P-V Criticality of the FRW Universe in the Novel 4D Gauss-Bonnet Gravity

In this paper, we study the thermodynamics especially the $P$-$V$ criticality of the Friedmann-Robertson-Walker (FRW) universe in the novel 4-dimensional Gauss-Bonnet gravity, where we define the thermodynamic pressure $P$ from the cosmological constant $\Lambda$ as $P=-\frac{\Lambda}{8\pi}$. We obtain the first law of thermodynamics and equation of state of the FRW universe. We find that, if the Gauss-Bonnet coupling constant $\alpha$ is positive, there is no $P$-$V$ phase transition. If $\alpha$ is negative, there are $P$-$V$ phase transitions and critical behaviors within $-1/3\leq\omega\leq1/3$. Particularly, there are two critical points of the $P$-$V$ criticality in the case $\alpha<0,~-1/3<\omega<1/3$. We investigate these $P$-$V$ criticality around the critical points, and calculate the critical exponents. We find that these critical exponents in the $-1/3<\omega\leq1/3$ case are consistent with those in the mean field theory, and hence satisfy the scaling laws.