
Inflation is a theoretical rapid exponential expansion of the early universe, explaining its large-scale homogeneity and flatness.Cosmic inflation is a hypothetical stage in the early Universe's history when its size grew exponentially: over equal tiny time intervals, the scale increased by the same factor. It lasted from roughly 10⁻³⁶ to 10⁻³² seconds after the Big Bang, and during this time the Universe expanded by at least a factor of 10²⁶. The cause of such rapid growth was a special field (inflaton) with negative pressure — it created not attraction but powerful repulsion, similar to antigravity.
The concept of inflation was put forward by Alan Guth in 1980, but his initial model encountered the graceful exit problem (inflation couldn't end smoothly). Soon Andrei Linde, as well as Paul Steinhardt and Andreas Albrecht independently proposed the slow-roll model, solving this difficulty. Later Linde developed the theory of chaotic inflation. The ideas of inflation build on earlier work by Alexei Starobinsky and on the Big Bang theory of Georges Lemaître.
Inflation is driven by the inflaton — a scalar field slowly rolling toward the minimum of its potential. According to Einstein's equations, a field with negative pressure generates accelerated expansion. Quantum fluctuations of this field during inflation turn into perturbations of the spacetime metric. After inflation ends, they become adiabatic density perturbations with a nearly scale-invariant spectrum (n_s < 1), which is confirmed by CMB observations. Inflation also predicts primordial gravitational waves.
Inflation explains why the Universe is so flat and homogeneous, and predicts specific temperature patterns in the cosmic microwave background, detected by the COBE and WMAP satellites.
Thanks to inflation, opposite points on the sky, separated by billions of light-years, have the same temperature: before inflation they were close together and had time to reach thermal equilibrium.
| n_s | variable | scalar spectral index — spectral index |
| N | variable | number of e-folds of inflation — e folds |
| M_{\rm ext} | variable | Observed apparent magnitude — apparent magnitude |
| M_{\rm int} | variable | Intrinsic apparent magnitude — apparent magnitude |
| A | variable | Extinction in magnitudes — extinction |
| T_{\text{rh}} | variable | Reheating temperature after inflation — temperature kelvin |
| g_* | variable | Effective number of relativistic degrees of freedom |
| \Gamma | variable | Inflaton decay rate — decay rate per second |
| M_P | variable | Reduced Planck mass — mass kilogram |
| \sqrt{} | operator | Takes the square root of the argument — square root |
| \simeq | operator | Indicates approximate equality — approximate equality |












