[Paper Review] DBI Inflation in N=1 Supergravity

Michael Koehn, Jean-Luc Lehners+1 more|MPG.PuRe (Max Planck Society)|Aug 3, 2012

Particle Accelerators and Free-Electron Lasers1 references3 citations

TL;DR

This paper resolves the issue of negative potentials in N=1 supergravity DBI inflation by coupling a single chiral superfield with higher-derivative kinetic terms to one or more additional chiral supermultiplets with canonical kinetic terms. By carefully constraining the Kähler potential and choosing specific holomorphic superpotentials, the authors construct models with arbitrary positive potentials, enabling viable relativistic DBI inflation in a supersymmetric framework, including both single- and multi-field scenarios with stable, observationally consistent dynamics.

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.

Motivation & Objective

• To address the fundamental problem that DBI inflation fails in N=1 supergravity when higher-derivative terms dominate, due to the resulting potential becoming negative.
• To develop a mechanism for constructing viable DBI inflation models within N=1 supergravity that remain stable and predictive in the relativistic regime.
• To generalize single-field DBI inflation to multi-field models with hybrid-type potentials using additional chiral supermultiplets.
• To ensure that the effective potential remains stable and independent of higher-derivative terms during inflation, enabling reliable cosmological predictions.

Proposed method

• Couple a chiral superfield with a DBI-type higher-derivative kinetic term to one or more additional chiral supermultiplets with canonical two-derivative kinetic terms.
• Impose a constrained Kähler potential on the additional chiral superfields to stabilize their auxiliary fields and suppress unwanted contributions to the scalar potential.
• Use a holomorphic superpotential of the form W = S·w(Φ¹, Φ², ..., Φ^N) to generate a positive, effective potential for the inflaton field φ = √2 Re(Φ¹).
• Eliminate the auxiliary fields of the additional chiral supermultiplets via their equations of motion, ensuring the potential remains independent of higher-derivative terms in the inflationary regime.
• Construct multi-field models where the inflaton φ has a DBI action while other scalars have canonical kinetic terms, enabling hybrid-like potential structures.
• Demonstrate that the potential remains unchanged during dynamical evolution, even as higher-derivative terms become dominant, by ensuring their contributions vanish in the relevant field space.

Experimental results

Research questions

• RQ1 Can DBI inflation be consistently realized in N=1 supergravity when higher-derivative terms dominate, given that the potential becomes negative in the single-superfield case?
• RQ2 What conditions on the Kähler potential and superpotential are required to generate a positive, stable potential for the inflaton in a higher-derivative supergravity framework?
• RQ3 How can multi-field DBI inflation models with hybrid-type potentials be constructed in N=1 supergravity using additional chiral supermultiplets?
• RQ4 Can the effective potential remain independent of higher-derivative terms during inflation, ensuring reliable predictions despite strong non-linear dynamics?
• RQ5 Is it possible to stabilize the scalar components of additional chiral superfields with masses above the Hubble scale to avoid destabilizing the inflationary trajectory?

Key findings

• The inclusion of one or more additional chiral supermultiplets with canonical kinetic terms and constrained Kähler potentials allows the construction of positive, arbitrary potentials for the DBI inflaton field, overcoming the negative potential problem in single-superfield models.
• The effective potential remains stable and independent of higher-derivative terms during inflation, even when these terms dominate, due to cancellation of their contributions in the relevant field space.
• Multi-field DBI inflation models can be constructed where the inflaton φ has a DBI action while other real scalar fields have canonical kinetic terms, enabling hybrid-type potential structures.
• The scalar potential for the additional chiral superfields can be stabilized with masses above the Hubble scale by satisfying specific constraints on the Kähler potential.
• The method generalizes to N additional chiral supermultiplets, allowing for a wide range of potential functions for the inflaton and additional scalars, with stable dynamics.
• The construction provides a proof-of-principle for viable, observationally consistent multi-real-scalar-field DBI inflation in N=1 supergravity, with potential for future embedding in string compactifications.