The article doesn't even explain how they come to the conclusion that the universe has been there forever from the "rainbow gravity" concept.
But if there is no red shift, then there is no Big Bang, and the Universe is not expanding. Therefore we go back to where we were in 1900, when everyone assumes that the universe is eternal.
Also, you can have a static universe with a beginning, or an expanding universe with no beginning. Rainbow gravity falls into this latter category.