[Paper Review] Running Dark Energy and Dark Matter from Dynamical Spacetime

Shreya Banerjee, David Benisty+1 more|arXiv (Cornell University)|Oct 8, 2019

Cosmology and Gravitation Theories4 citations

TL;DR

This paper formulates an action principle for the Running Vacuum Model (RVM) of dark energy and dark matter using a dynamical spacetime vector field and scalar field realization, where the scalar field's kinetic term mimics dark matter and its potential drives dark energy. Although the $Λ$CDM model remains statistically favored by AIC, the work provides a first-order action-based derivation of RVM-type dynamics, offering a framework for future extensions with running vacuum and interacting dark sectors.

ABSTRACT

Running Dark Energy and Dark Matter models are candidates to resolve the Hubble constant tension. However the model does not consider a Lagrangian formulation directly. In this paper we formulate an action principle where the Running Vacuum Model (RVM) is obtained from an action principle, with a scalar field model for the whole dark components. The Dynamical Spacetime vector field $χ_μ$ is a Lagrange multiplier that forces the kinetic term of the scalar field to behave as the modified dark matter. When we replace the vector field by a derivative of a scalar the model predicts diffusion interactions between the dark components with a different correspondence to the RVM. We test the models with the Cosmic Chronometers, Type Ia Supernova, Quasars, Gamma ray Bursts and the Baryon Acoustic Oscillations data sets. We find that $Λ$CDM is still the best model. However this formulation suggests an action principle for the $Λ$CDM, the RVM model and other extensions.

Motivation & Objective

• To address the lack of a fundamental action principle for the Running Vacuum Model (RVM), a leading candidate to resolve the Hubble tension and $σ_8$ tension.
• To unify dark energy and dark matter within a single scalar field framework using a dynamical spacetime vector field as a Lagrange multiplier.
• To explore the correspondence between the dynamical spacetime (DST) model and the RVM, particularly in the context of modified gravity and running vacuum energy.
• To test the model against observational data including Cosmic Chronometers, Type Ia Supernovae, Quasars, Gamma-Ray Bursts, and Baryon Acoustic Oscillations.
• To compare the DST and its diffusive extension with $Λ$CDM using information criteria like AIC, assessing model fitness.

Proposed method

• Formulate an action principle where the dynamical spacetime vector field $\chi_\mu$ acts as a Lagrange multiplier to enforce a modified kinetic term for a scalar field, mimicking dark matter behavior.
• Replace the vector field $\chi_\mu$ with the derivative of a scalar field to derive a diffusive interaction model between dark energy and dark matter components.
• Derive the Friedmann equations for the DST and diffusive models, showing their asymptotic correspondence to the RVM with running $\Omega_\Lambda(H)$, $\nu$, and $\alpha$ parameters.
• Use observational data sets: Cosmic Chronometers (CC), Type Ia Supernovae (SNe Ia), Quasars, Gamma-Ray Bursts (GRB), and Baryon Acoustic Oscillations (BAO) to constrain model parameters.
• Apply the Akaike Information Criterion (AIC) to compare model fitness, with $\Lambda$CDM as the benchmark.
• Set priors on cosmological parameters: $\Omega_m \in [0.1, 0.4]$, $H_0 \in [50, 100]$, $r_d \in [130, 160]$, and $\beta \in [0, 2]$ for the additional parameter in the diffusive model.

Experimental results

Research questions

• RQ1 Can a consistent action principle be constructed for the Running Vacuum Model (RVM) that unifies dark energy and dark matter without introducing additional fundamental fields?
• RQ2 How does the dynamical spacetime vector field $\chi_\mu$ enforce a kinetic term that effectively behaves as dark matter in the scalar field model?
• RQ3 What is the correspondence between the dynamical spacetime (DST) model and the RVM, particularly in terms of the running vacuum energy density $\Omega_\Lambda(H)$?
• RQ4 Does the diffusive extension of the DST model, derived by replacing $\chi_\mu$ with a scalar field derivative, yield a physically viable interaction between dark energy and dark matter components?
• RQ5 Is the DST or its diffusive extension statistically favored over $\Lambda$CDM when tested against a combination of late-time cosmological data sets?

Key findings

• The dynamical spacetime (DST) model yields $\Omega_m = 0.2780 \pm 0.0214$, $\Omega_\Lambda = 0.703 \pm 0.024$, and $H_0 = 69.63 \pm 1.10$ km/s/Mpc, consistent with other models but slightly lower than $\Lambda$CDM.
• The diffusive model gives $\Omega_m = 0.278 \pm 0.021$, $\Omega_\Lambda = 0.704 \pm 0.0203$, and $H_0 = 69.33 \pm 1.24$ km/s/Mpc, showing close agreement with the DST model.
• The BAO scale $r_d$ is constrained to $147.1 \pm 2.45$ Mpc in the DST model and $146.7 \pm 2.64$ Mpc in the diffusive model, both within the range of Planck and SDSS measurements.
• The AIC value for $\Lambda$CDM is $264.7$, lower than $267.0$ for the DST model and $269.9$ for the diffusive model, indicating $\Lambda$CDM remains the statistically preferred model.
• The $\Lambda$CDM model can be recovered as a limit when $\lambda_2 = 0$, confirming consistency of the action-based framework with the standard model.
• The model confirms that radiation cannot deviate from $1/a^4$ due to conformal invariance, ruling out running dark radiation in this Lagrangian framework.