Emergence of cosmic structure from Planckian discreteness

In the standard inflationary paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state. This picture suffers from two well-known weaknesses. First, it assumes that quantum field theory remains valid at trans-Planckian scales, without modifications from quantum gravity. Second, it necessitates a quantum-to-classical transition in which fluctuations of a homogeneous quantum state become the classical inhomogeneities seen in the CMB. Recently, an alternative paradigm has been proposed in which such inhomogeneities are present from the very beginning, emerging from the assumed discreteness of spacetime at the Planck scale predicted by certain approaches to quantum gravity. Within this framework, scale-invariant scalar perturbations are generated naturally, without relying on trans-Planckian assumptions or invoking a quantum-to-classical transition. Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales. Here, we extend the aforementioned proposal to the most realistic case of a quasi-de Sitter expansion; in particular, we compute the scalar perturbation spectrum as a function of the slow-roll parameters, systematically encoded through the Hubble flow functions.

💡 Research Summary

The paper proposes a novel alternative to the standard inflationary mechanism for generating the primordial perturbations observed in the cosmic microwave background (CMB). In the conventional picture, quantum fluctuations of an initially homogeneous Bunch‑Davies vacuum are stretched by an almost de Sitter expansion, and a separate “quantum‑to‑classical” transition is invoked to turn these fluctuations into classical inhomogeneities. This framework suffers from two well‑known conceptual problems: (i) the trans‑Planckian issue, which assumes that quantum field theory remains valid for modes whose wavelengths are far below the Planck length, and (ii) the lack of a physical mechanism that breaks the perfect symmetry of the initial vacuum state.

The authors address both problems by postulating that spacetime is fundamentally discrete at the Planck scale, as suggested by several approaches to quantum gravity. This discreteness is assumed to excite the inflaton (or effective scalar) modes already at the moment when a smooth field‑theoretic description first becomes applicable. Consequently, the initial quantum state of each mode is not the adiabatic vacuum but a highly excited, inhomogeneous state determined by the underlying granularity. Once the mode’s physical wavelength is stretched beyond the Planck length by the rapid expansion, it behaves as an ultra‑damped harmonic oscillator; its expectation value follows the classical equation of motion (Ehrenfest theorem), while quantum fluctuations around this mean freeze when the mode crosses the Hubble horizon. In this way, the “quantum‑to‑classical” transition is replaced by a unitary evolution from an initially excited state.

The paper first illustrates the mechanism in an exact de Sitter background, showing how the Planck‑scale excitation leads to a scale‑invariant power spectrum. It then generalizes the analysis to a realistic quasi‑de Sitter (slow‑roll) inflationary phase. The authors adopt the Hubble‑flow function formalism (ε₁, ε₂, …) to parametrize deviations from a pure de Sitter expansion in a model‑independent way. Using the Mukhanov‑Sasaki variable, they solve the mode equation with the new initial conditions and expand the resulting scalar power spectrum to first order in the slow‑roll parameters. The final expression reads

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