Cosmology of F-theory GUTs

TL;DR

The paper analyzes how F-theory GUTs accommodate cosmology, revealing that the axion supermultiplet and saxion dynamics can naturally reconcile gravitino dark matter with BBN and baryogenesis. The key mechanism is saxion-driven entropy production, which dilutes thermal relics and makes the relic abundance largely independent of the initial reheating temperature, while remaining compatible with leptogenesis and light-element abundances. The gravitino mass window of roughly 10–100 MeV emerges as a natural outcome, with decays of the NLSP addressing Li-7 overproduction concerns; the axion sector may also contribute to dark matter. Overall, the study links UV PQ-breaking dynamics to late-time cosmology, offering a robust and largely parameter-insensitive cosmological framework for F-theory GUTs and highlighting testable implications for saxion decay channels and NLSP phenomenology.

Abstract

In this paper we study the interplay between the recently proposed F-theory GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT models is very narrow, we find that F-theory GUTs beautifully satisfy most cosmological constraints without any further restrictions. The viability of the scenario hinges on the interplay between various components of the axion supermultiplet, which in F-theory GUTs is also responsible for breaking supersymmetry. In these models, the gravitino is the LSP and develops a mass by eating the axino mode. The radial component of the axion supermultiplet known as the saxion typically begins to oscillate in the early Universe, eventually coming to dominate the energy density. Its decay reheats the Universe to a temperature of ~ 1 GeV, igniting BBN and diluting all thermal relics such as the gravitino by a factor of ~ 10^(-4) - 10^(-5) such that gravitinos contribute a sizable component of the dark matter. In certain cases, non-thermally produced relics such as the axion, or gravitinos generated from the decay of the saxion can also contribute to the abundance of dark matter. Remarkably enough, this cosmological scenario turns out to be independent of the initial reheating temperature of the Universe. This is due to the fact that the initial oscillation temperature of the saxion coincides with the freeze out temperature for gravitinos in F-theory GUTs. We also find that saxion dilution is compatible with generating the desired baryon asymmetry from standard leptogenesis. Finally, the gravitino mass range in F-theory GUTs is 10-100 MeV, which interestingly coincides with the window of values required for the decay of the NLSP to solve the problem of Li(7) over-production.

Figures (5)

• Figure 1: Plot of the “ toy model” branching ratio of the saxion to axions and one (red) to five (black) species of MSSM fields as a function of $\Delta_{PQ}$ for fixed values of $f_{a}=10^{12}$ GeV and $m_{soft}=200$ GeV. For the decay to a representative MSSM field, we have used the crude estimate provided by equation (\ref{['GMSSM']}). This situation is somewhat idealized, because as $\Delta_{PQ}$ increases, the number of decay channels will increase, decreasing the overall branching ratio to axions.
• Figure 2: Plot of the branching ratio of the saxion to axions and one (red) to five (black) species of MSSM fields as a function of $\Delta_{PQ}$ for fixed values of $f_{a}=10^{12}$ GeV and $m_{soft}=500$ GeV. For the decay to a representative MSSM field, we have used the crude estimate provided by equation (\ref{['GMSSM']}). This situation is somewhat idealized, because as $\Delta_{PQ}$ increases, the number of decay channels will increase, decreasing the overall branching ratio to axions.
• Figure 3: Schematic plot of the dilution factor $D$ of the F-theory GUT saxion, the gravitino relic abundance in the absence of dilution, $\Omega_{3/2}^{(0)}h^{2}$ and the net relic abundance after taking account of the dilution factor of the saxion as a function of the initial reheating temperature $T_{RH}^{0}$. The graph of the dilution is given with respect to a scale distinct from that for the relic abundances. The plot depicts the special case where the freeze out temperature for the gravitino $T_{3/2}^{f}\sim T_{osc}^{s}$, the temperature at which the saxion begins to oscillate. When $T_{RH}^{0}$ is below $T^{s}_{D_{min}}$, there is no dilution factor $(D=1)$. In the special case where $T_{3/2}^{f}\sim T_{osc}^{s}$, for all values of $T_{RH}^{0}>T^{s}_{D_{min}}$, the total relic abundance of gravitinos is independent of $T_{RH}^{0}$. See figures \ref{['sketcha']} and \ref{['sketchb']} for schematic plots of scenarios where $T_{3/2}^{f}\neq T_{osc}^{s}$.
• Figure 4: Schematic plot of the dilution factor $D$ of the F-theory GUT saxion, the gravitino relic abundance in the absence of dilution, $\Omega_{3/2}^{(0)}h^{2}$ and the net relic abundance after taking account of the dilution factor of the saxion as a function of the initial reheating temperature $T_{RH}^{0}$. The graph of the dilution is given with respect to a scale distinct from that for the relic abundances. The plot depicts the case where the freeze out temperature for the gravitino $T_{3/2}^{f}>T_{osc}^{s}$, the temperature at which the saxion begins to oscillate. When $T_{RH}^{0}<T^{s}_{D_{min}}$, there is no dilution factor. Note that in this case, the total relic abundance of gravitinos increases for values of the initial reheating temperature such that $T_{osc}^{s}<T_{RH}^{0}<T_{3/2}^{f}$.
• Figure 5: Schematic plot of the dilution factor $D$ of the F-theory GUT saxion, the gravitino relic abundance in the absence of dilution, $\Omega_{3/2}^{(0)}h^{2}$ and the net relic abundance after taking account of the dilution factor of the saxion as a function of the initial reheating temperature $T_{RH}^{0}$. The graph of the dilution is given with respect to a scale distinct from that for the relic abundances. The plot depicts the case where the freeze out temperature for the gravitino $T_{3/2}^{f}<T_{osc}^{s}$, the temperature at which the saxion begins to oscillate. When $T_{RH}^{0}<T^{s}_{D_{min}}$, there is no dilution factor. Note that the total relic abundance of gravitinos decreases as $T_{RH}^{0}$ increases in the range $T_{3/2}^{f}<T_{RH}^{0}<T_{osc}^{s}$.