From Citizendium, the Citizens' Compendium
The Cosmic Inflation theory proposes that there was a period in the very early stages of the cosmos in which extremely rapid, exponential expansion of the universe took place prior to the more gradual Big Bang expansion. During the period of inflation, the energy density of the universe was dominated by a cosmological constant-type of vacuum energy. Later, the vacuum energy decayed to produce the matter and radiation we see in our universe at present. Inflation was rapid. It increased the size of the universe by a factor of ~1026 in only a small fraction of a second. When the period of inflation had ceased, essentially, the universe, which began as a quantum fluctuation about 1020 times smaller than a proton, had grown to a sphere about 10 centimeters in diameter in 15 X 10-33 seconds. The inflation was rapid enough to overcome gravity and in fact had expanded faster than light. 
The inflation theory was developed by Alan Guth, Andrei Linde, Paul Steinhardt, and Andy Albrecht but the evidence for the expansion and the Big Bang theory predate their work. By 1913, Vesto Melvin Slipher had already published his research on the movement of the galaxies through their spectral shift and is credited with having established this as a viable theory by the early 1920s. In 1922 Alexander Friedmann proposed that the universe might be expanding. Using Slipher's data, by 1929, Edwin Hubble had measured the spectral shift of galaxies and was able to determine that the vast majority of galaxies are receding from us. He also discovered that the further a galaxy is from ours, the faster it is receding. One explanation for this observation is that the space of the Universe is expanding. That is, over time two points grow further apart; the very fabric of the Universe is growing.
Support for the Inflation Theory
Inflation provides theoretical answers to three problems that appeared in the traditional version of the Big Bang Theory—the Horizon Problem, Flatness Problem and the Monopole Problem:
The horizon problem is simply this; the universe looks the same on opposite sides of the sky. This is counterintuitive given that there has not been sufficient time since the Big Bang for light to travel across the universe and back again: the horizons could never have been in causal contact with each other. However, the microwave background temperature strongly indicates that these regions were in contact in the past. How, then, do opposite horizons look the same?
The horizon problem may be explained by the rate of initial expansion of the Universe. Initially the horizons of the universe were in close proximity after which they were separated at a rate exceeding the speed of light. Thus, prior to Inflation, these regions of the cosmos could have been in causal contact and would possibly have attained a uniform temperature.
The second problem is that of the Universe’s peculiar spacetime geometry. The Wilkinson Microwave Anistropy Probe (WMAP) has provided data that implies that the universe is geometrically nearly flat. This would seem to be in contradiction with Big Bang cosmology, which indicates that the curvature of spacetime grows in time. So, if the universe is as flat as the WMAP data indicates, it would mean that there were very specific conditions in the past that are very much unlike what we see today.
This flattened geometric configuration also implies that the Universe’s critical density is at the point between eternal expansion and eventual collapse. The probability of such a situation, being at that very small point between the two alternative futures of the cosmos, is itself highly unlikely. In fact the critical density of the universe, the density that would determine the geometry of the universe, would have to be accurate to within 15 decimal places at the beginning to manifest the flat geometry of the universe today. The traditional Big Bang Theory does not provide an explanation for this critically exact balance.
Inflation offers solutions to this quandary. There are two possibilities. The inflation and its subsequent expansion has essentially expanded the curvature of the universe to such proportions that the human perspective is that of a flat surface. Just as the world appears flat to a casual observer on the surface of the ocean for example, so does that vast extent of the more spherical universe appear flat to astronomers. The other possibility is that the inflation was so rapid that the initial curvature of the universe has actually been flattened during the initial inflation meaning the expansion would seem to have been diametrically rather than evenly distributed throughout all regions of the cosmos.
The Monopole Problem is also in apparent contradiction with earlier versions of Big Bang theory since it predicted that there should be a great many heavy and stable magnetic monopoles. However, they have never been observed.
The answer provided by the Inflation Theory is that the monopoles thought to have been formed in the initial stages of the formation of the universe and prior to inflation are still there. It is not a matter of their existing but their relative density which makes them so rare. In the initial stages of inflation, their abundance was dispersed, decreasing their density exponentially. Now they are still there but in a much more vast cosmos with the result that their distribution is extremely broad and virtually undetectable.
The Inflation Theory provides a significant degree of understanding of the current expansion of the universe and the original problems posed by the Big Bang Theory and as such is it now understood to be an extension of the Big Bang Theory.
Primary concepts of Inflation and Big Bang theories
The "cosmological principle" is, in sum, two principles of spatial invariance based on the perspective of the universe as a whole: On a large scale, the universe is both isomorphic under translation or "homogeneous" and isomorphic under rotation or "isotropic". Currently this has been strongly supported by studies of large-scale structure in the universe and analysis of the microwave background radiation such as that done by WMAP and COBE.
"Isotropy" or isomorphism under rotation means the universe is the same in all directions. No matter from which point observations are made, there is no distinctive variation that would indicate directions such as we understand something like a North Pole or a South Pole.
- ↑ 1.0 1.1 1.2 1.3 WMAP Inflation Theory NASA
- ↑ 2.0 2.1 2.2 Inflation for beginners John Gribben, School of Life Sciences, University of Sussex
- ↑ The spectral shift of light traveling through space is often compared to the audible pitch shift that occurs when a train is approaching or receding from an observer. The additional relative speed of the train causes the compression waves of sound to bunch up (go higher) or spread out (go lower). However, the speed of light is constant. No matter what the relative speed of an object is, the light emitted from it travels at a constant rate. A different mechanism is responsible for the spectral shift of light - cosmic expansion. While light travels at a constant speed, the very space it occupies expands causing the wave nature of light to lengthen, thus lowering its perceived frequency. The further the light travels, the more of this space lengthening it will experience, and the more frequency shift it will exhibit.
- ↑ Vesto Melvin Slipher John Peacock, Royal Observatory Edinburgh
- ↑ 5.0 5.1 Was cosmic inflation the bang of the big bang? Alan Guth (1997). "The Beamline" 27, 14
- ↑  "cosmologists use the word "horizon" to indicate the largest distance that information or energy could have traversed since the instant of the Big Bang, given the restriction of the speed of light." A. Guth (1997)
- ↑ 7.0 7.1 7.2 What do homogeneity and isotropy mean? Cornell University
- ↑ 8.0 8.1 8.2 Cosmological Principle Gary S. Watson, Dept. of Physics, Brown U.