Inflationary potentials in DBI models

Abstract

We study DBI inflation based upon a general model characterized by a power-law flow parameter $\epsilon (\varphi )\propto {\varphi }^{\alpha }$ and speed of sound $c_s(\varphi )\propto {\varphi }^{\beta }$, where $\alpha$ and $\beta$ are constants. We show that in the slow-roll limit this general model gives rise to distinct inflationary classes according to the relation between $\alpha$ and $\beta$ and to the time evolution of the inflaton field, each one corresponding to a specific potential; in particular, we find that the well-known canonical polynomial (large- and small-field), hybrid and exponential potentials also arise in this non-canonical model. We find that these non-canonical classes have the same physical features as their canonical analogs, except for the fact that the inflaton field evolves with varying speed of sound; also, we show that a broad class of canonical and D-brane inflation models are particular cases of this general non-canonical model. Next, we compare the predictions of large-field polynomial models with the current observational data, showing that models with low speed of sound have red-tilted scalar spectrum with low tensor-to-scalar ratio, in good agreement with the observed values. These models also show a correlation between large non-gaussianity with low tensor amplitudes, which is a distinct signature of DBI inflation with large-field polynomial potentials.

Minor changes, reference added. Version submitted to JCAP

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• Tsallis holographic inflation in $f(R,T)$ gravity: CMB constraints, reheating, and swampland implications
• Effective Action of a Dynamical D$p$-brane with Background Fluxes
• Bouncing cosmologies in the presence of a Dirac-Born-Infeld field