Constraining deviations from $\Lambda$CDM in the Hubble expansion rate

TL;DR

This paper investigates potential deviations from the standard $\\Lambda$CDM model in the Hubble expansion rate using phenomenological models and observational data, finding that some models show significant deviations while others remain consistent.

Contribution

It introduces three phenomenological models for deviations in the Hubble rate and constrains them with observational data, revealing significant deviations in one model.

Findings

Model III shows a deviation exceeding 2σ from $\\Lambda$CDM.

Models I and II are consistent with $\\Lambda$CDM across datasets.

Model III is statistically preferred over $\\Lambda$CDM based on AIC.

Abstract

The $\Lambda$CDM cosmolgical model has long been regarded as highly successful in accurately describing a wide range of astronomical observations. However, numerous observational findings have also provided hints of discrepancies from the predictions of the $\Lambda$CDM framework. We explore a phenomenological model that quantifies the deviation of the Hubble expansion rate from the standard scenario, which is expressed as $H^{2}(z) = H^{2}_{\rm \Lambda CDM}(\Omega_m, z)[1+\delta(z)]$. We consider three distinct forms for the deviation parameter $\delta(z)$: in model I, $\delta(z)=\delta_c$; in model II, $\delta(z)=\delta_{c}z/(1+z)$, and in model III, $\delta(z)=\delta_{c}{\rm ln}(1+z)$. Here, $\delta_c$ represents a constant value. We utilize a comprehensive set of observational data to constrain the models. Our results show that for most combined datasets, $\delta_c$ tends to take on negative values for models I and II, while consistently taking positive values in model III. Furthermore, we find that both models I and II remain consistent with the standard $\Lambda$CDM model across all datasets examined. In contrast, model III exhibits a significant deviation from the $\Lambda$CDM model, exceeding $2\sigma$ for the full combined datastes. The AIC indicates that models I and II are consistent with the $\Lambda$CDM model, whereas model III is preferred over the standard $\Lambda$CDM model, with the $\Lambda$CDM model being disfavored for the combined datasets DESI BAO + CMB + CC + DESY5. These results suggest that the Hubble expansion rate likely deviates from the standard $\Lambda$CDM prediction.