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

Understand

The luminosity distance can be used to determine the properties of large scale structure around the observer.

• To this purpose we develop a new inversion method to map luminosity distance to a LTB metric based on the use of the exact analytical solution for Einstein equations.
• The main advantages of this approach are an improved numerical accuracy and stability, an exact analytical setting of the initial conditions for the differential equations which need to be solved and the validity for any sign of the functions determining the LTB geometry.
• Given the fully analytical form of the differential equations, this method also simplifies the calculation of the red-shift expansion around the apparent horizon point where the numerical solution becomes unstable.