Dark Radiation predictions from general Large Volume Scenarios

TL;DR

The article investigates Dark Radiation (DR) in LVS compactifications, focusing on how different visible-sector realizations—sequestered (D3-branes at a singularity), geometric regime on D7-branes with D-terms or loops, non-perturbative stabilisation, and flavour-brane scenarios—affect the DR prediction via the modulus decay pattern. The authors compute ΔN_eff by comparing the lightest modulus decay rate into axions (DR) versus SM particles, showing that introducing tree-level couplings to SM gauge bosons or gauge bosons on flavour branes can suppress DR sufficiently to lie below current bounds, while non-perturbative stabilisation tends to tighten constraints. They derive explicit expressions for ΔN_eff in each setup, highlighting parameter regions (e.g., γ, z, N_f) where DR remains permissible, and discuss cosmological and astrophysical bounds (e.g., axion DM, isocurvature) that further shape the viable LVS landscape. The findings map how natural LVS variants can be compatible with present DR limits and identify clear directions—such as flavour-brane couplings or loop-stabilised geometries—for constructing DR-compatible string models, with future DR bound improvements capable of ruling out many simple realizations.

Abstract

Recent observations constrain the amount of Dark Radiation ($ΔN_{\rm eff}$) and may even hint towards a non-zero value of $ΔN_{\rm eff}$. It is by now well-known that this puts stringent constraints on the sequestered Large Volume Scenario (LVS), i.e. on LVS realisations with the Standard Model at a singularity. We go beyond this setting by considering LVS models where SM fields are realised on 7-branes in the geometric regime. As we argue, this naturally goes together with high-scale supersymmetry. The abundance of Dark Radiation is determined by the competition between the decay of the lightest modulus to axions, to the SM Higgs and to gauge fields. The latter decay channel avoids the most stringent constraints of the sequestered setting. Nevertheless, a rather robust prediction for a substantial amount of Dark Radiation can be made. This applies both to cases where the SM 4-cycles are stabilised by D-terms and are small "by accident" as well as to fibred models with the small cycles stabilised by loops. Furthermore, we analyse a closely related setting where the SM lives at a singularity but couples to the volume modulus through flavour branes. We conclude that some of the most natural LVS settings with natural values of model parameters lead to Dark Radiation predictions just below the present observational limits. Barring a discovery, rather modest improvements of present Dark Radiation bounds can rule out many of these most simple and generic variants of the LVS.

Figures (3)

• Figure 1: Contour plot of $\Delta N_{eff}$ vs. $z$ and $\gamma$ (defined in \ref{['Eq:gamma']}), with (a) $g_{*}=10.75$ and (b) $g_{*}=106.75$. While the predictions are valid for $\sin(2 \beta)=1$, they can be reinterpreted for general values of $\sin(2 \beta)$. To this end we define an effective parameter ${\tilde{z}}^2 = \sin^2(2 \beta) z^2$ and relabel $z \rightarrow \tilde{z}$ on the horizontal axis.
• Figure 2: Contour plot of $\Delta N_{eff}$ vs. $z$ and $\gamma$ (defined in \ref{['Eq:gamma2']}) for an LVS model with cycles stabilised by string loop corrections and D-terms, for (a) $g_{*}=10.75$ and (b) $g_{*}=106.75$. As before, the plots have been produced choosing $\sin (2\beta)=1$, but they can be reinterpreted for general values of $\sin(2 \beta)$. To this end we define an effective parameter ${\tilde{z}}^2 = \sin^2(2 \beta) z^2$ and relabel $z \rightarrow \tilde{z}$ on the horizontal axis.
• Figure 3: Contour plot of $\Delta N_{eff}$ vs. $z$ and the number of gauge bosons $N_{f}$ of the gauge theory living on the stack of flavour branes wrapping the bulk cycle. The plot was produced for $g_{*}=75.75$, corresponding to a reheating temperature $T_{d}\simeq 1$ GeV.