Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance

Abstract

Local structure can have important effects on luminosity distance observations, which could for example affect the local estimation of the Hubble constant based on low red-shift type Ia supernovae.Using a spherically symmetric exact solution of the Eistein's equations and a more accurate expansion of the solution of the geodesic equations, we improve the low red-shift expansion of the monopole of the luminosity distance in terms of the curvature function. Based on this we derive the coordinate independent low red-shift expansion of the monopole of the luminosity distance in terms of the monopole of the density contrast. The advantage of this approach is that it relates the luminosity distance directly to density observations, without any dependency on the radial coordinate choice.We compute the effects of different inhomogeneities on the luminosity distance, and find that the formulae in terms of the density contrast are in good agreement with numerical calculations, in the non linear regime are more accurate than the results obtained using linear perturbation theory, and are also more accurate than the formulae in terms of the curvature function.

Cosmic variance of $H_0$ in light of forthcoming high-redshift surveys

“…Our analysis considers the possibility, discussed in [28], that a statistically relevant number of Superluminous Supernovae could be detected in the next years by EDS [1] and LSST [2]. In this regards, less conservative studies about the Hubble diagram at high redshifts (z ≤ 1.5) have been also investigated by exploiting exact inhomogeneous models in general relativity [55][56][57][58].…”

New physics in light of the $H_0$ tension: an alternative view

“…Possible systematics in the Planck datasets have been studied in e.g. [23][24][25][26][27], whereas analogous studies in the case of the HST measurements have been conducted for instance in [28][29][30][31][32]: in both cases, no obvious solution to the dilemma has been found (see also [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]). It is worth pointing out the local measurements of H 0 alternative to those of [6] exist in the literature.…”

Precision Cosmology and Hubble tension in the era of LSS surveys

“…Our analysis considers the possibility, discussed in Inserra et al (2021) 6 , that EDS 17 and LSST 18 will have access to a statistically relevant number of Superluminous Supernovae in the next decade. In this regards, less conservative studies about the Hubble diagram at high redshifts (z ≤ 1.5) have been also investigated by exploiting exact inhomogeneous models in general relativity [21][22][23][24] or by considering strongly inhomogeneous dynamical dark energy models 25 . These attempts look interesting especially in light of recent analysis done in Krishnan et 30 for the SNe Ia Pantheon sample, suggesting that H 0 could be a decreasing function of redshift already at late time.…”