Parameter inference with non-linear galaxy clustering: accounting for theoretical uncertainties

TL;DR

This paper evaluates the impact of different non-linear matter power spectrum models on cosmological parameter inference, demonstrating that emulator-based predictions can improve sensitivity and reduce bias in parameter estimation.

Contribution

It introduces the EuclidEmulator1 into MCMC analysis and compares its performance with other models, highlighting its advantages in sensitivity and bias mitigation.

Findings

EuclidEmulator1 increases parameter sensitivity by up to 17%.

Bias in cosmological parameters can be reduced by a factor of 2 to 5 when accounting for theoretical uncertainties.

Choice of power spectrum predictor significantly affects parameter estimation accuracy.

Abstract

We implement EuclidEmulator (version 1), an emulator for the non-linear correction of the matter power spectrum, into the MCMC forecasting code MontePython. We compare the performance of Halofit, HMCode, and EuclidEmulator1, both at the level of power spectrum prediction and at the level of posterior probability distributions of the cosmological parameters, for different cosmological models and different galaxy power spectrum wave number cut-offs. We confirm that the choice of the power spectrum predictor has a non-negligible effect on the computed sensitivities when doing cosmological parameter forecasting, even for a conservative wave number cut-off of $0.2\,h\,{\rm Mpc}^{-1}$. We find that EuclidEmulator1 is on average up to $17\%$ more sensitive to the cosmological parameters than the other two codes, with the most significant improvements being for the Hubble parameter of up to $42\%$ and the equation of state of dark energy of up to $26\%$, depending on the case. In addition, we point out that the choice of the power spectrum predictor contributes to the risk of computing a significantly biased mean cosmology when doing parameter estimations. For the four tested scenarios we find biases, averaged over the cosmological parameters, of between 0.5 and 2$\sigma$ (from below $1\sigma$ up to $6\sigma$ for individual parameters). This paper provides a proof of concept that this risk can be mitigated by taking a well-tailored theoretical uncertainty into account as this allows to reduce the bias by a factor of 2 to 5, depending on the case under consideration, while keeping posterior credibility contours small: the standard deviations are amplified by a factor of $\leq1.4$ in all cases.