String loop origin for dark radiation and superheavy dark matter in type IIB compactifications

In this article, we study the significance of string loop corrections, in a perturbative moduli stabilization scenario, focusing on their role in unraveling the origin of dark radiation in the late cosmological epoch and their correlation to dark matter. More specifically, a detailed analysis is provided in which the mass hierarchy of the normalized fields in the Kähler moduli sector is determined by the scales of the integer fluxes and the quantum corrections. Furthermore, we compute the previously underestimated contributions to the decay rates of moduli to axions, which behave as dark radiation, highlighting their connection to the aforementioned higher-order corrections. Two contrasting reheating scenarios (low scale and high scale) are provided, depending on the decay rate of the longest-lived particle into the Standard Model degrees of freedom through a Giudice-Masiero mechanism, while the effective number of neutrino species <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:msub><a:mi>N</a:mi><a:mi>eff</a:mi></a:msub></a:math> remains below the respective bounds. Finally, a nonthermal dark matter scenario is proposed based on the decays of heavy scalar fields, where the main production mechanisms are investigated, leading to a dark matter candidate mass ranging from a few GeV up to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mn>10</d:mn><d:mn>12</d:mn></d:msup><d:mtext> </d:mtext><d:mtext> </d:mtext><d:mi>GeV</d:mi></d:math>.