Variational principle and a perturbative solution of non-linear string equations in curved space Original Research Article

String dynamics in a curved space-time is studied on the basis of an action functional including the small parameter of rescaled tension ε = γ/α′, where γ is a metric parametrizing constant. A rescaled slow world-sheet time T = ετ is introduced, and general covariant non-linear string equations are derived. It is shown that in the first order of an ε-expansion these equations are reduced to the known equation for geodesic deviation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann-Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant H(α′H2 ⪢ 1).