Abstract
Abstract
When fitting cosmological models to data, a Bayesian framework is commonly used, requiring
assumptions on the form of the likelihood and model prior. In light of current tensions between
different data, it is interesting to investigate the robustness of cosmological measurements to
statistical assumptions about the likelihood distribution from which the data was drawn. We
consider the impact of changes to the likelihood caused by uncertainties due to the finite number
of mock catalogs used to estimate the covariance matrix, leading to the replacement of the
standard Gaussian likelihood with a multivariate t-distribution. These changes to the likelihood
have a negligible impact on recent cosmic microwave background (CMB) lensing and baryon acoustic
oscillation (BAO) measurements, for which covariance matrices were measured from mock catalogs.
We then extend our analysis to perform a sensitivity test on the Gaussian likelihoods typically
adopted, considering how increasing the size of the tails of the likelihood (again using a
t-distribution) affects cosmological inferences. For an open ΛCDM model constrained by
BAO alone, we find that increasing the weight in the tails shifts and broadens the resulting
posterior on the parameters, with a ∼0.2–0.4σ effect on ΩΛ and
Ωk. In contrast, the CMB temperature and polarization constraints in ΛCDM
showed less than 0.03σ changes in the parameters, except for {τ,
ln(1010
A
s), σ
8, S
8, σ
8Ω0.25
m, z
re,
109
A
s
e
-2τ
} which shifted by around 0.1–0.2σ. If we use solely ℓ < 30 data, the amplitude A
s
e
-2τ
varies in the posterior mean by 0.7σ
and the error bars increase by 6%. We conclude, at least for current-generation CMB and BAO
measurements, that uncertainties in the shape and tails of the likelihood do not contribute to
current tensions.