Which of the following basic grooming tools is essential for maintaining a show cavy's coat?

A slicker brush is essential for maintaining a show cavy's coat because it is specifically designed to remove loose hair and debris while also helping to detangle any mats or knots in the fur. The pin-like bristles can penetrate into the dense fur of a cavy, lifting dirt and fluffing up the coat, which is crucial for achieving a well-groomed appearance prior to a show. Regular use of a slicker brush ensures that the cavy's coat remains healthy and shiny, which is important for presentation.

The other tools listed are less suitable for this purpose. For example, a vacuum cleaner is primarily used for cleaning spaces rather than personal grooming. While a sponge can be useful for spot cleaning or bathing, it does not effectively groom a cavy’s coat. A rake, which is typically used for larger animals or different types of fur, may not be appropriate for the delicate coat of a cavy. Thus, the slicker brush stands out as the fundamental tool for maintaining a show-worthy coat.