Two-field disformal transformation and mimetic cosmology

TL;DR

This paper extends disformal transformations to two scalar fields, deriving a mimetic cosmology model that mimics dark matter and analyzing perturbations showing stability and propagation characteristics.

Contribution

It introduces a two-field extension of mimetic gravity via disformal transformations and analyzes its perturbation stability and dynamics.

Findings

Adiabatic perturbation is frozen during evolution.

Entropy mode propagates with sound speed equal to unity.

Model mimics dark matter behavior at the background level.

Abstract

We extend the disformal transformation to models with two scalar fields and look at its singular limit. Solving the eigentensor equation for the Jacobian of the transformation of the metrics we find the two-field extension of the mimetic scenario in the singular conformal limit. At the background level the setup mimics the roles of dark matter cosmology. We decompose the perturbations into the adiabatic and entropy modes in which the adiabatic perturbation is tangential to the classical trajectory while the entropy mode is perpendicular to it. We show that the adiabatic mode is frozen while the entropy mode propagates with the sound speed equal to unity with no instabilities.