Existence of solutions between prescribed configurations is proved for spatially flat Robertson–Walker spacetimes coupled with homogeneous scalar field sources, using a modified version of the Euler–Maupertuis least action variational principle. The solutions are obtained as limits of approximating variational problems, solved using the techniques originally introduced by Rabinowitz.
REFERENCES
1.
2.
Y.
Bruhat
, Acta Math.
88
, 141
–225
(1952
).3.
4.
5.
R.
Giambó
, Class. Quantum Grav.
22
, 2295
(2005
).6.
R.
Giambó
, F.
Giannoni
, G.
Magli
, and P.
Piccione
, Commun. Math. Phys.
235
, 545
–563
(2003
).7.
8.
E.
van Groesen
, in Hamiltonian Flow on an Energy Surface: 240 Years After the Euler-Maupertuis Principle
, on “Geometric Aspects of the Einstein Equations and Integrable Systems
” edited by R. A.
Martini
Lecture Notes in Physics Vol. 239
, (Springer
, New York
, 1985
).9.
10.
T.
Hertog
, G. T.
Horowitz
, and K.
Maeda
, Phys. Rev. Lett.
92
131101
(2004
).11.
12.
J.
Kijowski
, D.
Bambusi
, and G.
Magli
, Elasticità finita e relativistica: introduzione ai metodi geometrici della teoria dei campi
, Pitagora, 1991
(in italian).13.
C. W.
Misner
, K. S.
Thorne
, and J. A.
Wheeler
, Gravitation
, (W. H. Freeman
, San Francisco
, 1973
).14.
N. J.
Nunes
, and J. E.
Lidsey
, Phys. Rev. D
69
, 123511
(2004
).15.
V.
Perlick
, Living Rev. Relativ.
, 7
(2004
);16.
P. H.
Rabinowitz
, Minimax Method in Critical Point Theory with Applications to Differential Equations
, CBMS Regional Conf. Series in Math.
, No. 65, (AMS
, Providence
, 1986
).17.
A. G.
Riess
et al. (Supernova Search Team Collaboration
), Astron. J.
116
, 1009
(1998
).18.
S.
Tsujikawa
, Phys. Rev. D
72
, 083512
(2005
).19.
R. M.
Wald
, General Relativity
(University of Chicago Press
, Chicago
1984
).© 2006 American Institute of Physics.
2006
American Institute of Physics
You do not currently have access to this content.
