# Time crystals in primordial perturbations

## TL;DR

This paper investigates the theoretical possibility of cosmological time crystals during inflation, showing they could induce observable periodic oscillations in the primordial perturbation spectrum, revealing crystalline patterns.

## Contribution

It introduces the concept of time crystals in the inflationary universe and analyzes their impact on primordial perturbations, a novel idea in cosmology.

## Key findings

- Time crystals can cause periodic oscillations in the primordial spectrum.
- Oscillation patterns depend on specific time crystal parameters.
- Crystalline patterns in the spectrum encode properties of the time crystal.

## Abstract

Cosmological time crystal (TC) corresponds to a matter state where the periodic motion of field forms a limit cycle in its phase space. We explore what would happen if it existed in inflationary phase. It is found that the limit cycle responsible for TC will inevitably cause the periodic oscillation of the primordial perturbation spectrum. The oscillatory patterns of the spectrum depend on the TC parameters, and so encode the crystalline patterns of TC.