The causal tail of stochastic gravitational waves can be used to probe the
energy density in free streaming relativistic species as well as measure
$g_\star(T)$ and beta functions $\beta(T)$ as a function of temperature. In the
event of the discovery of loud stochastic gravitational waves, we demonstrate
that LISA can measure the free streaming fraction of the universe down to the
the $10^{-3}$ level, 100 times more sensitive than current constraints.
Additionally, it would be sensitive to $\mathcal{O}(1)$ deviations of $g_\star$
and the QCD $\beta$ function from their Standard Model value at temperatures
$\sim 10^5$ GeV. In this case, many motivated models such as split SUSY and
other solutions to the Electroweak Hierarchy problem would be tested. Future
detectors, such as DECIGO, would be 100 times more sensitive than LISA to these
effects and be capable of testing other motivated scenarios such as WIMPs and
axions. The amazing prospect of using precision gravitational wave measurements
to test such well motivated theories provides a benchmark to aim for when
developing a precise understanding of the gravitational wave spectrum both
experimentally and theoretically.
