Differing Manifestations of Spatial Curvature in Cosmological FRW Models

We find statistical evidence for a mismatch between the (global) spatial curvature parameter $K$ in the geodesic equation for incoming photons, and the corresponding parameter in the Friedmann equation that determines the time evolution of the background spacetime and its perturbations.

The mismatch hereafter referred to as `curvature-slip' is especially evident when the SH0ES prior on the current expansion rate is assumed.

This result is based on joint analyses of cosmic microwave background (CMB) observations with the PLANCK satellite (P18), first year results of the Dark Energy Survey (DES), Baryonic Oscillation (BAO) data, and - at a lower level of significance - also on Pantheon SNIa (SN) catalog.

For example, the betting odds against the Null Hypothesis are greater than $10^7$:1, 1400:1 and 1000:1 when P18+SH0ES, P18+DES+SH0ES, and P18+BAO+SH0ES, respectively, are considered.

Datasets involving SNIa weaken this curvature slip considerably.

Notably, even when the SH0ES prior is not imposed the betting odds for the rejection of the Null Hypothesis are 70:1 and 160:1 in cases where P18+DES and P18+BAO are considered.

When the SH0ES prior is imposed, global fit of the modified model (that allows for a nonvanishing `curvature slip') strongly outperforms that of $\Lambda$CDM as is manifested by significant Deviance Information Criterion (DIC) gains, ranging between 7 and 23, depending on the dataset combination considered.

Even in comparison to K$\Lambda$CDM the proposed model results in significant, albeit smaller, DIC gains when SN data are excluded.

Our finding could possibly be interpreted as an inherent inconsistency between the (idealized) maximally symmetric nature of the FRW metric, and the dynamical evolution of the GR-based homogeneous and isotropic $\Lambda$CDM model (abridged) ;Comment: Submitted.

Comments are welcome