Can I go inside the Matrimandir at Auroville?

Not quite. The Matrimandir is a place for silent individual concentration, not a tourist site. Passes to the Viewing Point are free, and there's a free electric shuttle for people who need it. Concentration in the inner chamber has to be booked separately through matrimandir.org. Start at the Visitors Centre, where private and hired vehicles must park, and note that drones aren't allowed.