Observational constraints on DBI constant-roll inflation

Using the constant-roll approach, DBI inflationary scenario will be studied and it is sought to compare the result with observational data. By considering the cosmological perturbations of the model, it is realized that some extra terms appear in the amplitude of scalar perturbations which indicate that there shuold be a modified version of the scalar spectral index and tensor-to-scalar ratio. In order to compare the model with observational data, some specific functions of scalar field are assumed for the function $f(\phi)$ function. For the power-law and exponential functions, a constant slow-roll parameter $\epsilon$ is obtained which produced difficulties for the graceful exit from inflation. Then, a product of linear and exponential function, and also a hyperbolic function of scalar field are selected for $f(\phi)$ that result in a $\epsilon$ with an end for accelerated expansion phase. Considering the scalar spectral index, the amplitude of scalar perturbations and tensor-to-scalar ratio shows that for some values of the constant $\eta = \beta$ there could be a good consistency between the model predictions and observational data. In addition, based on the form of the equation of motion of the scalar field, a new interesting definition for the second slow-roll parameters is presented and the behavior of the perturbations is reconsidered. The results come to good consistency with data. Finally, the attractor behavior of these two cases is investigated and it is determined that this feature could be satisfied.