Directional dependence of the local estimation of $H_0$ and the nonperturbative effects of primordial curvature perturbations

Recent measurements of the cosmic microwave background (CMB) radiation have shown an apparent tension with the present value of the Hubble parameter inferred from local observations of supernovae, which look closer, i.e. brighter, than what is expected in a homogeneous model with a value of H(0) equal to the one estimated from CMB observations. We examine the possibility that such a discrepancy is the consequence of the presence of a local inhomogeneity seeded by primordial curvature perturbations, finding that a negative peak of the order of less than two standard deviations could allow to fit low-redshift supernovae observations without the need of using a value of the Hubble parameter different from H(0)CMB. The type of inhomogeneity we consider does not modify the distance to the last scattering, making it compatible with the constraints of the PLANCK mission data. The effect on the luminosity distance is in fact localized around the region in space where the transition between different values of the curvature perturbations occurs, producing a local decrease, while the distance outside the inhomogeneity is not affected. Our calculation is fully relativistic and nonperturbative, and for this reason shows important effects which were missed in the previous investigations using relativistic perturbations or Newtonian approximations, because the structures seeded by primordial curvature perturbations can be today highly nonlinear, and relativist Doppler terms cannot be neglected. Because of these effects the correction to the luminosity distance necessary to explain observations is associated to a compensated structure which involves both an underdense central region and an overdense outer shell, ensuring that the distance to the last scattering surface is unaffected. Comparison with studies of local structure based on galaxy surveys analysis reveals that the density profile we find could in fact be compatible with the one obtained for the same region of sky where most of the supernovae used for the local H(0) estimation are located, suggesting a possible directional dependence which could be partially attributed to the presence of the Sloan Great Wall and hinting to the need of a more careful investigation, including a wider set of low-redshift supernovae in different regions of the sky.

Note:

New updated references have been added. Some more information has been included about the region of sky in which the density profile predicted by our model is in agreement with luminosity density and galaxy surveys observations. Our model predicts the consequent overall supernovae luminosity distance calibration bias effect due to the presence in that region of the Cepheids

98.80.-k
98.80.Es
curvature: perturbation
supernova: redshift
curvature: primordial
redshift: low
effect: nonperturbative
cosmic background radiation
Hubble constant: precision measurement
scattering