Uncertainty-controlled Kaluza-Klein emission constraints on cosmic superstrings: loop-population inputs, KK-mode lifetimes, and compactifications beyond the Klebanov-Strassler throat

Cosmic superstrings radiate a substantial fraction of their energy into massive Kaluza-Klein (KK) graviton modes of the warped extra dimensions in which they live. Dufaux (2012) turned this into exclusion regions in the string-coupling/string-tension plane by requiring that the Standard-Model decay products of the KK modes neither spoil big-bang nucleosynthesis nor overproduce the diffuse gamma-ray background. Those constraints, however, rest on unverified inputs the source paper itself flags: the loop production function and birth size for reduced reconnection probability, the cusp count per loop, an approximate rather than full loop-population evolution with KK losses, assumed prompt KK decay, and coupling/reconnection parameters computed only for the Klebanov-Strassler throat. The problem is to determine these inputs -- from string-network simulations and compactification calculations -- and to propagate them into uncertainty-controlled exclusion (or detection) regions for cosmic-superstring parameters.

Background

Cosmic strings are one-dimensional topological defects that can form during symmetry-breaking phase transitions in the early universe; a network of infinite strings and closed loops evolves toward a self-similar 'scaling' regime, with loops radiating away their energy. In string-theory scenarios of brane inflation, macroscopic fundamental strings and D-strings can survive to the present as 'cosmic superstrings'. A key difference from field-theory strings is their intercommutation (reconnection) probability $p$, which can be far below the field-theory value $p\simeq1$ (as small as $10^{-3}$ for intersecting F-strings); a reduced $p$ changes both the network density and the population of small loops, weakening standard gravitational-wave constraints. In warped compactifications with extra dimensions -- the canonical example being the Klebanov-Strassler (KS) throat, a string/gauge-theory duality construction describing a warped, smoothly capped conifold -- a superstring moving in the throat can radiate its energy into massive Kaluza-Klein (KK) graviton modes, i.e. gravitational excitations of the compact dimensions, with an effective coupling $\kappa_E$ fixed by the throat geometry and string coupling $g_s$. Loop emission is dominated by cusps (points on an oscillating loop that momentarily move at the speed of light, producing beamed high-frequency radiation) and kinks (sharp corners from string intercommutation).

Dufaux (Phys. Rev. Lett. 109, 011601 (2012); companion JCAP paper) computed the KK-emission power of cosmic-superstring loops, modeled the loop population with a one-scale distribution $n_L\propto p^{-1}$ and initial loop size $\alpha\simeq0.1$ (in units of the horizon scale at formation), took of order one cusp per loop oscillation, and assumed the KK modes decay into Standard Model particles within less than a Hubble time at the epoch of interest ($\gamma\tau\lesssim t$, with $\gamma$ the boost and $\tau$ the KK lifetime). Requiring the injected electromagnetic energy to remain compatible with big-bang nucleosynthesis (BBN, the light-element-synthesis epoch) and with the diffuse gamma-ray background (DGRB) yields exclusion regions in the $(g_s,G\mu)$ plane, where $G\mu$ is the string tension times Newton's constant. The paper explicitly lists the quantitative uncertainties that limit these constraints, and its companion long paper defers the same items: the loop birth size $\alpha$ and the $p$-dependence of the loop production function; the average cusp number $c$ per loop oscillation; the absence of a dedicated study of loop-population time evolution including KK losses (only an approximate $n_L(t)$ was used); the assumption of prompt KK decay, whose failure for lifetimes near the BBN limit $\tau\sim1\,\mathrm{s}$ could tighten the constraints and requires tracking when the energy is injected; the model dependence of $\kappa_E$ and of $p(g_s,R/\sqrt{\alpha'})$ beyond the KS throat; and unstudied further consequences of KK emission such as cosmic-ray production or long-lived relics. Later work supplies enabling pieces but not the missing inputs: Blanco-Pillado, Olum and Shlaer (Phys. Rev. D 89, 023512 (2014)) determined the loop production function and initial-size distribution, but only for ordinary $p=1$ Nambu-Goto strings; Auclair, Steer and Vachaspati (Phys. Rev. D 101, 083511 (2020)) solved the full loop-population evolution with particle emission and derived observational constraints, but for field-theory strings emitting Standard Model particles, not KK modes.

Problem Statement

Rebuild the Kaluza-Klein emission constraints on cosmic superstrings on uncertainty-controlled inputs. Specifically: (i) determine, for reduced intercommutation probability $p<1$, the loop production function and the initial loop-size distribution $\alpha$ that replace the ansatz $n_L\propto p^{-1}$, $\alpha\simeq0.1$; (ii) determine the distribution of the number of cusps (and kinks) per loop oscillation on realistic loop ensembles, replacing the estimate $c\sim1$ that directly scales the KK emission power; (iii) solve the full time evolution of the loop population including KK radiation losses, going beyond the approximate one-scale $n_L(t)$, and establish how the non-scaling loop density modifies the injected-energy history; (iv) compute the constraints without assuming prompt KK decay -- for KK lifetimes up to the BBN limit $\tau\sim1\,\mathrm{s}$, track when and where the KK decay products inject their energy and rederive the BBN and diffuse-gamma-ray bounds as functions of $\tau$; (v) compute the KK coupling $\kappa_E$ and the reconnection probability $p(g_s,R/\sqrt{\alpha'})$ for at least one representative compactification other than the Klebanov-Strassler throat, and propagate the changed numerical coefficients into the bounds; and (vi) evaluate further phenomenological consequences of KK emission flagged but not computed in the source work, such as cosmic-ray production or long-lived KK relics, as additional constraints or signatures. Items (i)-(v) are the inputs jointly required to deliver the objective -- the uncertainty-controlled KK-emission exclusion (or detection) map for cosmic-superstring parameters such as the string coupling $g_s$, the tension $G\mu$, and the compactification geometry -- while item (vi) is an optional extension that would supplement that map with additional constraints or signatures. Here 'uncertainty-controlled' means that each exclusion (or detection) region must be quoted with uncertainty bands propagated from the uncertainties in the inputs (i)-(v) -- in particular the loop production function and birth size $\alpha$, the cusp/kink count $c$, the KK coupling $\kappa_E$, and the KK lifetime $\tau$ -- rather than as a single central-value curve qualified only by qualitative caveats.

References

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