This is, at least potentially, a very complicated, philosophical question if you want to answer it accurately. There is a practical side to the answer, however. The initial difficulty with the question is how to define the word “love”. Love is an emotional and mental state. There are different kinds of love. You might love food and you might love somebody: these are different forms of love.
And love means different things to different people. It is, arguably, an abused word in the English language. But let’s for the sake of this discussion refer to love as an emotional state of strong attraction and personal attachment to another living creature.
The next difficulty is deciding whether domestic cats have higher level emotions. It is agreed that cats have emotions but do they feel the emotion of love? Scientists would generally agree that cats feel affection towards other cats. You can see it in their behaviour. Within a colony of cats you will see identifiable “preferred associates” (friendships). These are cats which are found close to each other more often than they are with other cats. Cats who are “preferred associates” engage in what is called allogrooming (licking each other) and allorubbing which is when two cats rub their heads, bodies and tails against each other. This is similar to the human hug. They might sleep next to another cat. The tail is sometimes used to stroke another cat. Sometimes cats may intertwine their tails. This appears to be a form of social bonding. Physical contact facilitates and maintains friendship and a social bond. Body scent is exchanged during allorubbing.
These forms of behaviour are indicative of mutual affection. It should be said therefore that cats feel affection for each other.
As for humans, it is argued that cats relate to their human owner as if they are surrogate mothers and therefore they relate to humans as domestic cats although they might not physically recognise us as domestic cats.
Therefore, it could be argued that cats are able to be affectionate towards humans. In fact, this is plainly evident in domestic cat behaviour when interacting with their human owner. Their behavior is as described above between cats. Domestic cats lick us, they rub against us and scent exchange, they play with us, they touch noses with us which is a friendly greeting behaviour. Therefore, domestic cats form relationships with their human companion which show signs of a strong affection towards us.
Therefore, on the basis that love is a form of strong affection towards another being then it could be argued that cats can love us.
The question then follows as to whether your domestic cat loves you. This depends upon the relationship. In general, humans lead the relationship. If a human makes their cat’s home emotionally very warm, friendly and loving then it is perfectly reasonable to make the assumption that the cat will respond affectionately and demonstrate a form of love towards their owner. But cats are individuals. They vary in their ability to be affectionate and to demonstrate it. Putting that variation to one side for moment, the answer to the question in the title is, yes, provided that the human cat guardian loves her cat and demonstrates that to her cat through affectionate interaction and the creation of an enriched and loving environment.