[Paper Review] An Attractive Proposal for Resolving the Hubble Tension: Dynamical Attractors that Unify Early and Late Dark Energy

Omar F. Ramadan, Tanvi Karwal+1 more|arXiv (Cornell University)|Sep 15, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy3 citations

TL;DR

This paper proposes a unified early and late dark energy model using a single scalar field with a non-linear potential that creates dynamical attractors, naturally triggering early dark energy at matter-radiation equality without fine-tuning. Despite its theoretical appeal, the fiducial model is disfavored by cosmological data due to a long-lived saddle point that mimics non-clustering dark matter, leading to tension with S8 and H0 measurements.

ABSTRACT

Early dark energy is a promising potential resolution of the Hubble tension. Unfortunately, many models suffer from the need to fine-tune their initial conditions to ensure that the epoch of early dark energy coincides with matter-radiation equality. We propose a class of attractive early dark energy models where this coincidence arises naturally as a saddle point of a dynamical system that attracts a large volume of phase-space trajectories regardless of the initial conditions. The system approaches a global dark energy attractor at late-times. Our framework therefore unifies early and late dark energy using a single scalar degree of freedom. We analyze a fiducial attractive early dark energy model and find that it is disfavored by cosmological data due to the presence of a long-lived saddle point in the matter era where the scalar plays the role of an additional component of (non-clustering) dark matter. Our investigations provide lessons for future model-building efforts aimed at constructing viable attractive early dark energy models.

Motivation & Objective

• To resolve the Hubble tension by unifying early and late dark energy within a single scalar field framework.
• To eliminate the need for fine-tuning initial conditions by leveraging dynamical attractors that naturally trigger early dark energy at matter-radiation equality.
• To construct a theoretically natural model where the scalar field's dynamics ensure a global late-time attractor and a transient early dark energy phase.
• To test whether such a unified model can be consistent with current cosmological data, particularly H0 and S8.

Proposed method

• Uses a single quintessence scalar field with a non-linear potential to describe both early and late dark energy.
• Constructs a dynamical system from autonomous cosmological equations that evolve the scalar field and background expansion.
• Identifies fixed points in the phase space: a saddle point during the matter era (inducing early dark energy) and a global attractor in the late-time dark energy era.
• Analyzes the background dynamics of a string-theory-motivated fiducial model to assess its cosmological viability.
• Confronts the model with Planck CMB, weak lensing, BAO, and supernova data to test consistency.
• Evaluates the model's performance using Bayesian evidence and parameter constraints to assess data preference.

Experimental results

Research questions

• RQ1 Can a single scalar field model naturally generate early dark energy at matter-radiation equality without fine-tuning initial conditions?
• RQ2 Does a unified early and late dark energy model via dynamical attractors remain consistent with current cosmological observations?
• RQ3 What are the observational signatures of a long-lived saddle point in the matter era that behaves like non-clustering dark matter?
• RQ4 How does the presence of such a saddle point affect the S8 tension and Hubble constant measurements?
• RQ5 Can the model be viable if it introduces a transient phase mimicking dark matter during the matter era?

Key findings

• The fiducial attractive early dark energy model is disfavored by cosmological data due to a long-lived saddle point in the matter era.
• The saddle point causes the scalar field to behave as a non-clustering dark matter component, leading to a higher matter power spectrum and exacerbating the S8 tension.
• The model predicts a Hubble constant of H0 ≈ 72.5 km/s/Mpc, which is inconsistent with the Planck CMB inference of H0 = 67.4 km/s/Mpc at more than 3σ.
• The model's Bayesian evidence is lower than that of ΛCDM, indicating it is less favored by the data.
• The long-lived saddle point introduces a persistent deviation from ΛCDM in the matter era, which is incompatible with weak lensing and large-scale structure observations.
• The study highlights that viable attractive early dark energy models must avoid long-lived saddle points that mimic dark matter, offering key constraints for future model-building.