Phase 2 Trial of Tributyrin in People With Parkinson's Disease and Cognitive Impairments

The goal of this clinical trial is to learn if taking a tributyrin supplement works to improve memory and thinking and walking and balance in adults with Parkinson disease Parkinson disease dementia. It will also learn about the safety of tributyrin supplementation. The main questions it aims to answer are: 1. Does tributyrin improve memory/thinking test scores and walking/balance ability? 2. What medical problems do participants have when taking tributyrin? Researchers will compare tributyrin to a placebo (a look-alike substance that contains no drug) to see if tributyrin works to treat Parkinson disease symptoms. Participants will: 1. Take tributyrin 3 times a day for 80-100 days 2. Complete motor and cognitive testing at the clinic before and after the supplementation period 3. Complete brain imaging (MRI scans and PET scans) before and after the supplementation period.