Inflation and long-range force from clockwork $D$-term

TL;DR

This paper presents a clockwork framework that explains the vastly different energy scales of inflation and long-range forces mediated by an ultra-light gauge boson, unifying these phenomena without fine-tuning.

Contribution

It introduces a clockwork mechanism with a chain of U(1) symmetries to naturally generate the large scale of inflation and the tiny couplings of long-range forces.

Findings

The model can accommodate inflationary energy scales and long-range force constraints simultaneously.

Constraints on gauge coupling and Z' mass are derived from neutrino oscillations and pulsar timings.

The framework explains the coexistence of vastly different energy scales without fine-tuning.

Abstract

Cosmic inflation driven by the vacuum energy associated with the $D$-term of a supersymmetric abelian gauge group and a possible existence of long-range force mediated by an ultra-light gauge boson $Z^\prime$ are two extreme examples of models based on extra $U(1)$ symmetries. Large vacuum energy sets the scale of inflation while the scales of long-range forces induced by anomaly free extra gauged $U(1)$ symmetries are constrained by neutrino oscillations, binary pulsar timings and invisible neutrino decay. There exists a difference of about 40 orders of magnitude between the scales of these two. Also, gauge couplings associated with the long-range forces are very small compared to the standard model couplings and the one required for inflation. We propose a framework based on clockwork mechanism in which these vastly different scales and associated new physics can coexist without invoking any arbitrarily small or large parameter in the fundamental theory. A chain of $U(1)$ is introduced with characteristic nearest-neighbour interactions. A large $D$-term introduced at one end governs the dynamics of inflation. $Z^\prime$ is localized on the other end of the chain, and it can be massless or can get naturally suppressed mass. The standard model fields can be charged under one of the intermediate $U(1)$ in the chain to give rise to their small effective coupling $g^\prime$ with $Z^\prime$. Constraints on $g^\prime$ and $M_{Z^\prime}$ are discussed in the context of the long-range forces of type $L_\mu - L_\tau$, $L_e - L_\mu$ and $B-L$. These, along with the inflation observables, are used to constraint the parameters of the underlying clockwork model.