Short answers, pulled from the story.
Cosmic inflation is a theory proposing that the very early universe underwent a period of exponential expansion, stretching space itself at a rate that defied conventional physics. Distances between points doubled every 10 to the power of minus 37 seconds, a process that lasted for at least 10 to the power of minus 35 seconds.
Alan Guth, a theoretical physicist at Cornell University, coined the term inflation in 1980 and proposed the mechanism of false vacuum decay to solve the monopole problem. Alexei Starobinsky, at the Landau Institute for Theoretical Physics, was the first to propose an inflationary phase in 1979, using quantum corrections to general relativity to generate an effective cosmological constant.
Cosmic inflation resolved the horizon problem by positing that the universe began as a tiny patch in thermal equilibrium, which was then stretched exponentially. This expansion separated the equilibrated parts to vast distances, creating the appearance of homogeneity on large scales and explaining why the universe looks the same in all directions to within one part in 100,000.
Tiny quantum fluctuations in the inflaton field were magnified to cosmic size, becoming the density variations that allowed gravity to clump matter together. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov, and later confirmed by four groups working independently at the 1982 Nuffield Workshop on the Very Early Universe.
The Planck spacecraft has provided strong evidence for inflation, showing that the universe is flat and homogeneous to one part in 100,000. Observations from the Planck spacecraft confirm that the total curvature of a space-slice at constant global time is zero, implying that the universe is flat to within a few percent.
Cosmic inflation faces severe challenges regarding the fine-tuning of its initial conditions, as the inflaton potential must be exceptionally flat and the inflaton particles must have a small mass. Roger Penrose has argued that inflation aggravates the problem of initial conditions, as the reheating at the end of the inflation era increases entropy, making the initial state of the universe even more orderly than in other Big Bang theories.