Quantum noise or fluctuations during cosmic inflation that seed large-scale structure formation.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.
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.
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.
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.
The largest structures in the universe — superclusters of galaxies spanning hundreds of millions of light-years — originated from quantum fluctuations smaller than an atom.
| P | variable | Tunneling probability — probability |
| V(φ_*) | variable | Inflaton potential at the tunneling point — potential energy density joule per cubic metre |
| P(k) | variable | Perturbed power spectrum — power spectrum cubic metre |
| P_0(k) | variable | Background power spectrum — power spectrum cubic metre |
| A | variable | Amplitude of the bump — amplitude |
| k | variable | Wavenumber — wavenumber per metre |
| k_0 | variable | Central wavenumber of the bump — wavenumber per metre |
| σ | variable | Width of the bump in log-k — width |
| exp | operator | Exponential function — exponential |
| log | operator | Natural logarithm — logarithm |
| η_i(t) | variable | noise term at time t for component i — noise newton |
| η_j(t') | variable | noise term at time t' for component j — noise newton |
| T | variable | temperature — temperature kelvin |
| γ | variable | dissipation coefficient — dissipation coefficient kilogram per second |
| δ_ij | variable | Kronecker delta — kronecker delta |
| δ(t-t') | variable | Dirac delta function — dirac delta function per second |
| k_B | constant | relates energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| ⟨...⟩ | operator | average over many realizations — ensemble average |









