concept

inflation

Inflation is a theoretical rapid exponential expansion of the early universe, explaining its large-scale homogeneity and flatness.
40 related articles · 3 formulas · 6 who worked here

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$n_s \approx 1 - \frac{2}{N}$$
Spectral index depends on number of e-folds during inflation.
What is in the formula
n_svariablescalar spectral index — spectral index
Nvariablenumber of e-folds of inflation — e folds
n_s\approx1-\frac{2}{n_{{cmb}}} · 2605.15374v1
$$M_{\rm ext} = M_{\rm int} + A$$
Observed magnitude equals intrinsic magnitude plus extinction.
What is in the formula
M_{\rm ext}variableObserved apparent magnitude — apparent magnitude
M_{\rm int}variableIntrinsic apparent magnitude — apparent magnitude
AvariableExtinction in magnitudes — extinction
m_{\rmext}=m_{\rmint}+r_b*e · 2606.06593v1
$$T_{\text{rh}} \simeq \left(\frac{30}{\pi^2 g_*}\right)^{1/4} \sqrt{\Gamma M_P}$$
Temperature after inflation from decay rate and Planck mass.
What is in the formula
T_{\text{rh}}variableReheating temperature after inflation — temperature kelvin
g_*variableEffective number of relativistic degrees of freedom
\GammavariableInflaton decay rate — decay rate per second
M_PvariableReduced Planck mass — mass kilogram
\sqrt{}operatorTakes the square root of the argument — square root
\simeqoperatorIndicates approximate equality — approximate equality
t_{{rh}}\simeq(\frac{40}{π^2g_*})^{1/4}\sqrt{\gamma_φm_p} · 2607.23200v1

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