ИСТИНА

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct theequation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We also develop the cosmological perturbations formalism nonlocal modified gravity models, which are equivalent to local gravity models with nonminimally coupling nonlocal scalar fields. We construct the equation for the energy density perturbations of the nonlocal scalar field and analyse the perturbations in the neighbourhood of the exact bounce solutions.