The Big Bang's Backward Music ✛ ✎ ✦

Original: "Inverse-k Primordial Oscillations from a Symbolic Regression Search"
· Ze-Yu Peng, Qing-Yu Lan, Yun-Song Piao
arXiv:2607.04925 · 2026-07-06 · arXiv non-exclusive · independent analysis · 1 min
In ancient light, an algorithm stumbled upon oscillations where low tones tremble faster than high ones — as if a record is played in reverse.

Almost a century ago, Edwin Hubble noticed that galaxies are rushing apart: the Universe expands. But what was inflating it in the first moments? Inflation theory, born from the ideas of Alan Guth and Andrei Linde, predicted tiny density ripples that later grew into stars. The imprint of those events is preserved in the cosmic microwave background — a faint microwave glow that pervades space. It is captured by radio telescopes and is like an ancient photographic film: develop it, and you see the past.

An ordinary vinyl record encodes bass with a smooth groove and high notes with a dense ripple. Here the pattern is flipped: the slow 'sounds' of space are scribbled with rapid trembling, as if the needle moves from the center to the edge.

To decipher this pattern, they used symbolic regression — an algorithm that sifts through millions of formulas and finds the best one, like a child assembling a construction set without instructions. After feeding it spectra from several surveys, the computer identified oscillations that speed up as the wavelength grows. Numerical simulations confirmed that this model fits the data better than standard ones. It seems that in the early universe, a expansion mechanism with jerks was at work — perhaps due to phantom energy that made space jitter.

That same algorithm which detected the reverse rhythm had earlier, without any hints, derived the law of energy conservation — simply by watching pendulums swing.

P_R(k) = P_{R,0}(k) [1 + f(k)], \quad P_{R,0}(k) = A_s \left( \frac{k}{k_*} \right)^{n_s-1}
The standard power-law spectrum is multiplied by a factor (1+f), where f describes the sought oscillations, allowing the capture of minuscule deviations from the predictions of the simplest inflation model.
f_X(k) = A_X \cos\left( \omega_X \, \frac{k_*}{k} + \phi_X \right)
Amplitude A_X, frequency ω_X, and phase φ_X for argument k_*/k—this exact form, with a cosine of the inverse wave number, was picked out by symbolic regression as the best description of the data.
Scientists
Alan GuthAlexander FriedmannAndrei LindeGeorges LemaîtreJames PeeblesAdam Riess
Concepts
symbolic regression fundamental tone autoregressive model template first principles calculations