Roleplaying a pet?

I have a friend potentially interested in playing, and he wanted to know if he'd be allowed to role play a tiger as a pet, of course with this tiger in question carrying no applicable IG abilities or relevance, merely existing as an extension of his own character, most likely for mere comical value.

Would he be carrying around a physical representation (phys rep) of the tiger?

To the best of my knowledge, no. He'd most likely just refer to it and occasionally pretend to talk to it and give it nonsense orders to do something purely imaginary and irrelevant like doing invisible back flips. But is there a difference if he brings a phys rep?

If he is role playing it as an imaginary friend type of deal, there's no problem.

Having a phys rep as a pet on the other hand would make it more difficult to accomplish and currently there are no rules on pets in game.