English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The luminosity distance can be used to determine the properties of largescale structure around the observer. To this purpose we develop a new inversionmethod to map luminosity distance to a LTB metric based on the use of the exactanalytical solution for Einstein equations. The main advantages of thisapproach are an improved numerical accuracy and stability, an exact analyticalsetting of the initial conditions for the differential equations which need tobe solved and the validity for any sign of the functions determining the LTBgeometry. Given the fully analytical form of the differential equations, thismethod also simplifies the calculation of the red-shift expansion around theapparent horizon point where the numerical solution becomes unstable. We testthe method by inverting the supernovae Ia luminosity distance functioncorresponding to the the best fit $\Lambda CDM$ model. We find that only alimited range of initial conditions is compatible with observations, or atransition from red to blue shift can occur at relatively low redshift. DespiteLTB solutions without a cosmological constant have been shown not to becompatible with all different set of available observational data, thosestudies normally fit data assuming a special functional ansatz for theinhomogeneity profile, which often depend only on few parameters. Inversionmethods on the contrary are able to fully explore the freedom in fixing thefunctions which determine a LTB solution. Another important possibleapplication is not about LTB solutions as cosmological models, but rather astools to study the effects on the observations made by a generic observerlocated in an inhomogeneous region of the Universe where a fully nonperturbative treatment involving exact solutions of Einstein equations isrequired.

A new method to determine large scale structure from the luminosity distance