No, the speed of light is always constant throughout the universe. Many experiments have been done to validate Einstein's theory of special relativity.
Light like every other particles that are traveling in a straight line will eventually decelerate in time and space.
Photos aren't something like a football that deaccelerates due to aerodynamic resistance.
This billions and billions of light year (up to 13.3 billion light-years) are nothing more then errors in calculations based ont the assumption that the speed of light is constant.
Any evidence to back this statement? I don't think there is any. The data collected by the Hubble Space Telescope are widely accepted in the scientific community.
Without proper evidence to back up your claim, this is nothing more than a science fiction post. Also, please properly cite the images.

RE: Can The Assumption That The Speed Of Light Is Constant Be Wrong?