Non-integrability of density perturbations in the FRW universe

Stachowiak, Tomasz; Szydlowski, Marek; Maciejewski, Andrzej J.

Non-integrability of density perturbations in the FRW universe

Authors

Stachowiak, Tomasz

Szydlowski, Marek

Maciejewski, Andrzej J.

Description

We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept of solvability by quadratures is defined and used to prove that there are no "closed form" solutions except for the known Chernin, Heath, Meszaros and simple degenerate ones. The analysis is performed applying Kovacic's algorithm. The possibility of the existence of other, more general solutions involving special functions is also investigated.
13 pages. The latest version with added references, and a relevant new paragraph in section II