P-term, D-term and F-term inflation

TL;DR

This work presents P-term inflation as a unified framework in which D-term and F-term inflation arise from an underlying N=2 supersymmetric gauge theory, with their difference controlled by the orientation of the FI triplet and, upon coupling to N=1 supergravity, by a tunable parameter f that interpolates between D-term (f=0) and F-term (f=1) regimes. The model leverages the SU(2,2|2) superconformal structure, its breaking to N=2 via the P triplet, and the D3/D7 brane fluxes to connect brane inflation to cosmology, predicting distinct perturbation spectra and potential cosmic-string contributions. Loop corrections uplift the inflaton potential, and gravity-induced SUGRA terms (modulated by f) influence the running of the spectral index, enabling a range of phenomenologies from nearly scale-invariant to mildly running spectra. Post-inflation, tachyonic preheating drives rapid, inhomogeneous field dynamics along a fixed trajectory, a robust feature across P-term realizations. Overall, P-term inflation offers a controlled bridge between D-term and F-term models within a string-inspired setting, with testable implications for inflationary perturbations and preheating dynamics, while highlighting the ongoing need for moduli stabilization in brane cosmology.

Abstract

P-term inflation is a version of hybrid inflation which naturally appears in some brane inflation models. It was introduced in the framework of N=2 supersymmetric gauge theory where superconformal SU(2,2|2) symmetry is broken down to N=2 supersymmetry by the vev of the auxiliary triplet field P. Depending on the direction of this vev, one can get either D-term inflation or F-term inflation with a particular relation between Yukawa and gauge coupling, or a mix of these models. We show that F and D models, before coupling to gravity is included, are related by a change of variables. Coupling of this model to N=1 supergravity breaks this symmetry and introduces a class of P-term models interpolating between D-term and F-term inflation. The difference between these models is determined by the direction of the vector P, which depends on the fluxes in the underlying D3/D7 model of brane inflation. We discuss cosmological consequences of various versions of P-term inflation.