Can you analyze sleep with Arduino?

I'm going to make a smart pillow using Arduino as a school project.
Using a vibration sensor or acceleration sensor, we are going to observe the movement of REM sleep.
And I'm going to detect snoring with a sound sensor.

But the professor wants a more rigorous measurement, is it possible with Arduino?

Can you analyze sleep with Arduino?

First you must DETECT sleep.

The problem is not the Arduino, rather it is with which sensor you are going to use. For instance, if you can detect brain activity with a sensor of some kind and amplify the signals to a suitable level then it would be possible to analyse the data using an Arduino

Before you ask, I do not know of such a sensor

You need to identify what signals or effects characterise what you want to detect ( sleep /REM etc) , then look at how you can translate those effects into electrical signals .
So what are the characteristics of the parts of sleep you wish to measure .