Inflation in Supersymmetric Unified Theories

TL;DR

Jeannerot shows that supersymmetric unified theories with an extra $U(1)_x$ naturally realize false-vacuum hybrid inflation, which can be driven by either an $F$-term or a $D$-term depending on whether SUSY is global or local. In supergravity, $D$-term inflation is favored and requires a Fayet-Iliopoulos term, leading to the formation of cosmic strings at the end of inflation that can dominate the CMB anisotropies. Through COBE normalization, the $U(1)_x$ breaking scale is constrained to about $ξ_x^{1/2} oughly 4.7 imes 10^{15}$ GeV and the inflationary energy scale to $V_0^{1/4} oughly 3.3 imes 10^{15}$ GeV, with strings contributing roughly 75% to the CMB multipoles in the preferred D-term scenarios. The paper outlines three model classes—where the extra $U(1)_x$ is a subgroup of the GUT, belongs to the visible sector, or sits in the hidden sector—demonstrating viable paths to incorporate $B-L$ physics, baryogenesis via leptogenesis, and natural inflation without fine-tuning. The results emphasize the importance of including cosmic strings in predictions of early-Universe structure formation and CMB signatures in SUSY GUT cosmology.

Abstract

We construct supersymmetric unified models which automatically lead to a period of inflation. The models all involve a U(1) symmetry which does not belong to the MSSM. We consider three different types of models depending on whether this extra U(1) is the subgroup of a non abelian gauge group, is a U(1) factor belonging to the visible sector or is a U(1) factor belonging to the hidden sector. Depending on the structure of the unified theory, on the spontaneous symmetry breaking pattern and on whether we have global or local supersymmetry, inflation may be driven by the non-vanishing vacuum expectation value of a F-term or by that of a D-term. In both scenarios cosmic strings form at the end of inflation, and they have different properties in each model. Both inflation and cosmic strings contribute to the CMBR temperature anisotropies. We show that the strings contribute to the $C_l$'s up to the level of 75 %. Hence the contribution from strings to the CMBR and to the density perturbations in the early Universe which lead to structure formation cannot be neglected. We also discuss a very interesting class of models which involve a $U(1)_{B-L}$ gauge symmetry.