https://doi.org/10.1140/epjc/s10052-025-15088-8
Regular Article - Theoretical Physics
Constraining deviations from 
CDM in the Hubble expansion rate
School of Physics and Physical Engineering, Qufu Normal University, 273165, Qufu, Shandong, China
a
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Received:
2
September
2025
Accepted:
15
November
2025
Published online:
24
November
2025
Abstract
The CDM cosmological 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 CDM framework. We explore a phenomenological model that quantifies the deviation of the Hubble expansion rate from the standard scenario, which is expressed as ![Mathematical equation: $$H^{2}(z) = H^{2}_\mathrm{\varLambda CDM}(\varOmega _m, z)[1+\delta (z)]$$](/articles/epjc/abs/2025/11/10052_2025_Article_15088/10052_2025_Article_15088_tex_eq5.png)
. We consider three distinct forms for the deviation parameter 
: in model I, 
; in model II, 
, and in model III, 
. Here, 
represents a constant value. We utilize a comprehensive set of observational data to constrain the models. Our results show that for most combined datasets, 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 CDM model across all datasets examined. In contrast, model III exhibits a significant deviation from the CDM model, exceeding 
for the full combined datasets. The AIC indicates that models I and II are consistent with the CDM model, whereas model III is preferred over the standard CDM model, with the 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 CDM prediction.
© The Author(s) 2025
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