Does adding radiation make R² gravity exactly solvable?

R² gravity (which adds a curvature-squared term to Einstein's equations) is notoriously hard to solve, but adding a radiation component turns out to make the flat-universe version exactly integrable. The authors find the full general solution and show that a specific scalar field with a quartic potential mimics radiation perfectly, connecting the problem to a two-field model solvable by a conformal transformation. Exact solutions in modified gravity are rare and anchor numerical and observational work on early-universe inflation.