Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology  

作　　者：Alessandro Trinchera Alessandro Trinchera(Independent Researcher, Stuttgart, Germany)

机构地区：[1]Independent Researcher, Stuttgart, Germany

出　　处：《Journal of High Energy Physics, Gravitation and Cosmology》2024年第3期930-957,共28页高能物理（英文）

摘　　要：This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

关 键 词：COSMOLOGY Distance Luminosity Transverse Comoving Distance Incomplete Elliptic Integrals 

分 类 号：O17[理学—数学]