“States of consciousness” are more about perception than they are about consciousness itself as defined by Vedanta. More often that not, scientific study of the nature of consciousness is studying something other than what Vedanta refers to when invoking the word “consciousness,” a unit of enduring existence, cognizance, and ecstasy.
In the scientific and philosophical community, consciousness is often conflated with various psychological and neuro-physical phenomena such that consciousness—first person subjective experiential reality itself—is completely eluded.
The focus of cognitive science is almost entirely on functional properties of the individual or mechanisms that relate to an individual’s operation. As such, these mechanisms can be explained in terms of how the organization of a physical system such as the brain allows it to react with the environment, process information, and generate behavior in appropriate ways. Such study focus for example on reportability, awareness, attention, intentionality, perception, wakefulness, and so on. The ontology of such psychological properties is not metaphysically baffling, and there is reason to believe that they could be explained in physical or functional terms.
Consciousness, however, as I am referring to it, is not a functional property or even individual qualitative experiences (qualia). It is the subjective existence in which these experiences manifest. As the International Dictionary of Psychology defines it, consciousness is “impossible to define except in terms that are unintelligible without a grasp of what consciousness means.” Thus with words we can only offer some calculation, and much of that as to what it is not, neti neti. It can only be defined in terms of itself because it is like nothing else, like no “thing.” Thus the method for understanding it lies not within the scope of modern science.
That said, we have to rely upon first person reporting, which arguably should not be excluded from scientific inquiry. But this is then where science and meditation meet. However, first person experience of consciousness proper as described by mystics should result in observable evidence in the physical and mental dimensions of the adept doing the reporting/meditating. This would take the form of the ability to harness the mind and human passions, which in and of itself is arguably evidence of the supernatural, an observable supernatural.