Geodesic
Exact string solutions in $2+1$-dimensional de Sitter spacetime
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 232-240 
H. J. de Vega; A. V. Mikhailov; N. Sánchez. Exact string solutions in $2+1$-dimensional de Sitter spacetime. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 232-240. http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a4/
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     author = {H. J. de Vega and A. V. Mikhailov and N. S\'anchez},
     title = {Exact string solutions in $2+1$-dimensional de {Sitter} spacetime},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {232--240},
     year = {1993},
     volume = {94},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Exact and explicit string solutions propagating in $2+1$ dimensional de Sitter spacetime are presented and physically analized. (In this case the string equations reduce to a $sinh$-Gordon model.) Strings generically tend to inflate or either to collapse. The world-sheet time $\tau$ interpolates between the cosmic $\tau \to \pm \infty$ and conformal $\tau \to 0$ times. For $\tau \to 0$, the typical string instability is found, while for $\tau \to \pm \infty$, a new string behavior appears. In that regime, the string expands (or contracts) but not with the same rate as the universe does. The string constraints select periodic solutions of the $sinh$-Gordon equation associated to the lower boundary of the allowed zone, therefore excluding elliptic solutions.

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