Seeing higher-dimensional grand unification in primordial non-gaussianities

Abstract

A bstract The observed low-energy values of the SU(3) × SU(2) × 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 ∼ 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 × 10 13 GeV ∼ 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 ∼ $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi></mml:math> ( 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 AdS 5 /CFT 4 correspondence when such a cosmological constant is included.