Research on meditation in general is substantial, and more modest than its popular reputation. A systematic review by Goyal and colleagues (2014, JAMA Internal Medicine) found moderate evidence that meditation programmes improve anxiety, depression and pain, and weaker or insufficient evidence for other outcomes, including attention.
Slow breathing at around six breaths per minute, used in resonance frequency biofeedback (Lehrer and Gevirtz, 2014), has moderate evidence for increasing heart rate variability, a marker of parasympathetic activity. Studies of meditative states also report changes in alpha and theta brain activity (Cahn and Polich, 2006).
Cosmic Meditation itself has not been tested in controlled trials. The honest position is this: its breathing and attention components rest on reasonable evidence, and its benefits for a specific leader are something to track with your own data, sleep, resting heart rate and HRV, rather than to take on trust.