What percent of change in the speed of light is needed, to affect significantly the evolution of our universe?
First, it will not be possible to detect a change in the speed of light (in vacuum)! It is only possible to detect a change in dimensionless numbers that are ratios of other constants that have dimensions (like c). I refer you to this article.
That said, if the fine structure constant (an important number in atomic physics, involving the charge of the electron, Planck's constant, speed of light) changes by an amount more than about 0.01, then things will be significantly different. There cannot be any more production of carbon in stars from burning helium; In other words, we would not exist today if the value of the fine structure constant in the past was significantly different from what it is today! For a more esoteric discussion, refer here.
Jagadheep built a new receiver for the Arecibo radio telescope that works between 6 and 8 GHz. He studies 6.7 GHz methanol masers in our Galaxy. These masers occur at sites where massive stars are being born. He got his Ph.D from Cornell in January 2007 and was a postdoctoral fellow at the Max Planck Insitute for Radio Astronomy in Germany. After that, he worked at the Institute for Astronomy at the University of Hawaii as the Submillimeter Postdoctoral Fellow. Jagadheep is currently at the Indian Institute of Space Scence and Technology.