Warm Modified Chaplygin Gas Shaft Inflation

In this paper, we examine the possible realization of a new family of inflation called "shaft inflation" by assuming the modified Chaplygin gas model and tachyon scalar field. We also consider the special form of dissipative coefficient as $\Gamma={a_0}\frac{T^{3}}{\phi^{2 }}$ and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the planes of $n_s - \phi,~n_s - r$ and $n_s - \alpha_s$ (where $n_s,~\alpha_s,~r$ and $\phi$ represent spectral index, its running, tensor to scalar ratio and scalar field respectively) are being developed which lead to the constraints: $r< 0.11$, $n_s=0.96\pm0.025$ and $\alpha_s =-0.019\pm0.025$. It is quite interesting that these results of inflationary parameters are compatible with BICEP$2$, WMAP $(7+9)$ and recent Planck data.