Alan Guth who first proposed Inflation in 1979 and had it published in 1981.
Andrei Linde
Paul Steinhardt
These 3 physicists shared the 2003 Dirac Prize for their work on developing the concept of cosmic inflation.
Cosmic inflation is a theory of cosmology where, the space in the early Universe expanded at an exponentially rapid rate. This expansion would have been characterized by an inflationary epoch. This epoch probably lasted from 10^-36 seconds after the Big Bang's initial state of being in a singularity to about 10^-33 to 10^-32 seconds after this initial singularity. The universe continued to expand after this period, however, not as rapidly. During this period of time the universe increased in size by a factor of 10^22.
Alan Guth wanted to solve several problems in cosmology with his theory of Inflation:
The horizon problem: why is the spatial distribution of matter in the universe homogeneous and isotropic? This phenomenon is known as the cosmological principle. These are causally disconnected regions of space. Without inflation, there is no mechanism that would set the initial conditions to be the same everywhere. Why do these distant parts of the universe appear isotropic, if light is not even fast enough to communicate between them? This kind of communication would take longer than the age of the universe.
In Inflation, the universe would have expanded from a state of being a small and causally connected region, in a kind of equilibrium. The uniformity would be preserved throughout the subsequent exponential expansion.
Regions of the universe that appear similar, however, are not causally connected in any way, could have been connected by extremely close distances during the very early stages of Inflation. The explosion caused by Inflation could explain why they are now far away from each other. Prior to this exponential expansion that Inflation predicts, regions that are now distant from one another, could have been much closer. This would explain the uniform temperature of distant regions of space that are no longer in contact to each other.
The flatness problem: the density of matter and energy in the universe, would affect the curvature of spacetime. The value of this density would have to be very specific to achieve the flat universe that we observe. Observations, such as the WMAP, show that the Universe does indeed, appear to be geometrically flat. This is inconsistent with Big Bang cosmology as we currently understand it, since, as space expands, so does its curvature. To reconcile these two insights, a massive fine-tuning of conditions would be required.
Inflation can help answer: what is the mechanism that caused the universe to have exactly the correct density to allow for it's extreme flatness, even so early in it's evolution. The universe appears flat because it is actually remarkably big.
We only see a portion of the observable universe. With Inflation, the size of the universe can become much larger, thus, from our perspective, making it look much flatter. It will merely appear flat to you. However, it has curvature on larger scales. Inflation has stretched the universe to near flatness!
The magnetic monopole problem: A magnetic monopole is a hypothetical particle that is a magnet with only one pole. The problem is that many of our current theories predict their existence, however, evidence for their existence has never been observed.
In fact, Big bang cosmology predicts the existence of many magnetic monopoles. These monopoles should be heavy, stable and should have been produced in the early universe. Even if they do exist, then they are far more rare than the Big Bang theory predicts.
In Inflation, magnetic monopoles could have existed before the period of cosmic inflation. The presence of monopoles would have become undetectable during the Inflation.
Alan Guth is going to propose an idea to solve both the horizon problem and the flatness problem. This occured in several steps.
This had to do with the density and fate of the Universe. If the Universe was too dense, it would have collapsed into a singularity. Also, if the Universe were not dense enough, then, the Universe would have been much bigger. The universe is poised on a knife edge between collapse and over-expansion. Guth had these insights in 1978 while attending a lecture by Robert Dicke.
Next, in 1979, while attending a lecture by Steven Weinberg, Guth had his next insight. Weinberg was talking about the Grand Unified Theory, which would be able to provide an explanation for the imbalance between matter and antimatter in the universe. The idea behind a Grand Unified Theory is that it can explain electromagnetism, and the strong and weak nuclear forces, in one theoretical framework. These forces were one single unified force in a very hot (hotter than 10^27 K) phase that followed the Big Bang. This is the Grand Unified epoch. This is when Guth had the insight that, by looking at the first few seconds of the Universe's evolution, precise calculations could be made about particles.
Robert Dicke
Steven Weinberg
Between 10^-43 and 10^-36 seconds after the Big Bang was the grand unification epoch. This period began when gravity separated from the other three fundamental interactions: electromagnetism and the strong and weak nuclear forces.
Alan Guth's proposal, which was consistent with general relativity, was that the universe could have undergone a remarkable explosion. The universe would be doubling it's size at regular intervals of time. Inflation would be caused by a field that permeates all of space and drives the expansion. The energy density of this field would remain constant during this expansion. This kind of growth in size is known by mathematicians as exponential growth. The idea is that our baby universe would double in size at regular intervals causing it to grown from the subatomic scale to a scale larger than our own observable universe in a split second. Perhaps this is what put the "bang" in the Big Bang. This accelerated growth phase, where the universe would be doubling in size at regular intervals, was followed by a decelerated growth phase. The inflating material decayed into ordinary matter, which would continue to expand, however, not as rapidly. Gravity would also work toward this gradual deceleration. When the baby universe doubled in size, it also doubled it's speed of acceleration. In a very popular model of Inflation, the baby universe would double in size every 10^-38 of a second. This probably occurred about 260 times to achieve the amount of mass in our observable universe.
That being said, Inflation could answer the question of what caused the Big Bang. It was the repeated process of doubling in size.
Inflation would also explain the uniform expansion that was first observed by Edwin Hubble. Hubble observed that regions of the universe that are twice as far away from each other are also moving apart twice as fast.
It was shown in 1983 by Paul Steinhardt and later by Alexander Vilenken that Inflation could be eternal. This would result in a multiverse. Each patch of the multiverse would be a different pocket "universe" with different physical constants. These are the places where inflation has stopped. We would have been inhabiting one of these pockets for about 13.8 billion years. The Big Bang would not be the beginning, however, the end of inflation in our pocket of space. Almost all of the Inflation models studied today lead to some form of the idea of eternal inflation.