  Vortex tilt response in Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex
lattice is theoretically examined as a probe reflecting the spatial structure
of this state. In the FFLO state with nodal planes perpendicular to the
magnetic field in a quasi 2D material under a parallel field, the tilt modulus
E_{2} {\it of the nodal planes} decreases as the paramagnetic effect is
effectively enhanced, and this reduction of E_{2} in turn reduces the vortex
tilt modulus. This reduction of vortex tilt modulus, more remarkable in more
anisotropic systems, accompanying the FFLO transition may be an origin of the
monotonous reduction of sound velocity detected upon cooling in a ultrasound
measurement for CeCoIn5.
