concentrate on the case of a $D$-particle embedded in a four-dimensional RW spacetime. It must be stressed that we shall not attempt here to present a complete discussion of the associated space time curvature effects, which - as mentioned earlier - is a very difficult task, still unresolved. Nevertheless, by concentrating on times much larger than the moment of impulse on the $D$-particle defect, one may ignore such effects to a satisfactory approximation. As we shall see, our analysis produces results which look reasonable and are of sufficient interest to initiate further research.

The vertex operators which describe the impulse in curved RW backgrounds obey a suitably extended (higher-order) logarithmic algebra. The algebra is valid at, and in the neighborhood of, a non-trivial infrared fixed point of the world-sheet Renormalization Group. For a RW spacetime of scale factor of the form $t^p$, where $t$ is the target time, and $p > 1$ in the horizon case, the algebra is actually a set of logarithmic algebras up to order $[2p]$, which are classified by the appropriate higher-order Jordan blocks [@lcft].

As in the flat case, which is obtained as a special limit of this more general case, the recoil deformations are 