Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.

Abstract:

We perform a Bayesian model selection analysis for different classes of phenomenological coupled scenarios of dark matter and dark energy with linear and non-linear interacting terms. We use a combination of some of the latest cosmological data such as type Ia supernovae (SNe Ia), cosmic chronometers (CC), cosmic microwave background (CMB) and two sets of baryon acoustic oscillations measurements, namely, 2-dimensional angular measurements (BAO2) and 3-dimensional angle-averaged measurements (BAO3). We find weak and moderate evidence against two-thirds of the interacting scenarios considered with respect to ΛCDM when the full joint analysis is considered. About one-third of the models provide a description to the data as good as the one provided by the standard model. Our results also indicate that either SNe Ia, CC or BAO2 data by themselves are not able to distinguish among interacting models or ΛCDM but the standard BAO3 measurements and the combination with the CMB data are indeed able to discriminate among them. We find that evidence disfavoring interacting models is weaker when we use BAO2 (data claimed to be almost model-independent) instead of the standard BAO3 measurements. These results help select classes of viable and non-viable interacting models in light of current data.