Constant-rollt achyon inflation and observational constraints

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of is an element of(1) by using the method of Bessel function approximation. The derived n(s)-r results are compared with the observations, we find that only the constant-roll inflation with eta(H) being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.