  We study theoretically the Raman spectrum of the rotated double-layer
graphene, consisting of two graphene layers rotated with respect to each other
by an arbitrary angle \theta. We find a relatively simple dependence of the
Raman G peak intensity on the angle \theta. On the other hand, the Raman 2D
peak position, intensity, and width show a much more complicated dependence on
the angle \theta. We account for all of these effects, including dependence on
the incoming photon energy, in good agreement with the experimental data. We
find that it is sufficient to include the interaction between the graphene
layers on the electronic degrees of freedom (resulting in the occurrence of van
Hove singularities in the density of states). We assume that the phonon degrees
of freedom are unaffected by the interaction between the layers. Furthermore,
we decompose the Raman 2D peak into two components having very different
linewidths; these widths are almost independent of the angle \theta. The change
in the intensity and the peak position of one of these two components gives
insight into the dependence of the overall Raman 2D peak features as a function
of the angle \theta. Additionally, we show regions in the phonon spectrum
giving rise to the Raman 2D peak signal. This work provides an insight into the
interplay between the mechanical degree of freedom (angle \theta) and the
electronic degrees of freedom (singularities in the density of states) in
rotated double-layer graphene. Additionally, this work provides a way to
establish experimentally the value of the rotation angle \theta using Raman
spectroscopy measurement. This procedure becomes even more robust if one
repeats the Raman spectroscopy measurement with a different incoming photon
energy.
