Gravitational waves originating from the early universe, detectable via pulsar timing.Primordial gravitational waves are ripples in spacetime that were generated in the very early universe, likely during a period of rapid expansion known as inflation, or during a bounce phase in non-singular cosmologies. Unlike gravitational waves from astrophysical sources like merging black holes, which are high-frequency and short-lived, primordial waves are expected to have very long wavelengths and form a stochastic background that fills the entire universe. Detecting them would provide a direct window into the physics of the universe's first moments, potentially revealing the energy scale of inflation and the nature of quantum gravity.
The concept of primordial gravitational waves was developed in the 1980s alongside inflationary theory, with key contributions from Alexei Starobinsky and others. The first direct detection of a stochastic background of gravitational waves was announced in 2023 by the NANOGrav collaboration, which attributed it to a background of supermassive black hole binaries, though primordial waves remain a target for future searches.
During inflation, quantum fluctuations in the gravitational field are stretched to cosmic scales, creating a background of gravitational waves. These waves leave an imprint on the polarization of the cosmic microwave background (CMB) — specifically, a pattern called B-modes. Alternatively, primordial waves can be detected through pulsar timing arrays, which measure tiny variations in the arrival times of radio pulses from millisecond pulsars caused by passing gravitational waves. The timing residuals from a network of pulsars can reveal a common signal characteristic of a stochastic background.
Detecting primordial gravitational waves would allow scientists to probe physics at energies far beyond those achievable in particle accelerators, potentially confirming or ruling out specific models of inflation and quantum gravity.
The gravitational wave background from the early universe is so faint that it would take decades of pulsar timing data to distinguish it from noise, but it carries information from when the universe was less than a second old.
| h_{ij}^{\text{TT}} | variable | Transverse-traceless gravitational wave strain tensor — gravitational wave strain |
| D | variable | Distance from source to observer — distance metre |
| I_{ij} | variable | Mass quadrupole moment tensor — mass quadrupole moment kilogram metre squared |
| t | variable | Time — time second |
| G | constant | Constant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Universal speed limit and speed of light in vacuum — speed of light = 299792458 metre per second |
| d^2/dt^2 | operator | Second derivative with respect to time — second time derivative |
| P(k) | variable | Dimensionless power spectrum — power spectrum |
| k | variable | Wavenumber — wavenumber reciprocal metre |
| k_* | variable | Pivot wavenumber — wavenumber reciprocal metre |
| n_s | variable | Spectral index — spectral index |
| A_s | constant | Amplitude of primordial scalar perturbations at the pivot scale — scalar amplitude = 2.1e-9 |


















