  The Stochastic Gravitational-Wave Background (SGWB) is expected to be a key
observable for Gravitational-Wave (GW) interferometry. Its detection will open
a new window on early Universe cosmology, on the astrophysics of compact
objects and, as shown in this Letter, on the particle physics content of the
Universe. In this Letter we show that, besides their effects on the Cosmic
Microwave Background (CMB) and on Large Scale Structure (LSS), relativistic
particles in the early Universe leave a clear imprint on the anisotropies of
the SGWB. In particular we show that a change in the number of decoupled
relativistic particles shifts the angular power spectrum of the SGWB, as both
the Sachs-Wolfe (SW) and the Integrated Sachs-Wolfe (ISW) terms are affected.
Being very large-angle effects, these lead to new testable predictions for
future GW interferometers.
