New universal property of cosmological gravitational wave anisotropies

The anisotropies of the stochastic gravitational wave background, as produced in the early phases of cosmological evolution, can act as a key probe of the primordial universe particle content. We point out a new universal property of gravitational wave anisotropies of cosmological origin: for adiabatic initial conditions, their angular power spectrum is insensitive to the equation of state of the cosmic fluid driving the expansion before big-bang nucleosynthesis. Any deviation from this universal behaviour points to the presence of non-adiabatic sources of primordial fluctuations. Such scenarios can be tested by gravitational wave detectors operating at a frequency range which is fully complementary to CMB experiments. In this work we prove this general result, and we illustrate its consequences for a representative realisation of initial conditions based on the curvaton scenario. In the case of the simplest curvaton setup, we also find a significant cross-correlation between gravitational wave anisotropies and the CMB temperature fluctuations. There is a fourfold enhancement vis-\`{a}-vis the purely adiabatic scenario. We discuss the implications of our findings for identifying the origin of the (cosmological) gravitational wave background when, as is often the case, this cannot be determined solely on the basis of its spectral shape.