phenomenon

cosmic inflation

Rapid exponential expansion of the early universe, explaining large-scale structure formation.
28 related articles · 6 formulas

Description

Cosmic inflation is a theory proposing that the universe underwent a period of extremely rapid exponential expansion in the first tiny fraction of a second after the Big Bang. This expansion, driven by a hypothetical field (the inflaton), would have stretched any initial irregularities to cosmic scales, seeding the large-scale structure we observe today — galaxies, clusters, and the cosmic microwave background (CMB) anisotropies. Inflation elegantly explains why the universe appears so homogeneous and flat on large scales, and why we see the specific pattern of temperature fluctuations in the CMB.

History

Inflation was proposed by Alan Guth in 1980, with important refinements by Andrei Linde and Andreas Albrecht & Paul Steinhardt in 1982. The theory was developed to solve problems of the standard Big Bang model, such as the horizon and flatness problems.

How it works

Inflation postulates that a scalar field, the inflaton, dominated the universe's energy density and caused it to expand exponentially (doubling in size every ~10^-35 seconds). During this phase, quantum fluctuations in the field were stretched to macroscopic scales, creating density perturbations. After inflation ended, the inflaton decayed, 'reheating' the universe with particles and radiation. The density perturbations then grew via gravitational instability into the cosmic web of matter we see today. The theory makes specific predictions about the statistical properties of these perturbations, which have been confirmed by observations of the CMB.

In practice

Inflation is a cornerstone of modern cosmology, guiding the interpretation of CMB data from missions like Planck and informing models of the early universe's particle physics.

Fun fact

Inflation is so fast that a region smaller than a proton could have expanded to the size of a grapefruit in just 10^-32 seconds, and then continued to grow to the entire observable universe.

Concept graph →

Formulas

$$P(x) = \lambda e^{-\lambda x}$$
Probability density function for exponential distribution.
What is in the formula
xvariableValue of the random variable — random variable value
λvariableRate parameter (inverse of mean) — rate parameter
P(x)variableProbability density at x — probability density
p(n)=2ε_ve^{-2ε_vn} · 2605.05317v2
p(e)=\frac{1}{τ}\exp(-\frac{e}{τ}) · 2606.06593v1
$$v_k'' + ig(k^2 - rac{z''}{z}ig) v_k = 0$$
Describes evolution of cosmological perturbations in inflation.
What is in the formula
v_kvariableMukhanov-Sasaki variable for mode k — mukhanov sasaki variable
kvariablecomoving wavenumber — wavenumber reciprocal metre
zvariablepump field related to background cosmology — pump field
''operatordifferentiates twice with respect to conformal time — second conformal time derivative
v''_k+(k^2-\frac{z''}{z})v_k=0 · 2607.00636
$$M_{\text{enriched}} \propto M_{\text{system}}$$
Enriched material mass must exceed observed stellar mass.
What is in the formula
M_{\text{enriched}}variableMass of enriched material — mass kilogram
M_{\text{system}}variableMass of the system — mass kilogram
\proptooperatorProportional to — proportionality
m_{{загрязн}}\approx10*m_{{скопл}} · 2607.05509v1
$$\theta = \nabla_\mu u^\mu$$
Classifies spacetime regions by sign of expansion rates.
What is in the formula
θvariableexpansion scalar — expansion scalar per second
u^μvariablefour-velocity of the fluid or congruence — four velocity
∇_μoperatorcovariant derivative with respect to spacetime coordinate μ — covariant derivative
θ_{\pm}=\frac{2}{r}[\pm1+\dot{r}] · 2605.07848v2
$$H(z) = H_0 \sqrt{\Omega_m(1+z)^3 + \Omega_r(1+z)^4 + \Omega_k(1+z)^2 + \Omega_\Lambda + \Omega_x f(z)}$$
Describes expansion rate of the universe.
What is in the formula
HvariableHubble parameter — hubble parameter per second
zvariableredshift — redshift
H0variableHubble constant — hubble constant per second
Ωmvariablematter density parameter — density parameter
Ωrvariableradiation density parameter — density parameter
Ωkvariablecurvature density parameter — density parameter
ΩΛvariablecosmological constant density parameter — density parameter
Ωxvariabledark energy density parameter (general) — density parameter
f(z)variabledark energy equation-of-state function — equation of state function
sqrtoperatorsquare root — square root
h(z)=h_0\sqrt{ω_m(1+z)^3+ω_\lambda+ω_x\exp(-3\int_0^z\frac{1+w(z')}{1+z'}dz')} · 2601.06656
\frac{a'^2}{a^2}-\frac{1}{a^2}+\frac{1}{3m_p^2}(v(φ)-\frac{φ'^2}{2})-\frac{\tilde{ρ}_i}{a^{n_i}}=0 · 2605.13777v2
(\frac{\dot{a}}{a})^2=\frac{\kappaρ(v)}{3}+\frac{\kappaρ_f(v)}{3} · 2605.15045v1
h^2=\frac{1}{3}(\frac{1}{2}\dot{φ}^2+\frac{1}{2}\dot{\varphi}^2+\frac{1}{2}b(φ,\varphi)\dot{φ}\dot{\varphi}+v_{ic}(φ,\varphi)+β^4(φ)(ρ_m+ρ_r)) · 2605.15374v1
$$P \propto \exp\left(\frac{24\pi^2}{V(\phi_*)}\right)$$
Probability of inflationary universe creation suppressed for large inflaton potential.
What is in the formula
PvariableTunneling probability — probability
V(φ_*)variableInflaton potential at the tunneling point — potential energy density joule per cubic metre
p\propto\exp(\frac{24π^2}{v(φ_*)}) · 2605.13777v2
p\approxae^{-s_e/ħ} · 2605.16150

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