There is noise in the background of the image. Although it is not easily seen at the current brightness level of the image, it is there. It will be a problem when the faint stars are "pulled" out with the use of curves. To lessen this noise problem I used a "Gaussian" blur.

Use a radius of 2 pixels for this blur. You do not want to obliterate the stars but you want to smooth the noise in the background.

This reduced the star brightness a bit but don't worry. We will bring it back! The important thing here is to reduce the background noise.