Cosmic Inflation attempts to explain why the universe is so uniform by positing that the universe may have expanded faster than the speed of light, at least for a time. It is a very successful theory which allows us to think of the forces as having not changed with time. But what if Gravity itself has changed with time? What if the early universe had little or no gravity and later, through a sort of phase change (like water turning to ice) gravity was switched on? Could that be an alternative way to explain the state of the universe today and if so how might it have happened? Those are the questions that Brian Greene, Kurt Hinterbichler, Simon Judes, and Maulik K. Parikh try to address in a new arXiv paper.
The basic premise is that things are uniform now in the universe and if the universe had expanded at a constant rate with gravity acting all the time the laws would predict a more lumpy universe. Cosmic inflation questions whether the universe expanded at a constant rate. 
If the early universe expanded faster that the speed of light then the clumping effect of gravity would have been frozen out for a time. Then when expansion slowed down the effect would become more pronounced. As an alternative the new paper questions whether gravity was uniformly powerful the whole time. If a gas is unaffected by gravity the gas will distribute uniformly in space but when gravity is added the gas atoms will eventually form into clouds, condense into stars, and collapse into black holes. The new paper suggests that gravity itself might have been weaker for a time, leading to less clumping.
We tend to imagine our surroundings on geological or cosmological time scales as being governed by gradual change. If things do change the changes must certainly be brought about by constant laws. We think of the speed of light and the strength of the forces as being constant. But as we are able to see at greater time scales we have found over and over that things we thought were constant do change—stars die, galaxies form, hot rocks flows like water, and the universe expands at an accelerating pace. There are a growing number of people asking whether the laws of nature also change. Until we ask this we aren’t done looking at the possibilities so I was excited to read the paper.
Luboš Motl lambasts the idea here.