Constant-roll inflation with tachyon field in the holographic braneworld

Abstract: We study inflation driven by the tachyon field in the holographic braneworld by assuming the second slow-roll parameter $\eta$ is constant. The parameter $\eta$ can be either defined by the tachyon scalar field and the Hubble parameter or by the Hubble parameter only. By assuming a constant $\eta$, we derive and numerically solve a differential equation for the Hubble expansion rate. We calculate numerically the scalar spectral index and the tensor-to-scalar ratio. We confront the results with the observational data and find some constraints on the free model parameters. The swampland conjectures are discussed in the context of the constant-roll inflation, with some accent on the holographic model.