The cover art is mostly what I remember.
There was a being in a space suit coming through an archway (similar to a metal detector); the being resembled a gorilla.
It was carrying its helmet under one arm. The plot as I recall had to do with a Transporter, each time the transporter was used the user would come out the other end in a somewhat different version of their world. The longer the distance traveled the more distorted the version of their world was at the other end.