Testing and selection of cosmological models with $(1+z)^6$ corrections

TL;DR

This paper investigates whether a specific $(1+z)^6$ correction term in the Friedmann equation can be tested with current astronomical data, comparing models from quantum cosmology, braneworlds, and other theories, and finds $ ho^2$ effects are very small and hard to distinguish from $ ext{Lambda}$CDM.

Contribution

The study applies multiple astronomical tests and Bayesian model selection to constrain the impact of $(1+z)^6$ corrections, demonstrating their observational indistinguishability from standard cosmology.

Findings

$ ho^2$ corrections are very small and difficult to detect.

Current data favor $ ext{Lambda}$CDM over bouncing models with quantum effects.

Bounds on the correction term are weak, making models observationally indistinguishable from standard cosmology.

Abstract

In the paper we check whether the contribution of $(-)(1+z)^6$ type in the Friedmann equation can be tested. We consider some astronomical tests to constrain the density parameters in such models. We describe different interpretations of such an additional term: geometric effects of Loop Quantum Cosmology, effects of braneworld cosmological models, non-standard cosmological models in metric-affine gravity, and models with spinning fluid. Kinematical (or geometrical) tests based on null geodesics are insufficient to separate individual matter components when they behave like perfect fluid and scale in the same way. Still, it is possible to measure their overall effect. We use recent measurements of the coordinate distances from the Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, supernovae type Ia (SNIa) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations to obtain stronger bounds for the contribution of the type considered. We demonstrate that, while $\rho^2$ corrections are very small, they can be tested by astronomical observations -- at least in principle. Bayesian criteria of model selection (the Bayesian factor, AIC, and BIC) are used to check if additional parameters are detectable in the present epoch. As it turns out, the $\Lambda$CDM model is favoured over the bouncing model driven by loop quantum effects. Or, in other words, the bounds obtained from cosmography are very weak, and from the point of view of the present data this model is indistinguishable from the $\Lambda$CDM one.