phenomenon

quantum fluctuations inflation

Quantum noise or fluctuations during cosmic inflation that seed large-scale structure formation.
20 related articles · 3 formulas

Description

During cosmic inflation — the rapid exponential expansion of the universe in its first fraction of a second — quantum fluctuations were stretched to macroscopic scales. These tiny random variations in energy density became the seeds for all large-scale structure we see today: galaxies, galaxy clusters, and the cosmic web. The pattern of these fluctuations is imprinted in the cosmic microwave background radiation, the afterglow of the Big Bang.

History

The idea that quantum fluctuations during inflation seed cosmic structure was developed in the early 1980s by physicists including Viatcheslav Mukhanov and Gennady Chibisov, and independently by Stephen Hawking and others.

How it works

Quantum mechanics dictates that even empty space is not truly empty; it is filled with temporary fluctuations in energy. During inflation, the universe expanded so fast that these microscopic fluctuations were 'frozen' and stretched to astronomical sizes. After inflation ended, these density variations acted as gravitational wells, attracting matter and eventually forming the structures we observe. The statistical properties of these fluctuations — nearly scale-invariant and Gaussian — are a key prediction of inflationary theory.

In practice

This concept is central to interpreting data from cosmic microwave background missions like Planck, which measure the precise statistical patterns of the fluctuations to test inflationary models and constrain the physics of the early universe.

Fun fact

The largest structures in the universe — superclusters of galaxies spanning hundreds of millions of light-years — originated from quantum fluctuations smaller than an atom.

Concept graph →

Formulas

$$P \propto \exp\left(\frac{24\pi^2}{V(\phi_*)}\right)$$
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
$$P(k) = P_0(k) \left[1 + A \exp\left(-\frac{(\log k - \log k_0)^2}{\sigma^2}\right)\right]$$
A Gaussian-shaped enhancement in power spectrum.
What is in the formula
P(k)variablePerturbed power spectrum — power spectrum cubic metre
P_0(k)variableBackground power spectrum — power spectrum cubic metre
AvariableAmplitude of the bump — amplitude
kvariableWavenumber — wavenumber per metre
k_0variableCentral wavenumber of the bump — wavenumber per metre
σvariableWidth of the bump in log-k — width
expoperatorExponential function — exponential
logoperatorNatural logarithm — logarithm
p_{{bump}}(k)=p_{\lambda{cdm}}(k)[1+a\exp(-\frac{(\logk-\logk_0)^2}{σ_k^2})] · 2606.07357v1
$$\langle \eta_i(t) \eta_j(t') \rangle = 2 \gamma k_B T \delta_{ij} \delta(t-t')$$
Relates noise intensity to temperature and dissipation in equilibrium.
What is in the formula
η_i(t)variablenoise term at time t for component i — noise newton
η_j(t')variablenoise term at time t' for component j — noise newton
Tvariabletemperature — temperature kelvin
γvariabledissipation coefficient — dissipation coefficient kilogram per second
δ_ijvariableKronecker delta — kronecker delta
δ(t-t')variableDirac delta function — dirac delta function per second
k_Bconstantrelates energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
⟨...⟩operatoraverage over many realizations — ensemble average
\langle\eta_i(t)\eta_j(t')\rangle=2γ_ik_bt_iδ_{ij}δ(t-t') · 2606.29765
s_j(ω)=|χ(ω)|^2n_{{ir}}(ω) · 2607.04115

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