Seeing Higher-Dimensional Grand Unification In Primordial Non-Gaussianities

Abstract

The observed low-energy values of the $SU(3)\times SU(2)\times U(1)$ gauge couplings, extrapolated via the minimal Standard Model Renormalization Group evolution, hint at the exciting possibility of a Grand Unified Theory (GUT) at $M_U\sim 10^{14}$ GeV --- a scale, however, too high to probe directly via collider searches. Fortunately, since the Hubble scale H can be as high as $5\times 10^{13}$ GeV $\sim M_U$ during the inflationary era, such GUT scale states can be cosmologically produced at that time and leave direct on-shell signatures such as their masses and spins, via primordial non-Gaussianity (NG). We explore this possibility in one of its simplest realizations given by the extra-dimensional framework of orbifold GUTs, in which proton decay can be straightforwardly suppressed to be within the stringent bounds. Here, along with the massive GUT states there must also be H-mass spin-2 Kaluza-Klein (KK) gravitons, collectively giving rise to striking NG signatures. In our set-up we localize the inflaton on one of the boundaries of an extra dimension. The inflationary vacuum energy can readily lead to formation of a horizon in the bulk, where the KK modes then form a continuum above a mass gap of $\sim \mathcal{O}(H)$. We find that the optimal case for observable NG signals is when the extra dimension is stabilized close to the onset of this horizon, ensuring a discrete KK spectrum such that the lightest KK modes can be cosmologically produced without significant Boltzmann suppressions. Although we mostly focus on the case where there is no higher-dimensional cosmological constant, we also obtain considerable holographic insights from the ${\text{AdS}}_5/{\text{CFT}}_4$ correspondence when such a cosmological constant is included.

Comments: v1: 30+10 pages, 6 figures; v2: discussion added at the end of subsection 4.3, reference added, conclusions unchanged, journal version