[Paper Review] Cosmological future singularities in interacting dark energy models

Jose Beltrán Jiménez, Diego Rubiera-García+2 more|arXiv (Cornell University)|Jul 21, 2016

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates future cosmological singularities in interacting dark energy-dark matter models, demonstrating that all known singularities (e.g., Big Rip, Sudden, Big Freeze) can be mapped to divergences in the interaction term $Q$, termed $Q$-singularities. It further identifies a novel singularity type driven by the divergence of the time derivative of dark energy's equation of state, signaling potential instabilities in perturbations despite regular background evolution.

ABSTRACT

The existence of interactions between dark matter and dark energy has been widely studied, since they can fit well the observational data and may provide new physics through such an interaction. In this work we analyze these models and investigate their potential relation with future cosmological singularities. We find that every future singularity found in the literature can be mapped into a singularity of the interaction term, that we call $Q$-singularity, where the energy flow between the dark components diverges. Furthermore, this framework allows to identify a new type of future singularity induced by the divergence of the first derivative of the dark energy equation of state parameter.

Motivation & Objective

• To explore the connection between interacting dark energy models and future cosmological singularities.
• To determine whether known future singularities can be induced by specific forms of the interaction term $Q$ in dark energy-dark matter coupled systems.
• To investigate whether new types of singularities emerge from the dynamics of the dark energy equation of state's time derivative.
• To assess the implications of such singularities for cosmological stability and perturbation theory.
• To provide a unified framework where all future singularities arise from singularities in the interaction term $Q$.

Proposed method

• The study analyzes continuity equations with a phenomenological interaction term $Q$, ensuring total energy conservation while allowing energy flow between dark matter and dark energy.
• It employs a general parametrization of the Hubble parameter and dark energy equation of state to derive asymptotic solutions near singularities.
• Analytical solutions are derived for specific power-law forms of the interaction term, particularly $Q \propto \rho_{DE}^n$, to map singularities to divergences in $Q$.
• Phase space analysis and numerical solutions are used to validate the analytical findings and confirm the emergence of singularities like Big Rip, Sudden, and Big Freeze.
• The time derivative of the dark energy equation of state, $\dot{w}_{DE}$, is examined to identify a new singularity type not tied to background divergence.
• The framework is tested using specific interaction models, including those proportional to $\rho_{DE}^n$, to demonstrate how they induce effective phantom behavior even when $w_{DE} > -1$.

Experimental results

Research questions

• RQ1 Can all known future cosmological singularities be traced to a divergence in the interaction term $Q$ between dark energy and dark matter?
• RQ2 Does the time derivative of the dark energy equation of state, $\dot{w}_{DE}$, give rise to a new type of singularity not previously classified?
• RQ3 Can an interaction term induce a Big Rip singularity even if the dark energy equation of state satisfies $w_{DE} > -1$?
• RQ4 How do different power-law forms of the interaction term $Q \propto \rho_{DE}^n$ lead to distinct types of future singularities?
• RQ5 What are the implications of $Q$-singularities for the stability of cosmological perturbations?

Key findings

• All known future singularities (Big Rip, Sudden, Big Freeze) can be mapped to a divergence in the interaction term $Q$, which the authors term a $Q$-singularity, indicating a divergent energy flow at finite time.
• A novel type of future singularity is identified, characterized by the divergence of the time derivative of the dark energy equation of state, $\dot{w}_{DE} \to \infty$, which may signal instabilities in perturbations despite regular background evolution.
• For $n=3$, the interaction term $Q \propto \rho_{DE}^3$ leads to a Sudden (Type II) singularity with $H$ finite but $\dot{H} \to \infty$ at finite time $t_s$, as $H \simeq C\sqrt{t_s - t} + H_s$.
• For $n=5/3$, the interaction induces a Big Freeze (Type III) singularity with $H \to \infty$ as $H \simeq C(t_s - t)^{-1/2}$, while the scale factor remains finite.
• The interaction term can induce effective phantom behavior ($w_{\text{eff}} < -1$) even when $w_{DE} > -1$, enabling a Big Rip singularity without requiring intrinsic phantom dark energy.
• Phase space analysis and numerical solutions confirm the analytical asymptotic behavior, validating the emergence of singularities across different $n$ values and interaction forms.