Warm DBI inflation with constant sound speed

We study inflation with the Dirac–Born–Infeld (DBI) noncanonical scalar field in both the cold and warm scenarios. We consider the Anti-de Sitter warp factor $$f(\phi )=f_{0}/\phi ^{4}$$ for the DBI inflation and check viability of the quartic potential $$V(\phi )=\lambda \phi ^{4}/4$$ in light of the Planck 2015 observational results. In the cold DBI setting, we find that the prediction of this potential in the $$r-n_s$$ plane is in conflict with Planck 2015 TT, TE, EE + low P data. This motivates us to focus on the warm DBI inflation with constant sound speed. We conclude that in contrary to the case of cold scenario, the $$r-n_s$$ result of warm DBI model can be compatible with the 68% CL constraints of Planck 2015 TT, TE, EE + low P data in the intermediate and high dissipation regimes, whereas it fails to be observationally viable in the weak dissipation regime. Also, the prediction of this model for the running of the scalar spectral index $$dn_s/d\ln k$$ is in good agreement with the constraint of Planck 2015 TT, TE, EE + low P data. Finally, we show that the warm DBI inflation can provide a reasonable solution to the swampland conjecture that challenges the de Sitter limit in the standard inflation