I'm not in TN, but I can tell you we've definitely got cougars/mountain lions/pumas (we call the mountain lions here) in Kansas. First of all, they make a VERY distinctive sound. The first time I heard her, I thought at first it was a woman screaming. Grabbed a shotgun, threw the dogs in the back end of the truck, and flew down the 1/2 mile driveway not sure what I was going to do but dang sure someone was in need of help. Nope... no one anywhere around. Then I got to thinking, that was such a strange sound. Not quite like screaming. More like yelling. No, more like yowling. Yeah, that's it... sort of like a cat. Holy cow, that must have been a really serious cat. Nah, couldn't have been...
Got online and searched "mountain lion sounds" and there it was. Unmistakeable. A 150 pound cat in heat... Oh wow. In heat means there's a 150 pound female AND bigger males in these here woods! (I'm in the middle of 25 acres of woods, a few miles from a public wildlife/hunting area and reservoir). Next day, I found her tracks and photographed them. Approx. 3-3/4" across. Chasing the deer tracks.
Since then I've heard her quite a few times, and several different types of sounds. Always too close to the house for comfort, given that I have little kids here and dogs, not to mention the poultry. But we've never seen her except once, just at dusk, when I had 13 young kids here for a bonfire who kept running back and forth along the trail, house to campfire circle. My own daughter is certain she saw it. I thought to myself "running kids look like running mice to a cat..." So I brought everyone in the house and called it quits on the marshmallows.
Of course, "there are no big cats in Kansas." Just ask the Game Commission