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.
Highlights
There exist a large number of well-motivated gauged extensions of the Standard Model (SM) containing an extra Uð1Þ group
These are proposed (i) on phenomenological grounds like explaining anomaly found in the muon anomalous magnetic moment [1] or as explanation of the universality violation observed in the B meson decays [3], (ii) on cosmological grounds such as need to explain the dark matter [4,5,6], to provide secret interactions between sterile neutrinos of eV masses [7,8] to suppress their cosmological production in the early Universe, etc., (iii) as a theoretical framework for the successful description of the inflation in the context of supersymmetric versions of the SM [9,10,11], and (iv) to provide a simple description of the long-range “fifth force” [12,13] if it exists
This offers an exciting possibility of unifying the large scale inflation and longrange interactions mediated by an ultralight gauge boson, and in-turn explains 40 orders of magnitude difference between the scales without relying on any unnatural parameter
Summary
There exist a large number of well-motivated gauged extensions of the Standard Model (SM) containing an extra Uð1Þ group These are proposed (i) on phenomenological grounds like explaining anomaly found in the muon anomalous magnetic moment [1] (see [2] for a review) or as explanation of the universality violation observed in the B meson decays [3], (ii) on cosmological grounds such as need to explain the dark matter [4,5,6], to provide secret interactions between sterile neutrinos of eV masses [7,8] to suppress their cosmological production in the early Universe, etc., (iii) as a theoretical framework for the successful description of the inflation in the context of supersymmetric versions of the SM [9,10,11], and (iv) to provide a simple description of the long-range “fifth force” [12,13] if it exists. The localization of chiral superfields away from Uð1Þ0 leads to an explanation of a large hierarchy between the scales of inflation and the mass of the gauge boson mediating long-range force.
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