New examples of $G_2$-instantons on ${\mathbb{R}}^4\times S^3$

We study the existence of $\text{SU}(2{)}^2$-invariant $G_2$-instantons on ${\mathbb{R}}^4\times S^3$ with the coclosed $G_2$-structures found on [arXiv:2209.02761]. We find an explicit 1-parameter family of $\text{SU}(2{)}^3$-invariant $G_2$-instantons on the trivial bundle on ${\mathbb{R}}^4\times S^3$ and study its ‘‘bubbling’’ behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined $\text{SU}(2{)}^2$-invariant $G_2$-instantons.