Voldemort's nasty, pallid, nose-less presence hovers over the first part of the play in the form of rumor and dreams. Harry often has Voldemort-themed nightmares (Voldemares?) and rumors swirl that Voldemort is Scorpius' father.
And Harry—whose tact game is not of point in this play—even brings up the rumor to Draco's face.
HARRY: Are you sure… are you really sure he's yours, Draco? (2.13.21)
Considering how broken Draco is when Harry says this, it's like watching Harry Potter kick a puppy.
But this isn't just cruel of Harry—it's hypocritical, too. Harry wishes Albus wasn't his son, yet he maligns Draco for believing in his own son. Harry isn't just being mean for the sake of meanness, though. He's also in some serious angst.
In one meaningful dream, Voldemort says to Harry:
VOLDEMORT: I smell guilt, there is a stench of guilt upon the air. (3.12.13)
For someone without a shnoz, Voldemort's got the olfactory skills of a Parisian perfumer.
But what's Harry feeling so guilty about? Surprising, it's not for his paternal failings. It's because he's using so much of his mental real estate for thoughts about Moldy Voldy. He knows that Voldemort will only really be dead and gone when the memory of Voldemort has faded into obscurity…but it's really hard for Harry to silence his Voldy-thoughts.
HARRY: The part of me that was Voldemort died a long time ago, but it wasn't enough to be physically rid of him—I had to be mentally rid of him. And that—is a lot to learn for a forty-year-old man.
Yup. It takes Harry until middle age to realize what Sarah Williams from The Labyrinth learns at age fifteen—that telling a threat "You have no power over me" is the best way to free yourself completely.