Seeing Higher-Dimensional Grand Unification In Primordial Non-Gaussianities

TL;DR

This work proposes that orbifold GUTs, with a relatively low unification scale around $M_U\sim 10^{14}$ GeV, can imprint observable primordial NG during high-scale inflation when $H$ is of order $M_U$. By analyzing a 5D setup with the inflaton on a boundary and a second boundary near a bulk horizon, the authors show that the KK spectrum of gravitons and gauge bosons can be discretized with masses around $\sim 3H/2$, enabling cosmological production and NG signatures without large Boltzmann suppression. They derive explicit NG templates for spin-2 and spin-1 exchanges, including angular dependences $\cos^2\theta-1/3$ and $\sin^2\theta$, and discuss holographic insights via AdS$_5$/CFT$_4$ when a bulk cosmological constant is included. The results indicate that, if primordial gravitational waves are detected (implying large $H$) and NG corresponding to KK gravitons and KK gauge bosons are observed, this would provide a direct probe of orbifold GUT structure and extra-dimensional dynamics in the early universe.

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.

Figures (6)

• Figure 1: SM Renormalization Group Evolution (RGE) of gauge couplings $g_i$ at 1-loop written in terms of $\alpha_i \equiv g_i^2/4\pi$. The label "i = 1,2,3" denotes the $U(1)$ , $SU(2)$ and $SU(3)$ SM subgroups respectively with the normalization that $g_1 =Ùè∞è\sqrt{5/3}g^\prime$ where $g^\prime$ is the SM hypercharge coupling.
• Figure 2: 5D spacetime having two boundaries at $y=0$ and $y=L$. (a) Dirichlet Boundary Conditions (BC's) on the gauge bosons of GUT/SM achieves the breaking $G\rightarrow \text{SM}$ on the left boundary, also housing the inflaton $\phi(x)$. Neumann BC's on all gauge bosons preserve $G$ on the right boundary.
• Figure 3: Tree level contributions to bispectrum due to massive particle exchange. From left to right: (a) single exchange diagram, (b) double exchange diagram, (c) triple exchange diagram. All the three diagrams depend on the mixing between the massive particle (in red) and the inflaton fluctuation (in black) in the (implicit) non-trivial background of slowly rolling $\phi_0(t)$. $\eta$ is (conformal) time, ending at the end of inflation.
• Figure 4: Same set-up as in Fig. \ref{['fig:extra-dim-geometry']} except the right boundary is absent and a "black brane" horizon has formed due to the backreaction of the inflationary vacuum energy on the left boundary.
• Figure 5: Strength of NG mediated by spin-2 KK graviton for tensor-to-scalar ratio $r=0.1$ and KK wavefunction on inflationary boundary $\psi(0)=1$. Such strengths for the range of masses shown are observable within cosmic variance (see Section \ref{['ininreview']})