Lattice QCD in curved spacetimes

We formulate the lattice QCD simulation with background classical gravitational fields. This formulation enables us to study nonperturbative aspects of quantum phenomena in curved spacetimes from the first principles. As the first application, we perform the simulation with the Friedmann-Lemaítre-Robertson-Walker metric and analyze particle production in the expanding universe.

Figure 1

Expanding lattice.

Figure 2

$\tau$-dependence of the total fermion number $N_I$ and the fermion number density $n_I$ with $a{H}_I=0.03$.

Figure 3

$H_I$-dependence of the total fermion number $N_I$ and the fermion number density $n_I$ at $\tau /a=10$.