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Observational Signatures of Planck-Mass Dark Matter

Authors: Ong, Edwin;

Observational Signatures of Planck-Mass Dark Matter

Abstract

The canvas model predicts that dark matter consists of Planck-mass black hole remnants formed at the Planck epoch. These remnants have mass M_{\text{rem}} \approx M_P \approx 2 \times 10^{-8} kg, size r_{\text{rem}} \sim \ell_P \approx 1.6 \times 10^{-35} m, and interact only gravitationally with a cross-section \sigma \sim 10^{-70} m². This paper derives the complete observational signature of this dark matter candidate and compares it with current experimental constraints and future detection prospects. What this paper provides: · A proof that direct detection is impossible. The interaction cross-section is 23 orders of magnitude below current WIMP search sensitivity. The event rate in a ton-scale detector is \sim 10^{-58} s⁻¹—approximately one event per 10^{50} years. The canvas model predicts that continued null results from XENONnT, LZ, PandaX, and future detectors are confirmations of the model, not failures.· A proof that indirect detection is impossible. Remnants do not annihilate (they are stable black holes, not particle-antiparticle pairs) and do not decay (there is no lower-mass state). No gamma-ray, cosmic-ray, or neutrino signals from dark matter annihilation are expected. Null results from galactic center, dwarf galaxy, and solar neutrino searches are predictions.· A derivation of gravitational wave echoes from remnant mergers. When two remnants merge, they form a 2M_P black hole that evaporates via Hawking radiation back to M_P in approximately one Planck time. The evaporation burst produces a characteristic gravitational wave echo with frequency f \sim 1/t_P \sim 10^{43} Hz and strain h \sim 10^{-60} at cosmological distances—far below current detector sensitivity.· A derivation of the stochastic gravitational wave background from mergers throughout cosmic history, with energy density \Omega_{\text{GW}}(f) \sim \alpha_0 (f/f_P)^{2/3}. At accessible frequencies (10^{-9} to 10^3 Hz), \Omega_{\text{GW}} \sim 10^{-30}—far below pulsar timing array and LIGO sensitivity.· An analysis of microlensing constraints. The Einstein radius for a Planck-mass lens is \sim 10^{-7} m at galactic distances—ten million times smaller than the wavelength of visible light. Microlensing by individual remnants is completely unobservable. Remnants are far below the mass range constrained by OGLE, MACHO, and HSC surveys.· A demonstration that structure formation remains standard. Remnants are non-relativistic at all epochs after the Planck time, with free-streaming length \sim \ell_P. They behave as perfectly cold dark matter, producing no suppression of small-scale structure and matching all \LambdaCDM predictions.· A clear falsifiability criterion. The model is falsified if any of the following occur: a statistically significant WIMP signal in direct detection, a gamma-ray line or excess from dark matter annihilation, an axion signal in a haloscope, an X-ray line from sterile neutrino decay, or missing energy signatures at colliders. Continued null results are consistent with the model and explain why decades of searches have found nothing. Why this matters: Planck-mass dark matter is the most economical dark matter candidate. It requires no new particles, no new symmetries, and no new physics beyond the discrete structure of spacetime at the Planck scale. It predicts null results for all ongoing dark matter searches, consistent with current data. It is falsifiable: a single positive detection of a WIMP, axion, or sterile neutrino would rule it out. The most promising signature—gravitational wave echoes from mergers—is currently inaccessible but represents a definitive test of the model should technology ever reach Planckian frequencies. Until then, the model stands as the simplest explanation for the dark matter puzzle. Keywords: dark matter, Planck mass, black hole remnants, Planck-scale dark matter, gravitational wave echoes, direct detection, indirect detection, microlensing, structure formation, falsifiability, canvas model

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