An approximate description of string and $p$-brane dynamics in curved sрace-times

A new formulation for the action of the Nambu–Goto string moving in curved space-time is studied. The action contains a two-dimensional “cosmological” world-sheet term multiplied by a tension parameter. It is shown that the consideration of this cosmological term as a perturbative addition allows one to linearise nonlinear equation for the string. It is argued that in zero approximation with respect to tension of strings and membranes can be considered as dominant gravitation sources for the Friedmann universe with $\kappa=0$.