$^{12}$C+$^{12}$C fusion reactions are essential for the evolution of massive stars and explosive astrophysical phenomena. However, reproducing the stellar environment is challenging in accelerator experiments, and theoretically, it is also difficult to handle because it is a multi-nucleon rearrangement reaction.
We show that a microscopic model treats the dominant decay channels, $\alpha+^{20}$Ne and $p+^{23}$Na, in addition to $^{12}$C+$^{12}$C and that $^{12}$C+$^{12}$C molecular resonance states exist near the $^{12}$C+$^{12}$C threshold. They increase the $^{12}$C+$^{12}$C fusion reaction rate in the astrophysical environment. The density functional dependence of the fusion reaction rate is also discussed as an uncertainty of the theory.