I googled this question during the weekend and there were no really conclusive answers, though many people, vets and animal psychologists had their opinions.
So let me add my own personal answer to the question.
This is Pebbles (AKA Fluffystuff).
Outgoing, playful, enjoys her food, not a talker but leaves you in no doubt as to her feelings about anything. Loves to be outside no matter the weather. I adopted her and her sister Ebony (AKA Black Cat) together, sixteen or so years ago, from a backyard breeder.
Sadly Black Cat died of various ailments a few weeks ago, and if Fluffy isn’t grieving then I don’t really have an answer for the way she is behaving. I left Black cat’s bed where it was for a few days after she passed, thinking it may be easier if everything didn’t change quite so fast for Fluffy. However, the morning after there was no Black Cat in her bed, I woke to find that Fluffy had pulled out her bed and disrupted all of the bedding , clearly confused as to where her sister was. I removed the bed and bedding at this point.
Meal times were always spent together. Black cat, being the talker, would come and find me (Fluffy in tow, simply observing quietly), and make a hustle in whatever way she could to get my attention. We would all three of us proceed to the kitchen where I would do my duty as cat mum, and provide tasty meals. They had designated places on the mat where the food bowls are kept. Having all the space to herself has made no difference to Fluffy, she goes to her place and if the bowl is not where it should be, she is confused again.
Fluffy has become a talker, looking at me and miaowing, which wasn’t really a feature of her personality before. She is staying inside the house most of the day, again not really like her old self at all. She is more clingy than before, and sits almost on top of me in the evenings when we are watching tv. She follows me around in the mornings for about half an hour before going to her daybed and staying there all day. This is not how she was before Black cat’s passing.
Clearly my girl is missing her sister and so am I. I have heeded some of the advice in the articles I read, spending more time with Fluffy, I am talking to her but trying not to indulge the behaviour so that it becomes habit.
Do I think pets/cats grieve? Oh yes I do. In fact I know they do. It’s quite heartbreaking because I can’t change the situation, I can’t explain. I hope that time is a healer for cats too.