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Slow-Roll Suppression of Adiabatic Instabilities in Coupled Scalar Field-Dark Matter Models

Pier Stefano Corasaniti

TL;DR

This work investigates the stability of linear perturbations in interacting scalar field–dark matter cosmologies with a Chameleon-like runaway potential and a dilatonic coupling. By formulating the background and perturbation equations and introducing a unified fluid description, it derives conditions for stability through the adiabatic and non-adiabatic regimes, highlighting the roles of the adiabatic sound speed $c_{aT}^2$ and the rest-frame sound speed $c_{sT}^2$. The key finding is that in the adiabatic slow-roll regime, negative $c_{aT}^2$ is strongly suppressed by slow-roll, yielding $c_{sT}^2\approx0$ and stable perturbation growth for moderate coupling $\beta$; instabilities only occur for $\beta$ much larger than the gravitational strength or in non-adiabatic large-field oscillations, where scalar fluctuations grow and transfer to dark matter. These results suggest that Chameleon-like cosmologies can be compatible with structure formation without encountering perturbative instabilities under natural parameter ranges.

Abstract

We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar self-interaction potential as in the case of the Chameleon model. We show that in the "adiabatic" background regime of the system the rise of unstable growing modes of the perturbations is suppressed by the slow-roll dynamics of the field. Furthermore the coupled system behaves as an inhomogeneous adiabatic fluid. In contrast instabilities may develop for large values of the coupling constant, or along non-adiabatic solutions, characterized by a period of high-frequency dumped oscillations of the scalar field. In the latter case the dynamical instabilities of the field fluctuations, which are typical of oscillatory scalar field regimes, are amplified and transmitted by the coupling to dark matter perturbations.

Slow-Roll Suppression of Adiabatic Instabilities in Coupled Scalar Field-Dark Matter Models

TL;DR

This work investigates the stability of linear perturbations in interacting scalar field–dark matter cosmologies with a Chameleon-like runaway potential and a dilatonic coupling. By formulating the background and perturbation equations and introducing a unified fluid description, it derives conditions for stability through the adiabatic and non-adiabatic regimes, highlighting the roles of the adiabatic sound speed and the rest-frame sound speed . The key finding is that in the adiabatic slow-roll regime, negative is strongly suppressed by slow-roll, yielding and stable perturbation growth for moderate coupling ; instabilities only occur for much larger than the gravitational strength or in non-adiabatic large-field oscillations, where scalar fluctuations grow and transfer to dark matter. These results suggest that Chameleon-like cosmologies can be compatible with structure formation without encountering perturbative instabilities under natural parameter ranges.

Abstract

We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar self-interaction potential as in the case of the Chameleon model. We show that in the "adiabatic" background regime of the system the rise of unstable growing modes of the perturbations is suppressed by the slow-roll dynamics of the field. Furthermore the coupled system behaves as an inhomogeneous adiabatic fluid. In contrast instabilities may develop for large values of the coupling constant, or along non-adiabatic solutions, characterized by a period of high-frequency dumped oscillations of the scalar field. In the latter case the dynamical instabilities of the field fluctuations, which are typical of oscillatory scalar field regimes, are amplified and transmitted by the coupling to dark matter perturbations.

Paper Structure

This paper contains 8 sections, 16 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Interacting Scalar Field-Dark Matter Model
  3. Background and Linear Perturbation Equations
  4. Effective Unified Fluid Description
  5. Scalar Field Dynamics and Evolution of Density Perturbations
  6. Adiabatic Regime
  7. Non-Adiabatic Regime: Large Field Oscillations
  8. Conclusions

Figures (3)

  • Figure 1: Scalar field effective potential at $z=10^3,10,3$ and $0$ (solid lines) for $\alpha=0.2$ and $\beta=1$. The amplitude of the scalar potential $M$ is set such that today $\Omega_{DM}=0.24$ ($\Omega_\phi=1-\Omega_{DM}$). The dashed line corresponds to the position of the minimum of the effective potential at different epochs.
  • Figure 2: Upper left panel: evolution of the scalar field equation of state $w_\phi$ and effective unified fluid equation of state $w_T$; Right upper panel: evolution of the scalar field velocity with respect to the Hubble rate; Lower left panel: redshift evolution of the adiabatic sound speed $c_{aT}^2$ and propagation of pressure perturbations $c_{sT}^2$; Right lower panel: Linear growth factor of the dark matter density contrast at $k=10^{-3},10^{-2}$ and $0.1$ Mpc$^{-1}$ .
  • Figure 3: Upper left panel: evolution of the scalar field equation of state $w_\phi$; Right upper panel: evolution of the scalar field; Lower left panel: evolution of the field fluctuations $\delta\phi_{k}$ at $k=10^{-3},10^{-2}$ and $0.1$ Mpc$^{-1}$ respectively; Right lower panel: evolution of dark matter density for $k$-values as in the case of $\delta\phi_k$.