Geodesic completion of big bangs from emergent geometry

TL;DR

This paper explores how emergent geometry in k-essence models can lead to non-singular bounces in cosmology, with a focus on the role of disformal metrics and causal frames.

Contribution

It demonstrates that emergent geometry allows for a robust, non-singular bounce in cosmology through disformal metrics and sign changes in the Einstein-frame lapse.

Findings

Disformal metrics define a causal frame with hyperbolic equations.

Einstein-frame lapse passes through zero and changes sign.

Spontaneous time-reversal occurs, enabling a non-singular bounce.

Abstract

Chaplygin gas and other k-essence models exhibit emergent geometry, with perturbations propagating on an acoustic metric disformally related to the Einstein-frame metric. For superluminal sound speed, we identify the disformal metric as the "causal frame," since choosing a finite causal-frame lapse yields hyperbolic equations of motion for fields propagating in either frame. We show that with a phantom Chaplygin gas, the Einstein-frame lapse is forced to pass smoothly through zero and change sign while the causal-frame lapse remains positive. As a result, Einstein-frame degrees of freedom (including the scale factor) undergo spontaneous time-reversal while the Chaplygin gas evolves monotonically, enforcing a robust non-singular bounce even in the presence of additional matter canonically coupled to the Einstein frame.