The American international rejoined the club last month on a short-term deal after fellow lock JP du Preez was ruled out for the season with a knee injury. Peterson left Glasgow four and a half years ago and spent some time in France with Bordeaux before a successful few years with Newcastle Falcons. Peterson left Tyneside at the end of last season with the intention of finding a club closer to family in Sydney but grabbed the opportunity to return to the Warriors and link up with head coach Franco Smith.
"It's definitely a stronger team," said Peterson The Scotsman. "There's a lot more continuity, and I think there's a lot of really good young players coming through too. When I was here before it was kind of a bit of an old guard, with a hard edge. Now, there's a bit more attacking flair, a bit more exciting rugby and still that underlying hard edge which Franco brings with his South African heritage. It's a really good team, and it's exciting to be a part of and I'm really enjoying it so far."
Peterson has already helped the Warriors beat two of the URC's top teams - Leinster and the Stormers - even if they were missing their World Cup players. Peterson's deal with Glasgow runs until January and he is unsure what will happen beyond that.
"That's not really up to me," he said. "The whole idea was to come over and play some rugby at a high level. If there is an opportunity to stay then I'm sure that'll come up in the next month or two. Like I said, I'm just here to put my foot in the door and play the best I can and help an organisation I love and be in a really good position at the start of the season. And this being a World Cup season, if you can make a really good start without your World Cup players against some top teams then it can help carry you through the rest of the season."