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

TL;DR

The paper investigates how string-loop corrections to the Kähler potential affect moduli stabilization in type IIB compactifications and the resulting cosmological relics. It develops the effective potential with loop-corrected Kähler terms and D-term uplifts, derives moduli-mass hierarchies controlled by flux scales $\mathcal{W}_0$, and shows off-diagonal kinetic-term corrections significantly alter moduli-axion couplings. The authors compute dark-radiation predictions through moduli decays to axions, obtaining $\Delta N_{eff}$ well below bounds in two flux regimes, and propose non-thermal dark-matter production via heavy-modulus decays, with annihilation and branching scenarios yielding DM masses from GeV to $\sim 10^{12}$ GeV. The work links high-energy string corrections to observable cosmology, offering a framework to probe the dark radiation–dark matter connection and guiding future studies in more complex Calabi–Yau geometries and inflationary embeddings.

Abstract

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 K{ä}hler 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 $ΔN_{eff}$ remains below the respective bounds. Finally, a non-thermal 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 $10^{12}\; GeV$.

Figures (4)

• Figure 1: Plot of potential \ref{['Potential']}$\xi=5$, $|\mathcal{W}_0|=(1,10^{-4})$, $d=(4\times 10^{-4},4 \times 10^{-12})$ and $\eta=-0.9$.
• Figure 2: Left: Plot of the allowed $d$ values for the first case of \ref{['casesmasses']}. The fluxes are set at $|\mathcal{W}_0|= 1$. Right: Plot of the allowed $d$ values for the second case of \ref{['casesmasses']}. The fluxes are set at $|\mathcal{W}_0|= 10^{-3}$.
• Figure 3: Plots for the first numerical example of Table 1. Upper left plot depicts the product of asymmetry with branching ratio with respect to the scale of fluxes, while the rest of the plots shows the required reheating temperature and the scale of the dark matter mass. In the lower right plot, the yellow horizontal lines characterize the allowed values for the parameter $q$ in order to have dS vacuum for the effective potential.
• Figure 4: Dark matter mass with respect to the ratio of cross sections. The horizontal line represents the lower bound on the allowed mass. The parameters of the first numerical example of Table 3. are used for this plot.