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Velocities as a probe of dark sector interactions

Kazuya Koyama, Roy Maartens, Yong-Seon Song

TL;DR

The paper analyzes possible non-gravitational couplings between dark matter and dark energy within General Relativity and develops covariant perturbation theory to understand how such interactions modify the continuity and Euler equations. By classifying interactions into those that affect only the background, those modifying the continuity equation, and those altering the Euler equation, it identifies observable signatures in galaxy velocities, weak lensing, and redshift-space distortions. The authors propose concrete cosmological tests to detect breakdowns of the continuity equation or weak equivalence principle for dark matter, offering a framework to constrain dark sector physics and distinguish these effects from modified gravity. This work thus provides a pathway to probe dark sector interactions using cosmological data, with implications for the underlying nature of dark matter and dark energy.

Abstract

Dark energy in General Relativity is typically non-interacting with other matter. However, it is possible that the dark energy interacts with the dark matter, and in this case, the dark matter can violate the universality of free fall (the weak equivalence principle). We show that some forms of the dark sector interaction do not violate weak equivalence. For those interactions that do violate weak equivalence, there are no available laboratory experiments to probe this violation for dark matter. But cosmology provides a test for violations of the equivalence principle between dark matter and baryons -- via a test for consistency of the observed galaxy velocities with the Euler equation.

Velocities as a probe of dark sector interactions

TL;DR

The paper analyzes possible non-gravitational couplings between dark matter and dark energy within General Relativity and develops covariant perturbation theory to understand how such interactions modify the continuity and Euler equations. By classifying interactions into those that affect only the background, those modifying the continuity equation, and those altering the Euler equation, it identifies observable signatures in galaxy velocities, weak lensing, and redshift-space distortions. The authors propose concrete cosmological tests to detect breakdowns of the continuity equation or weak equivalence principle for dark matter, offering a framework to constrain dark sector physics and distinguish these effects from modified gravity. This work thus provides a pathway to probe dark sector interactions using cosmological data, with implications for the underlying nature of dark matter and dark energy.

Abstract

Dark energy in General Relativity is typically non-interacting with other matter. However, it is possible that the dark energy interacts with the dark matter, and in this case, the dark matter can violate the universality of free fall (the weak equivalence principle). We show that some forms of the dark sector interaction do not violate weak equivalence. For those interactions that do violate weak equivalence, there are no available laboratory experiments to probe this violation for dark matter. But cosmology provides a test for violations of the equivalence principle between dark matter and baryons -- via a test for consistency of the observed galaxy velocities with the Euler equation.

Paper Structure

This paper contains 11 sections, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Interacting Dark Energy
  3. Different types of interaction
  4. Continuity and Euler equations unchanged
  5. Continuity equation modified
  6. Euler equation modified
  7. Testing for dark sector interactions
  8. Continuity and Euler equations unchanged
  9. Test of the continuity equation
  10. Test of weak equivalence principle
  11. Conclusions

Figures (3)

  • Figure 1: The ratio between the true matter density obtained from structure formation and the density estimated from geometrical tests assuming the non-interacting adiabatic behaviour $\rho_m \propto a^{-3}$.
  • Figure 2: The breakdown of the continuity equation by an interacting dark energy model. In this model, $v_b=v_c$ and $\delta_c'-k^2 v_c = a \Gamma_x (\rho_x/\rho_c)\delta_c$.
  • Figure 3: The breakdown of the weak equivalence principle for dark matter. In this model, the continuity equation is not broken but $v_c \neq v_b$.