Cosmological Perturbations in Unimodular Gravity
  We study cosmological perturbation theory within the framework of unimodular
gravity. We show that the Lagrangian constraint on the determinant of the
metric required by unimodular gravity leads to an extra constraint on the gauge
freedom of the metric perturbations. Although the main equation of motion for
the gravitational potential remains the same, the shift variable, which is
gauge artifact in General Relativity, cannot be set to zero in unimodular
gravity. This non-vanishing shift variable affects the propagation of photons
throughout the cosmological evolution and therefore modifies the Sachs-Wolfe
relation between the relativistic gravitational potential and the microwave
temperature anisotropies. However, for adiabatic fluctuations the difference
between the result in General Relativity and unimodular gravity is suppressed
on large angular scales. Thus, no strong constraints on the theory can be
derived.
