A cat with an arched back is an archetype of danger or fear. It's true that a cat's back is arched when the cat is in a defensive position. But you'll know your cat is feeling scared when that goes along with other body language, such as ears back, hissing, and a puffed-out tail. When your cat's back is raised when you're petting her, that's a good sign! It means your cat loves what you're doing.
Cat behavior and body language
When you're petting your cat, they may react with a variety of body language. They may purr, of course, but they may also roll over on their back (or not), arch their back (or not), rub their face on your hand (or not), nibble on your hand (or not) . . . well, you get the idea. Cat owners know cat behavior varies quite a bit.
The Tufts Catnip blog, of the Cummings School of Veterinary Medicine at Tufts University, explains that cats have scent glands on their chins, ears, neck, and the sides of their faces. When cats rub parts of their body on your hand or other surfaces, it's called bunting. Bunting leaves a scent mark and is done to communicate their presence to other cats, mark their territory, and deposit their scent so that their home feels more familiar. They say that bunting is also a sign of affection toward their cat owners.
Cats could be arching their back when you pet them as a just-waking-up sleepy stretch. Some cats also like having their back touched, so they may be trying to encourage you to scratch where they like it: on the base of their tail or the back of their head.
Cat "elevator butt"
The non-scientific term that some people use when cats raise their backs and butts when you pet them is "cat elevator butt." Animal Path says this is a clear sign that a cat trusts and appreciates the person who is petting them and that it's a good sign they like what you're doing. A cat who raises her back is also lifting her rear, which makes her vulnerable. She wouldn't be likely to do that if she didn't feel safe.
Cat Health says that when a cat raises its back or hindquarters, it's because of an instinct that they learned when they were kittens. Their moms had to lick and clean them before they could do it for themselves. When cats are stimulated in their back and hind-end area, it makes them feel like they used to feel when their mothers groomed them.
There are a lot of nerve endings in a cat's back and base of the tail, so raising their back could simply be a way to get more of the good feeling that they like, and keep you from moving your hand away. Cat Health says the abundance of nerves can mean that the sensation of being petted on their backs is like tickling; in other words it can be too much. This is why some cats love the base of their tail scratched and some don't.
A cat's body language will generally let you know if they like what you are doing or not. Cat owners know that a cat's back and the base of their tail is generally sensitive, with a lot of nerve endings. Raising their lower back and purring when you pet them is a good sign that your cat loves what you are doing. If they move away or roll over when you're doing it, they may not like it. The sides of a cat's face have scent glands, so they could be arching their lower back to get into a better position for leaving a scent mark on you.