The sky within the arc of the rainbow is quite clearly lighter than the sky above the rainbow. This is due to a phenomenon of light refraction through water droplets. The dark sky, especially if it occurs between two rainbows is known as Alexander's Dark Band after Alexander of Afrodisias who first recognised the effect.
It was well known to painters and countryfolk. This painting of 1794 by Joseph Wright of Derby clearly shows the phenomenon. A tribute to the artist's keen observation.