Dark Radiation in Anisotropic LARGE Volume Compactifications

TL;DR

The paper investigates dark radiation in an extended LARGE Volume Scenario with two bulk moduli, where the lightest modulus is a transverse direction and the Standard Model sits on D3 branes at a singularity to achieve sequestered soft terms. It finds that decays of the lightest modulus to axions overwhelmingly dominate over visible-sector decays, leading to an enormous predicted $\Delta N_{\rm eff}$ (over $3\times 10^4$), thereby excluding this fibred two-modulus, sequestered LVS as a cosmological model. The authors also discuss an anisotropic alternative with visible matter on D7 branes that could yield a smaller $\Delta N_{\rm eff}$ (around 0.6 for $Z=1$), but this approach faces substantial theoretical obstacles, including potential poly-instanton corrections and RG stability concerns. They note that upcoming or alternative cosmological hints (e.g., B-mode measurements) could shift the inferred $N_{\rm eff}$ and potentially affect the viability of minimal LVS, but the main conclusion remains: the two-modulus fibred LVS with sequestering is not compatible with current dark radiation constraints.

Abstract

Dark radiation is a compelling extension to $Λ$CDM: current experimental results hint at $ΔN_{\rm eff} \gtrsim 0.5$, which is increased to $ΔN_{\rm eff} \simeq 1$ if the recent BICEP2 results are included. In recent years dark radiation has been considered in the context of string theory models such as the LARGE Volume Scenario of type IIB string theory, forging a link between present-day cosmological observations and models of physics at the Planck scale. In this paper I consider an extension of the LARGE Volume Scenario in which the bulk volume is stabilised by two moduli instead of one. Consequently, the lightest modulus no longer corresponds to the compactification volume but instead to a transverse direction in the bulk geometry. I focus on scenarios in which sequestering of soft masses is achieved by localising the Standard Model on D3 branes at a singularity. The fraction of dark radiation produced in such models vastly exceeds experimental bounds, ruling out the sequestered LARGE Volume Scenario with two bulk moduli as a model of the early Universe.