How many cosmological parameters?

TL;DR

The paper tackles the problem of how many cosmological parameters are needed to describe observations by applying $AIC$ and $BIC$ to compare models with different parameter sets. It clarifies the definitions and trade-offs between $AIC$ and $BIC$ and applies them to WMAP+SDSS data, finding that a five-parameter base model in a spatially flat universe suffices and that adding parameters like curvature or spectral index running is not warranted by current data. The results highlight the risk of interpreting 95% confidence detections in the presence of many candidate parameters and advocate using $BIC$ to avoid overfitting and publication bias. Overall, the paper supports a minimal cosmological model with five fundamental parameters (plus a couple of phenomenological ones) and argues that $BIC$ provides a robust threshold for promoting candidate parameters into the base model, with future data potentially lifting some candidates into prominence.

Abstract

Constraints on cosmological parameters depend on the set of parameters chosen to define the model which is compared with observational data. I use the Akaike and Bayesian information criteria to carry out cosmological model selection, in order to determine the parameter set providing the preferred fit to the data. Applying the information criteria to the current cosmological data sets indicates, for example, that spatially-flat models are statistically preferred to closed models, and that possible running of the spectral index has lower significance than inferred from its confidence limits. I also discuss some problems of statistical assessment arising from there being a large number of `candidate' cosmological parameters that can be investigated for possible cosmological implications, and argue that 95% confidence is too low a threshold to robustly identify the need for new parameters in model fitting. The best present description of cosmological data uses a scale-invariant (n=1) spectrum of gaussian adiabatic perturbations in a spatially-flat Universe, with the cosmological model requiring only five fundamental parameters to fully specify it.