A new theoretical analysis turns the absence of a specific kind of noise in the cosmic density field into the strongest constraints yet on gravitational waves produced in the early universe. The paper, posted to arXiv on July 29 by Gabriela Barenboim of the Instituto de Fisica Corpuscular at the University of Valencia and Albert Stebbins of Fermilab, argues that a gravitational wave background would inevitably leave a signature called large-scale white noise, and that the failure of observations to find that signature rules out many early-universe sources of gravitational waves.
The argument builds on a framework the same authors developed with a colleague in two earlier papers. Non-linear couplings between density fluctuations on small scales generate white noise on the largest observable scales of the cosmic density field. Gravitational waves always produce a shear in the cosmic fluid, and that shear, through the same non-linear mode coupling, generates this large-scale white noise. Since the observed universe does not show the effect, the authors convert the observational upper limit on white noise into an upper limit on how much gravitational wave energy could have existed at any given epoch.
The observational input is a 99 percent confidence limit on the white noise amplitude derived from Planck 2018 data: the quantity called k_BH must be below 1.80 x 10^-13 per megaparsec. The main result of the new paper is a simple constraint relating three quantities: the redshift at which gravitational waves were produced, their energy density today, and their frequency. For waves generated inside the horizon during the radiation era, the constraint takes the form z^2 Omega_GW0 < 5 x 10^7 (f/nHz)^(3/2), where z is the production redshift, Omega_GW0 the present-day density parameter of the waves, and f their frequency today.
The authors apply this constraint to a concrete example: the gravitational wave background detected by pulsar timing arrays. They show the detected waves could not have been present before a redshift of about 10^8, which is long after the quark-hadron phase transition that ended around redshift 10^12, when the universe was about 100 MeV in temperature. The maximum cosmic temperature allowed at the redshift horizon of the detected waves is about 50 keV, well after big bang nucleosynthesis. The authors conclude it is more likely the pulsar timing array signal was generated at low redshifts by astrophysical sources, such as merging supermassive black holes, than by any process in the very early universe.
For the quark-hadron transition itself, the constraint is dramatic. A strongly first-order transition of the kind that would produce a detectable gravitational wave background with significant bulk kinetic energy is effectively ruled out: the present-day density parameter of such waves would have to be below 5 x 10^-16, and the density parameter at production below 8 x 10^-12. The paper compares this with existing bounds in a table: integrated constraints from big bang nucleosynthesis and the cosmic microwave background allow densities up to about 10^-5, direct gravitational wave searches reach about 10^-8, and the new white-noise bound reaches about 10^-15. The new constraint is seven orders of magnitude more stringent than previous ones at a frequency of about 1 nanohertz, the scale of the QCD horizon.
The authors stress what their constraint is not. The 5 x 10^-16 bound comes from a minimal model that assumes the gravitational waves were produced with Gaussian random phases, at horizon scale, and were the only source of white noise. Realistic early-universe production, they argue, would tighten the constraint by orders of magnitude, for two reasons. Localized sources of gravitational waves, such as bubble collisions in a phase transition, add granularity that generates more white noise. And the acoustic waves that accompany any phase transition, produced by direct mechanical coupling rather than gravity, generate white noise far more efficiently than the gravitational waves themselves. If acoustic waves dominate the white noise, the fraction of the signal traceable to gravitational waves could be very small, which would make the constraint on gravitational waves alone even stronger.
The paper also examines the prospects for future gravitational wave telescopes. The white-noise constraint does not completely exclude the possibility of detecting gravitational waves from the very early universe with proposed instruments, even up to cosmic temperatures above 1 TeV for the most sensitive designs. But the authors caution that redshift horizons computed from raw instrument sensitivity are likely optimistic, because astrophysical foregrounds and the white noise produced alongside any early-universe gravitational wave source would both reduce what is detectable. A discrete-event model of gravitational wave production, in which the waves come from a finite number of localized sources, yields constraints on the production redshift that are far more stringent than the minimal model, unless the number of events per horizon volume was very large.
The picture that emerges is of an early universe that must have been comparatively quiet, with no phase transition or other phenomenon generating significant bulk flows before the era of big bang nucleosynthesis. The paper notes this conclusion is model-dependent and that detailed modeling of specific early-universe scenarios will be required to obtain tighter bounds. The non-observation of large-scale white noise also carries an independent message: whatever produced the gravitational wave background detected at nanohertz frequencies, it almost certainly happened well after the first microseconds of cosmic history.
Sources
1. Barenboim, G. and Stebbins, A., “Gravitational Waves as a Source of Large-Scale White Noise: New Constraints,” arXiv:2607.27338: https://arxiv.org/abs/2607.27338
2. NANOGrav Collaboration, “The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background”: https://arxiv.org/abs/2306.16213
3. Barenboim, G., Ireland, A., and Stebbins, A., “The Noisy Universe”: https://arxiv.org/abs/2511.15803