The description of the subsequent dynamics and related questions in cosmology requires an understanding of the Standard Model quantum fields and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge. For example, a quantum field simulator can lead to insights.

Researchers at the University of Heidelberg have created an effective, manipulable spacetime in a laboratory experiment. They were able to generate an entire family of warped universes in their study of ultracold quantum gases to test and compare various cosmological theories with the predictions of a quantum field theory model.

prof. Dr. Markus Oberthaler, a researcher at the Kirchhoff Institute for Physics at the University of Heidelberg, said: *“However, it is conceivable that our universe was curved in its initial phase. Therefore, studying the consequences of warped spacetime is a pressing research question.”*

In this study, scientists demonstrated a quantum field simulator in a two-dimensional Bose-Einstein condensate. It consists of a cloud of potassium atoms cooled to just a few nanokelvins above absolute zero.

prof. Oberthaler explains, *“The Bose-Einstein condensate is a perfect background against which the smallest excitations, i.e. changes in the energy state of the atoms, become visible. The shape of the atomic cloud determines the dimensionality and properties of spacetime on which these excitations propagate as waves. In our universe there are three dimensions of space and a fourth: time.”*

In the experiment of Heidelberg physicists, the atoms are in a thin layer. Due to the two-dimensional nature of space, the excitations can only propagate in two spatial directions. Moreover, the atom cloud is remarkably malleable in the last two dimensions, making it conceivable to realize curved spacetimes. The wave-like excitations of the Bose-Einstein condensate can propagate at different speeds depending on how closely the atoms interact.

prof. Dr. Stefan Florchinger said: *“For the waves on the condensate, the speed of propagation depends on the density and the interaction of the atoms. This allows us to create conditions like those in an expanding universe.”*

A theoretical quantum field model was developed to quantitatively compare the experimental results.

Celia Viermann, the study’s lead author, said: *“With the help of the quantum field simulator, cosmic phenomena, such as the production of particles based on the expansion of space, and even the curvature of spacetime can be made measurable. Cosmological problems normally occur on an unimaginably large scale. Precisely being able to study them in the lab opens up completely new possibilities in research by enabling us to experimentally test new theoretical models.”*

Markus Oberthaler, whose research group is also part of the STRUCTURES Cluster of Excellence at Ruperto Carola, said: *“Studying the interplay of warped spacetime and quantum mechanical states in the lab will keep us busy for some time to come.”*

**Magazine reference:**

- C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, Á. Parra-López, M. Tolosa-Simeón, N. Sánchez-Kuntz, T. Haas, H. Strobel, S. Stefan Flörchinger, MK Oberthaler: quantum field simulator for dynamics in curved spacetime. Nature (November 9, 2022). DOI: 10.1038/s41586-022-05313-9