Microscopic primordial black holes as macroscopic dark matter from large extra dimensions

We study the coupled cosmological evolution of primordial black holes (PBHs) and radiation in the Arkani-Hamed-Dimopoulos-Dvali (ADD) framework with $n$ large extra dimensions and a fundamental gravity scale $M_\star$ at the TeV scale. For PBHs with horizon radius smaller than the compactification scale, the higher-dimensional geometry implies a larger horizon size at fixed mass and therefore a suppressed Hawking temperature. As a result, radiation accretion can overcome evaporation in the early Universe and drive a ``runaway'' phase of rapid mass growth. By numerically solving the coupled mass and energy-density evolution equations, we show that for $n \geq 2$ initially microscopic PBHs with initial mass $M_i \gtrsim 10^{12}\,$g can grow by many orders of magnitude and potentially reach macroscopic, even solar-mass, scales by matter-radiation equality. We determine the critical initial abundance $\beta_{\rm crit}$ required for PBHs to account for the observed dark matter density and find that extra dimensions dramatically lower this threshold, allowing viable scenarios with $\beta_{\rm crit}\sim 10^{-44}$. This identifies a previously unexplored region of parameter space in which the dark matter abundance is achieved through dynamical mass growth rather than large initial collapse fractions.