When light travels through any lens, light rays at the outside edges of the lens travel further than they do in the centre. This is especially noticeable on wide angle and super wide angle lenses and gets worse when you use a wide aperture.
When this happens, what is called the “cosine fourth law of illumination falloff” occurs, which states that this light falloff is proportional to the fourth power of the cosine of the angle between the peripheral lens light ray and the optical axis. This can get very complex and technical but basically the rays further away from the optical axis will always travel longer, so by the time they reach your digital camera sensor, vignetting shows up in your images. So some of this phenomenon of reduced peripheral image illuminance (darker outer images) is due to the cosine law of natural vignetting. In addition, the cross-sectional area of an oblique beam traversing the lens may be reduced in comparison to that of an equivalent axial beam.