Can gravity seed cosmic structure without an inflaton?

Two jobs usually given to one field

Inflation proposes that the early universe underwent accelerated expansion. In standard models, a hypothetical scalar field—the inflaton—both generates the initial variations that later grow into cosmic structure and controls when inflation ends.

In their November 2026 preprint, Daniele Bertacca and colleagues investigate an alternative called Inflation without an Inflaton. Here, quantum fluctuations of gravity supply the seeds. The study is theoretical, combining analytical calculations with numerical evolution of Einstein’s equations; it reports no detection of primordial gravitational waves or experimental confirmation of the scenario.

The paper addresses two questions: why would gravity generate substantial structure-seeding curvature without also producing excessive gravitational waves, and could that curvature survive the transition into a radiation-filled universe?

Why curvature grows but waves do not

The proposed seeds arise at second order: pairs of gravitational fluctuations contribute jointly to variations in spatial curvature. The authors calculate these contributions in de Sitter space, an idealized spacetime with constant accelerated expansion, using the standard Bunch–Davies quantum state.

Short-wavelength pairs can make an enhanced contribution to curvature on a much longer wavelength. Mathematically, the enhancement involves the squared ratio of the pair’s internal momentum to the momentum of the larger-scale disturbance. The authors check that their time-dependent scalar solution satisfies all four relevant second-order Einstein equations.

A concern is that the same process might generate an equally enhanced gravitational-wave signal, exceeding observational limits. Their calculation finds otherwise. Curvature is determined by gravitational constraint equations, whereas gravitational waves obey an evolving wave equation. Tracking the latter’s response across the full oscillatory history produces cancellations that prevent the enhancement.

For the calculated region where both internal momenta exceed the external momentum, the second-order tensor power is tiny compared with the original gravitational-wave power. This is not a complete one-loop calculation: another contribution needed to assess cancellations in the soft and collinear regions remains uncomputed.

The crucial assumption is a clock

Producing curvature during idealized inflation is not enough. The curvature that survives afterward depends on which physical condition determines when different regions stop inflating.

The authors assume a global clock associated with the depletion of vacuum energy. Each wavelength remains synchronized with a particular spacetime slicing, called zero-shear time, for a fixed interval after crossing the Hubble radius. It then runs according to local proper time while retaining its accumulated offset.

Giving every wavelength the same interval lets each collect the same enhancement, producing an approximately scale-invariant spectrum. The interval is measured in e-folds: each e-fold multiplies the cosmic scale factor by about 2.7.

This clock is explicitly nonlocal. Across the discussed parameter range, its synchronization reach spans roughly 10 trillion to 10 sextillion Hubble radii. The paper postulates the required synchronization, release and memory rather than deriving them from microscopic dynamics. It also imposes the change that completes inflation’s exit; steady vacuum depletion alone does not provide it.

Energy conservation requires the depleted vacuum energy to feed another component, modeled mainly as radiation. In the numerical configurations tested, the resulting large-scale curvature remains conserved to better than one part in 10,000 while sufficiently outside the Hubble radius. Tested adiabatic alternatives to radiation change its amplitude by less than 0.2%. Those checks do not establish robustness for every possible receiving medium.

Conditional observational targets

For a direct transition into radiation and a sharp clock release, the authors obtain an allowed interval of about 30.5–50.3 e-folds. The corresponding tensor-to-scalar ratio, which compares primordial gravitational-wave power with curvature power, ranges from about 0.0000026 to 0.036. Smoother release prescriptions change these bounds.

For a scale-independent clock response, the predicted gravitational-wave spectral tilt is half the scalar tilt. The authors also forecast possible sensitivity from cosmic microwave background polarization searches and proposed space interferometers. Their interferometer estimates assume four years of observations and successful subtraction of astrophysical foregrounds; they are not promised detections.

At smaller scales, the curvature spectrum turns downward because inflation ends before every wavelength completes its collection interval. That could reduce distortions of the microwave background’s spectrum, although the transition shape for a finite-width release has not been calculated.

The result is a conditional route from gravitational fluctuations to persistent cosmic structure—not yet a microscopic explanation of the clock that makes the route work.