This page is in by no means designed to give the comprehensive list of scientific studies that are going on in the field of Sleep, Meditation, consciousness etc. but to highlight the incident that probably could be the turning point in neuroscience and to validate how one's life can be altered by conscious & consistent practice of a time tested process like Yoga Nidra.
The first Scientific Study on Yoga Nidra & other processes
Elmer and Alyce Green of the Menninger Foundation in the US brought out the efficacy of Yoga practices using the well-equipped laboratory designed to investigate voluntary control of psychophysiological processes. Swami Rama met them in 1971and after listening to their work, He decided Menninger Foundation is the right place to realize his Master Bengali Baba's ambition to document scientifically the abilities manifested by a masterful practice of Yoga.
One of these involved a demonstration of a Yogic practice called Yoga-nidrā, conscious entry into deep, non-REM, delta wave sleep. He was connected to an electroencephalogram and Swāmī Rāma then entered into a delta wave state where he was creating delta waves almost exclusively.
During the period of the experiment, two technicians were quietly talking in the next room. When he resumed ordinary waking awareness after the experiment, Swāmī Rāma recounted that conversation verbatim. This illustrated the criterion he articulated that in addition to being focused on his inward state, he also remained aware of his external environment. There is no current explanation in neuroscience for his ability to do this.
Swāmī Rāma's close disciple Swāmī Veda Bhāratī set out to replicate his master's experiments at the Institute for Noetic Sciences in California in 2006 under the experimental leadership of Dean Radin Ph.D. During these trials, in addition to duplicating Swami Rama's experiment, Radin accidentally discovered that Swāmī Veda remained almost perpetually in a state of Yoga-nidrā, his brain producing theta and delta waves even with his eyes open, talking and moving around (Bhāratī, 2006, p. 69).
Again, there is no neurological explanation for the possibility of this. Swāmī Veda subsequently published a small book about his personal experiences and experiments with yoga-nidrā, which actually began from the age of three, even though he did not recognize it as such at the time (Bhāratī, 2014).