Cosmological scaling solutions with tachyon: Modified gravity model

Modifying the Einstein's gravity at large distance scales is one of the interesting proposals to explain the late time acceleration of the universe. In this Letter, we analyse scaling solutions in modified gravity models where the universe is sourced by a background matter fluid together with a tachyon type scalar field. We describe a general prescription to calculate the scaling potential in such models. Later on we consider specific examples of modifications and apply our method to calculate the scaling potential and the scale factor. Our method can be applied to any modified gravity model, in presence of tachyon field.