No Evidence for Extensions to the Standard Cosmological Model

Abstract

We compute the Bayesian evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilizing carefully defined nearest-neighbor distances in parameter space, we reuse the Monte Carlo Markov chains already produced for parameter inference to compute Bayes factors B for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (ΛCDM) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (lnB=-7.8), nonzero scalar-to-tensor ratio (lnB=-4.3), running of the spectral index (lnB=-4.7), curvature (lnB=-3.6), nonstandard numbers of neutrinos (lnB=-3.1), nonstandard neutrino masses (lnB=-3.2), nonstandard lensing potential (lnB=-4.6), evolving dark energy (lnB=-3.2), sterile neutrinos (lnB=-6.9), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (lnB=-10.8). Other models are less strongly disfavored with respect to flat ΛCDM. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does ΛCDM become disfavored, and only mildly, compared with a dynamical dark energy model (lnB∼+2).

Revisiting the decoupling effects in the running of the Cosmological Constant

“…In view of this, our results also might have impact on the models based on the dynamical cosmological constant which were confronted with new cosmological observations in [22,23] with the results being still inconclusive [24,25]. in two schemes is finite.…”

Dark sectors with dynamical coupling

“…Finally, we comment on the results from a Bayesian evidence analysis of the dynamical interacting scenarios here explored. In this framework, a comparison of a cosmological model is performed with respect to a standard and well-motivated cosmological model [76,77,78,79]. The ΛCDM provides the ideal choice for such a comparison.…”

“…Table IV shows the so-called Jeffreys scale, which, for different possible values of ln B ij , quantifies the strength of evidence of the underlying cosmological model with respect to the reference, canonical ΛCDM scenario. Following [76,77] we compute the values of ln B ij for all the observational datasets employed in this work, and present the results in Tab. V. From this table, we learn that the ΛCDM model is always preferred over the two IVS models analyzed here.…”

Testing non-minimally coupled inflation with CMB data: a Bayesian analysis

“…Indeed, while a model with more free parameters will always fit the data better (or at least as good as) a model with less parameters, such added complexity ought to be avoided whenever a simpler model provides an adequate description of the observations. The Bayesian model comparison offers a formal way to evaluate whether the extra complexity of a model is supported by the data, preferring the model that describes the data well over a large fraction of their prior volume (we refer the reader to [37][38][39][40][41][42] for some recent applications of Bayesian model selection in cosmology). It is worth mentioning that we use here the most accurate Importance Nested Sampling (INS) [36,43] instead of the vanilla Nested Sampling (NS), requiring INS Global Log-Evidence error < 0.1.…”