities
• A deep learning approach to cosmological dark energy models
• Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with the Hubble Parameter and SNe Ia
• The Redshift Space Momentum Power Spectrum II: measuring the growth rate from the combined 2MTF and 6dFGSv surveys
• Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft
• Neural Network Reconstruction of Late-Time Cosmology and Null Tests
• The growth rate of cosmic structures in the local Universe with the ALFALFA survey
• Machine Learning the Cosmic Curvature in a Model-independent Way
• Cosmology-informed neural networks to solve the background dynamics of the Universe
• Faster Bayesian inference with neural network bundles and new results for $f(R)$ models

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• Reconstructing the Type Ia Supernova Absolute Magnitude with Two-Probe Physics-Informed Neural Networks