# Constraints on interacting dynamical dark energy and a new test for $\Lambda$CDM

## TL;DR

This paper derives a general differential equation constraining the equation of state of interacting dynamical Dark Energy and proposes a new observable test to distinguish it from the standard $\\Lambda$CDM model.

## Contribution

It introduces a model-independent differential equation for $w(t)$ and $Q(t)$, and proposes a novel observable for testing $\\Lambda$CDM against interacting dark energy scenarios.

## Key findings

- Derived a differential equation linking $w(t)$ and $Q(t)$ for interacting dark energy.
- Proposed a new observable based on kinematic variables and density parameters.
- Provided a framework for testing $\\Lambda$CDM without relying on specific models.

## Abstract

We consider a generic description of interacting dynamical Dark Energy, characterized by an equation of state with a time dependent coefficient $w(t)$, and which may interact with both radiation and matter. Without referring to any particular cosmological model, we find a differential equation which must be satisfied by $w(t)$ and involving the function $Q(t)$ which describes the interaction between Dark Energy and the other cosmological fluids. The relation we find represents a constraint for various models of interacting dynamical Dark Energy. In addition, an observable is proposed, depending on kinematic variables and on density parameters, which may serve as a new test for $\Lambda$CDM.