Accounting for Correlations When Fitting Extra Cosmological Parameters

Abstract

Abstract Current cosmological tensions motivate investigating extensions to the standard Λ cold dark matter (ΛCDM) model. Additional model parameters are typically varied one or two at a time, in a series of separate tests. The purpose of this paper is to highlight that information is lost by not also examining the correlations between these additional parameters, which arise when their effects on model predictions are similar even if the parameters are not varied simultaneously. We show how these correlations can be quantified with simulations and Markov Chain Monte Carlo methods. As an example, we assume that ΛCDM is the true underlying model, and calculate the correlations expected between the phenomenological lensing amplitude parameter, A L , the running of the spectral index, n run, and the primordial helium mass fraction, Y P , when these parameters are varied one at a time along with the ΛCDM parameters in fits to the Planck 2015 temperature power spectrum. These correlations are not small, ranging from 0.31 (A L −n run) to −0.93 (n run–Y P ). We find that the values of these three parameters from the Planck data are consistent with ΛCDM expectations within 0.9σ when the correlations are accounted for. This does not explain the 1.8–2.7σ Planck preference for A L > 1, but provides an additional ΛCDM consistency test. For example, if A L > 1 was a symptom of an underlying systematic error or some real but unknown physical effect that also produced spurious correlations with n run or Y P our test might have revealed this. We recommend that future cosmological analyses examine correlations between additional model parameters in addition to investigating them separately, one a time.