  Dark radiation is a compelling extension to $\Lambda$CDM: current
experimental results hint at $\Delta N_{\rm eff} \gtrsim 0.5$, which is
increased to $\Delta N_{\rm eff} \simeq 1$ 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.
