DBI Inflation in N=1 Supergravity

TL;DR

The paper tackles the obstacle of realizing DBI inflation within ${\cal N}=1$ supergravity by showing that a single chiral superfield yields a negative potential in the relativistic DBI limit, preventing inflation. It introduces a method to overcome this by coupling to additional chiral superfields with canonical kinetic terms and carefully chosen constrained Kähler potentials and holomorphic couplings, enabling positive potentials for a DBI inflaton and, more generally, multi-field DBI scenarios. The main contributions include a concrete two-field construction with W = S w(Φ) that yields $V_{\rm rel.,2} = e^{K} ( K^{,BB^*} |D_B W|^2 - 3 e^{K} |W|^2 )$ and, on the $B=0$ plane, $V = e^{K} |w(A)|^2$, as well as a stabilization framework for the additional fields and an explicit Kähler potential satisfying the required constraints. Extending to three or more superfields, the authors present hybrid potentials like $V_{\rm hybrid} = a_0^2 ( \phi^2 + a_1 \phi^2 \rho^2 + (a_2 - a_3 \rho^2)^2 )$, with DBI kinetics for the inflaton and canonical kinetics for the others, illustrating rich multi-field DBI inflation in supergravity. Overall, the work provides a proof-of-principle that positive, microphysically motivated DBI inflationary models can be realized in ${\cal N}=1$ supergravity and generalized to arbitrary numbers of fields, with potential implications for string-inspired cosmology.

Abstract

It was recently demonstrated that, when coupled to N=1 supergravity, the Dirac-Born-Infeld (DBI) action constructed from a single chiral superfield has the property that when the higher-derivative terms become important, the potential becomes negative. Thus, DBI inflation cannot occur in its most interesting, relativistic regime. In this paper, it is shown how to overcome this problem by coupling the model to one or more additional chiral supermultiplets. In this way, one obtains effective single real scalar field DBI models with arbitrary positive potentials, as well as multiple real scalar field DBI inflation models with hybrid potentials.

Figures (1)

• Figure 1: This graph depicts the field space trajectory in a potential of the hybrid form (\ref{['Potential4']}), with $a_0=a_2=1, a_1 = 10, a_3=4$. For illustration purposes, we have plotted the logarithm of the potential rather than the potential itself. The trajectory first evolves along the $\phi$ direction with a $\phi^2$ potential, and then turns as the transverse direction becomes unstable. Inflation ends as the trajectory reaches a true minimum of the potential at $\phi=0,\rho=1/2$ (or $-1/2$). For the models we have constructed, the kinetic terms are also of a "hybrid" type: the $\phi$ field evolves according to a DBI kinetic term, while $\rho$ is governed by a standard two-derivative kinetic term.