Inflationary solution of Hamilton Jacobi equations during weak dissipative regime

In this paper, an elegant mathematical approach is introduced to solve the equations of warm inflationary model without using extra approximations other than slow-roll. This important inflationary method known as Hamilton-Jacobian formalism. Here tachyon field and the imperfect fluid are considered to be the cosmic ingredients to create inflation. A general formalism is developed for the considered inflationary model and further work is restricted to weak dissipative regime. A detailed analysis of the model is presented for three different choices of bulk and dissipative coefficients taking as constant as well as variable (function of Hubble parameter and inflaton). In each case, the involved model parameters are constrained to plot the physical acceptable range of scalar spectral index and tensor to scalar ratio. The parametric trajectories proved that the acquired results for all the three cases are compatible with Planck astrophysical data. Furthermore, the existence of warm inflation and slow-roll limit are also verified graphically.