Dangerous Angular KK/Glueball Relics in String Theory Cosmology

TL;DR

This work analyzes angular KK relics arising from approximate isometries in warped throat geometries of string compactifications. By treating isometry breaking from gluing KS-like throats to Calabi-Yau manifolds as perturbations, the authors compute spin-2 KK mode spectra, their couplings to themselves and to Standard Model brane fields, and the channels by which these relics decay. They derive relic abundances and lifetimes for KK0 and KK_L modes, and confront the results with cosmological constraints from BBN and the diffuse gamma-ray background, delineating viable regions of the warped-geometry parameter space. The findings show that angular KK relics can be either short-lived or long-lived, with significant implications for cosmology and for identifying potential dark matter candidates in certain long-throat setups; crucially, couplings to SM fields can be much weaker than gravity, providing interesting phenomenological possibilities and stringent constraints on throat geometries.

Abstract

The presence of Kaluza-Klein particles in the universe is a potential manifestation of string theory cosmology. In general, they can be present in the high temperature bath of the early universe. In particular examples, string theory inflation often ends with brane-antibrane annihilation followed by the energy cascading through massive closed string loops to KK modes which then decay into lighter standard model particles. However, massive KK modes in the early universe may become dangerous cosmological relics if the inner manifold contains warped throat(s) with approximate isometries. In the complimentary picture, in the AdS/CFT dual gauge theory with extra symmetries, massive glueballs of various spins become the dangerous cosmological relics. The decay of these angular KK modes/glueballs, located around the tip of the throat, is caused by isometry breaking which results from gluing the throat to the compact CY manifold. We address the problem of these angular KK particles/glueballs, studying their interactions and decay channels, from the theory side, and the resulting cosmological constraints on the warped compactification parameters, from the phenomenology side. The abundance and decay time of the long-lived non-relativistic angular KK modes depend strongly on the parameters of the warped geometry, so that observational constraints rule out a significant fraction of the parameter space. In particular, the coupling of the angular KK particles can be weaker than gravitational.

Figures (12)

• Figure 1: Zeros and signs on the spherical harmonics on $S^2$. We compare the $M=0$ with the $M\neq0$ case. The spherical harmonics with $M \neq 0$ vanish at the two poles. As a consequence, $KK$ modes with nonvanishing angular momentum along the directions whose isometries are left unbroken by the brane are not directly coupled to brane fields (see the main text for details).
• Figure 2: Left panel: for the isometric throat, the decay of angular KK modes localized around the tip of the throat is forbidden by higher-dimensional angular momentum conservation. Right panel: The isometry breaking leads to a new interaction, which corresponds to the decay of an angular KK mode into SM particles mediated by a background isometry breaking KK mode localized in the compact CY.
• Figure 3: Estimate for the $m / T$ ratio at which the scatterings ${\rm KK}_L + {\rm KK}_{-L} \rightarrow b + b$ freeze out. The value is strongly sensitive to the ratio $R/\sqrt{\alpha'}$.
• Figure 4: Relic abundance for the KK$_L$ species as function of parameter $R/\sqrt{\alpha'}$. We note that the lightest modes are more abundant than the heavier ones.
• Figure 5: Temperature of the universe at which the relic KK$_L$ particles start to dominate, (provided they have not decayed yet) as function of $R/\sqrt{\alpha'}$. The temperature $T_{eq} \simeq 7.4 \cdot 10^{-10} \, {\rm GeV} \,$ at the moment of matter--radiation equality is also shown for comparison. In the long throat, for $R / \sqrt{\alpha'} \simeq 6 \,$, the KK modes can be the dark matter candidate.