Imprint of relativistic particles on the anisotropies of the stochastic gravitational-wave background

The stochastic gravitational-wave background (SGWB) is expected to be a key observable for gravitational-wave interferometry. Its detection will open a new window on early Universe cosmology, on the astrophysics of compact objects, and, as shown in this paper, on the particle physics content of the Universe. In this article we show that, besides their effects on the cosmic microwave background and on large-scale structure, 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 and the integrated Sachs-Wolfe terms are affected. Being very large-angle effects, these lead to new testable predictions for future gravitational-wave interferometers.

Figure 1

SW contribution to the angular power spectrum of the SGWB. We can see that by increasing $f_{\mathrm{dec}}({\eta }_i)$ we are decreasing more and more the amplitude of the angular power spectrum. For values of $f_{\mathrm{dec}}({\eta }_i)$ close to 1 we observe a saturation.

Figure 2

ISW contribution to ${\tilde{C}}_{\ell ,S}$. We observe a bump at large $\ell$ due to the fact that the potentials at large $\ell$ have the maximum variation.

Figure 3

Total scalar contribution to the SGWB angular power spectrum, sum of the SW and the ISW terms.