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.
REFERENCES
1.
J. J.
Morales-Ruiz
, Differential Galois Theory and Non-integrability of Hamiltonian Systems
(Birkhäuser Verlag
, Basel
, 1999
).2.
J. M.
Stewart
, Class. Quantum Grav.
7
, 1169
(1990
).3.
J.
Bičák
, D.
Lynden-Bell
, and J.
Katz
, Phys. Rev. D
69
, 064011
(2004
).4.
M. P.
Dbrowski
and T.
Stachowiak
, “Phantom Friedmann cosmologies and higher-order characteristics of expansion
,” arxiv:hep-th/0411199.5.
6.
7.
8.
9.
10.
M.
Bronstein
and S.
Lafaille
, “Solutions of linear ordinary differential equations in terms of special functions
,” Proceedings of ISSAC’2002
(ACM Press
, 2002
), pp. 23
–28
.11.
© 2006 American Institute of Physics.
2006
American Institute of Physics
You do not currently have access to this content.