Upper tail large deviations of regular subgraph counts in sparse random regular graphs

For a $Δ$-regular connected graph $H$ we obtain the upper tail large deviations speed and rate function for the number of copies of $H$ in $\mathbb{G}_n^d$, a random $d$-regular graph on $n$ vertices, in the regime $np^{Δ/2} \gg (\log n)^{1/(v_H-2)}$ and $p \ll 1$, where $p:=d/n$ and $v_H$ is the nu