Absence of the Lavrentiev phenomenon for a general class of parabolic double phase problems

In this paper, we prove the absence of the Lavrentiev phenomenon for a general class of parabolic double phase functionals with Orlicz growth. The energy density is given by $$ G(|Dw|)+a(x,t)H(|Dw|), $$ where $G$ and $H$ are Young functions satisfying the $Δ_2$ and $\nabla_2$ conditions with $G\prec