Were Claudius and Gertrude having an affair before old Hamlet's death?

Do you think that Claudius and Gertrude were doing the "beast with two backs" (to quote Iago) before old Hamlet's murder?

I know there's no textural evidence within the play itself, but if I were directing the play, I'd consider Gertrude's behavior after her hubby's death a clue. Here are my purely speculative thoughts, minus any actual facts in the play:

Gertrude is likely a couple decades younger than Hamlet per. We're told his beard was grizzled and that he'd nap in the garden daily. He's obviously no longer the hero who "smote the sledded Polack on the ice" and is now in his semi-retirement.

I'm not saying that Gertrude was a child bride, but they were married at least 25-30 years, and that time period can be modest if you're starting out at 22 years old, substantial if you're starting at 40. They had only one child and that's uncommon for a royal couple.

I'm just speculating for sheer entertainment value here, but I'd think the physical passion had gone from the marriage and what remained was a genuine affection but not much adventure between the sheets.

Along comes Claudius, handsome, urbane, a boon companion. And smarmy. He'd easily find the energy to prey upon Gertrude, and after a few years' effort, she might have been attracted to him.

Of course Claudius is jealous of his brother but I also think his affection for Gertrude is genuine. He never tosses her under the bus like he does Laertes.

I've also read speculation that Claudius is Hamlet's true father. I don't think that's a given, necessarily. He bears young Hamlet a grudging affection, mostly out of his feelings for Gertrude. After all, he "inherits" Hamlet after Hamlet's grown and in grad school. But we know that he fears him (we're told that Hamlet bears lots of positive public admiration) and there's some legitimate argument as to whether Claudius was the rightful heir to the throne in the first place.

So, do you think that Gertrude was already involved with Claudius prior to hubby's death?

I dunno. It's a fun topic to entertain ourselves with, I think.

I think the answer to this is yes because it provides Claudius with a motive for murder, he knows with old Hamlet out of the way the crown is his (as young Hamlet says - I'm quoting from memory - Claudius comes between him and his hopes, which is taken to mean that Hamlet had expected to become king upon his father's death).

Not necessarily. I think Gertrude may be utterly seduced, entranced and thrilled to be doing something a little bit bad after her many years of wifely fealty. John Updike had another idea, which he detailed in his fun book, Gertrude and Claudius.