Reconstruction of f(R) models with scale-invariant power spectrum

Following our previous work in [T. Qiu, JCAP 1206 (2012) 041 [1]], in this Letter, we continue our study of reconstructing f(R) modified gravity models that can be connected to a single scalar field in general relativity via conformal transformation, which lead to scale-invariant power spectrum in the early universe. With f(R) modified gravity, one does not need to introduce extra scalar, the nature of which are to be explained. Different from general nonminimal coupling theory, the behavior of the f(R) theory has been fixed by its counterpart in Einstein frame, and thus have one-to-one correspondence. Numerical plots of the functional form of f(R) as well as the evolution of R in terms of cosmic time t are also presented.