Emergence of cosmic structure from Planckian discreteness

TL;DR

This work challenges the standard inflationary mechanism by proposing that Planck-scale spacetime discreteness seeds primordial inhomogeneities, avoiding trans-Planckian and quantum-to-classical issues. It develops a stochastic generation model in quasi-de Sitter space, deriving a Langevin-like dynamics for each mode, and expresses the scalar power spectrum through the diffusion coefficient γ and slow-roll Hubble flow functions. The authors obtain a nearly scale-invariant curvature spectrum with amplitude A_s and tilt n_s = 1 - 2ε_1 - ε_2, and show that a Planck-scale H during inflation can reproduce observed CMB amplitudes with γ ≈ 10^{-9} ε_1, while predicting a suppressed tensor signal. This framework links Planck-scale discreteness to observable CMB features and offers a quantum-gravity-inspired alternative to inflation, with implications for Lorentz invariance and the emergence of classical spacetime.

Abstract

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.