Exact string solutions in 2+1-dimensional de Sitter spacetime

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 τ interpolates between the cosmic (τ→±∞) and conformal (τ→0) times. For τ→0, the typical string instability is found, while for τ→±∞, 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.