I'm afraid that a summary of my comments would be that science doesn't really know much about inner peace because human behavior is so complex and hard to study. But I can share lots of nice-sounding hypotheses.
Science is sometimes thought of as an uninspiring body of facts. I think of science as the process of learning more about what we don't know. Science is a careful, methodical process, just like UUism is a process, rather than a set of dogmas. Expecting clear answers from science in areas as complex as biology, or human behavior, or for goodness sake, to finding the "path to inner peace" is a daunting task. It is easier for me to talk about things we understand well, like how the sun and shadows move during the solstice.
Part of the complexity of studying human behavior is that it is very hard to distinguish cause and effect. Is the habit of gathering in religious communitites able to cause improvement in health, or is being healthy the sort of thing that causes or allows people to gather in religious communities?
I would say that you shouldn't expect clear evidence onthis subject, not much beyond educated guesses and tentative hypotheses these days when trying to get to the heart of inner peace via science. Please take what I say with good-natured skepticism.
So just what is "inner peace"? How can we achieve it? I tried to find some careful scientific inquiry into these questions.
Elements of inner peace that I've come across include serenity, tranquility, gratitude, contentment, joy, and affection for others.
Based on the work of Roberts and Cunningham: serenity is: "a spiritual experience of inner peace, trust, and connectedness."
How can we achieve inner peace? Training in relaxation, meditation, and mindfullness seems very helpful. Another common recommendation is establishing a sense of connectedness and belonging. For me, this community is just what the doctor ordered (...or should have...).
When Norm Cousins was ill, he concluded after much study that laughter is important to well being. Perhaps in this setting he might say the way to inner peace and enlightenment is to lighten up.
My readings further suggest the importance of re-evaluating your view of the world and your place in it. Focussing on what you can do to solve your problems, and learning to accept those things that you can't change. Sitting around worrying is the opposite of inner peace. Either actively pursue reasonable avenues for solving the problem, or just let it go if it can't be fixed or isn't worth the trouble.
This is a lesson I've heard before, but which I really need to take to heart.
This familiar excerpt from the AA Serenity Prayer sums it up well:
I seek the serenity to accept the things I cannot change,
The courage to change the things I can,
And the wisdom to know the difference.
Living one day at a time,
Enjoying one moment at a time,
And, as my T-shirt says: "Don't Postpone Joy".
References:
http://www.ria.org/summaries/rib/rib001b.htm
Full Catastrophe Living - Using the Wisdom of your body and mind to face stress, pain and illness, by Dr. Jon Kabat Zinn, University of Massachusetts Medical Center Stress Reduction Clinic.