I usually sleep in the morning till noon, is it really important to sleep at nights rather than morning or other times in a day?
Are there any documented studies about when to sleep?
According to this answer, does it affect weight loss process?
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It's far better to attempt to sleep on a natural cycle with the sun, in order to keep your circadian rhythm (and the hormonal cycles behind it) in "tune". From Shawn Talbot's excellent Cortisol Connection:
Remember that cortisol levels normally peak in the early morning (about 6:00 a.m. to 8:00 a.m.) as a way to get a person moving and prepare her to face the challenges of the day. Between 8:00 a.m. and 11:00 a.m., cortisol levels begin to drop, and they continue to gradually decline throughout the day, typically causing us to feel a decrease in energy levels and ability to concentrate sometime around 3:00 p.m. to 4:00 p.m. (the "afternoon slump"). This dip in energy levels is the body's way of saying, "The day is almost over; better get ready for sleep." Unfortunately, instead of getting ready for sleep, our modern lifestyles cause most of us to search for a way to boost our energy levels in the evenings so that we can get through soccer practices, piano recitals, business dinners, and time with our families. Our body clock really wants us to eat our last meal of the day around 5:00 p.m. and to be asleep by 8:00 p.m., but our wristwatch has us awake late into the night. The major problem with our modern "late to bed, early to rise" lifestyles is that our cortisol levels never have enough time to fully dissipate (which is supposed to happen overnight), so our bodies never have a chance to fully recover and repair themselves from the detrimental effects of chronic stress.
Here's the full section on cortisol and sleep/insomnia.
In order to really be healthy on a delayed sleep schedule, you'd need to adjust and properly time a lot of factors, including:
Regarding weight, a different chapter examines a fat storage enzyme HSD and its connection to cortisol. It's not quite so simple as saying that more cortisol directly causes more HSD, but there is a more complex relationship. HSD in your cells amplifies their exposure to cortisol and other stress hormones, which results in more weight gain.
Researchers from the University of Helsinki, in Finland, have shown that cortisol causes fat accumulation in specific sites most likely to be associated with insulin resistance (prediabetes). These sites are abdominal fat tissue and the liver—and fat accumulates in these areas because of the activity of HSD. Higher activity of HSD means a higher rate of fat storage and a faster accumulation of fat stores. In abdominal areas, a high HSD activity leads to a rounder waistline, while in the liver it means a higher risk for diabetes.
I think the most important part is quality of sleep. In other words you want a deep REM sleep and you want your total stleep to be 8 hours a day, ideally. The things that can ruin the quality of sleep for you are:
The reason night time works for most people is that it is both quieter (because everyone else is sleeping) and there is no sunlight waking you up.
If you have a night job, then blackout curtains can be a very important investment. All you have to do after that is deal with the noise. Either invest in a white noise machine or fountain to drown out distracting noise or sound proof your room (very expensive).
As to documented studies, you can try this one.