Inflationary cosmology posits that the universe underwent exponential expansion within the first second following the Big Bang. During inflation the spatial extent of the universe may have increased by a factor of about 10^30 times its original size, within the brief interval of 10^-35 second to 10^-32 second. At times later than 10^-30 seconds after the Big Bang, the inflation scenario agrees with the standard cosmological model.
The initial motivation for inflation, invented by Alan Guth in the 1980s, was the unwanted prediction by Grand Unified Theories (GUTs) of a proliferation of unobserved cosmic magnetic monopoles. An immensely inflated universe would presumably make the density of magnetic monopoles so low they would escape detection.
Inflation may also overcome shortcomings in the predictive power of the standard cosmological model, evident in the flatness problem, which concerns why the universe seems to coincidentally have exactly zero spatial curvature; and also in the horizon problem, or why distant parts of the universe have the same temperature, even though they are not causally connected. The temperature of the cosmic microwave background radiation is observed to be isotropic (the same in all directions) to atleast one part in 10^5. But opposite parts of the sky have been separated by a much greater distance than light could have traveled since the Big Bang. There has been no way for these distant parts of the universe to exchange heat and reach thermal equilibrium. Inflation solves this problem by allowing thermalization to occur before exponential expansion causally separates regions.
Inflation also seems to solve the smoothness problem, or how matter in the universe became uniform. In order for galaxies to form, there needed to be a spectrum of mass density perturbations in the early universe. These perturbations are gravitationally unstable because regions of extra mass will gravitationally attract yet more mass. Therefore, these perturbations must have been exceedingly small. Inflation solves this problem by ironing out irregularities of the initial state, in order to explain the uniformity of matter.
There exist many different inflation models, but each requires a special scalar quantum field, called an inflaton. This quantum field creates an associated effective potential; inflation occurs as the state of the universe reaches the minimum of the effective potential. In the process, the universe undergoes a quantum mechanical phase transition to a false vacuum. This false vacuum would have an effective cosmological constant corresponding to a density of 10^110 times that of observations of the current value of the cosmological constant. The negative-pressure vacuum energy density caused by the false vacuum is the driving force behind the immense expansion of inflationary models.
Criticisms of inflationary cosmology include that thermalization implies an increase in entropy, by the second law of thermodynamics. Before distant spacetime regions could undergo thermalization, the universe would have to be in an even more special, lower entropy initial state, which is even harder to explain. The inflaton quantum field is presumably unrelated to other physical fields and is ascribed ad hoc properties, just to make inflation work. Inflation also may not be able to iron out irregularities of the initial state if that state was not smooth on a small scale.