In Scientific American (April 2011), Paul J. Steinhardt asks “The Inflation Debate: Is the theory at the heart of modern cosmology deeply flawed? (April 6, 2011) :
Summary Cosmic inflation is so widely accepted that it is often taken as established fact. The idea is that the geometry and uniformity of the cosmos were established during an intense early growth spurt.
But some of the theory’s creators, including the author, are having second thoughts. As the original theory has developed, cracks have appeared in its logical foundations.
Highly improbable conditions are required to start inflation. Worse, inflation goes on eternally, producing infinitely many outcomes, so the theory makes no firm observational predictions.
Scientists debate among (and within) themselves whether these troubles are teething pains or signs of a deeper rot. Various proposals are circulating for ways to fix inflation or replace it. (You have to pay to read most of the article.)