[Paper Review] Rock 'n' Roll Solutions to the Hubble Tension

Prateek Agrawal, Francis-Yan Cyr-Racine+2 more|arXiv (Cornell University)|Apr 1, 2019

Cosmology and Gravitation TheoriesPhysics and Astronomy159 references105 citations

TL;DR

The paper proposes scalar-field models with V(phi) ~ phi^{2n} that inject energy around recombination to ease the Hubble tension; n=2 provides the best fit to Planck, BAO, SH0ES, and Pantheon data, with detailed non-coarse-grained dynamics.

ABSTRACT

Local measurements of the Hubble parameter are increasingly in tension with the value inferred from a $Λ$CDM fit to the cosmic microwave background (CMB) data. In this paper, we construct scenarios in which evolving scalar fields significantly ease this tension by adding energy to the Universe around recombination in a narrow redshift window. We identify solutions with scalar field potential $V \propto ϕ^{2n}$ that have simple asymptotic behavior, both oscillatory (rocking) and rolling. These solutions consistently describe both the field evolution and its fluctuations without approximation. Our findings differ qualitatively from some of the existing literature, which rely upon a coarse-grained fluid description. Combining CMB data with low-redshift measurements, the best fit model has $n=2$ with a significantly higher value of the Hubble constant as compared to a $Λ$CDM fit to the same data. Future measurements of the late-time amplitude of matter fluctuations and of the reionization history could help distinguish these models from competing solutions.

Motivation & Objective

• Motivate and address the Hubble tension by introducing an early-universe energy injection using a rolling scalar field.
• Provide exact, non-approximate solutions for the scalar field evolution and its fluctuations for potentials V ~ phi^{2n}.
• Classify rolling and oscillatory solutions and identify regimes that can peak near recombination without dominating early or late times.
• Assess the impact of these solutions on CMB, BAO, and low-redshift measurements and compare to LambdaCDM.
• Explore whether current datasets prefer nonzero energy injection and how this affects H0 and sigma8 estimates.

Proposed method

• Define a scalar potential V(phi) = V0 (phi/Mpl)^{2n} + V_Lambda to generate a brief energy injection.
• Derive rolling (non-oscillatory) solutions with constant w_phi and relate V(phi) to rho_phi and w_phi.
• Show that rolling solutions arise from Emden-Fowler type equations and classify by n and background w_b.
• Track exact background and perturbation evolution without coarse-graining to capture peak dynamics.
• Fit to cosmological data (Planck, BAO, SH0ES, Pantheon) using MCMC with parameters f_phi_MC and z_c_MC that encode the energy-injection timing and amplitude.
• Compare to coarse-grained fluid approximations and highlight regimes where such approximations fail near the injection peak.

Experimental results

Research questions

• RQ1 Can a localized early-universe energy injection around recombination reduce the CMB sound horizon r_s sufficiently to reconcile H0 with local measurements?
• RQ2 Do scalar-field potentials V(phi) ~ phi^{2n} with rolling or oscillatory behavior provide exact, non-approximate solutions for both background and perturbations that alter CMB observables in a way that addresses the Hubble tension?
• RQ3 How do the timing (z_c) and amplitude (f_phi) of the energy injection correlate with CMB and low-redshift data, and which n values are favored?
• RQ4 What are the caveats and limitations of coarse-grained (cycle-averaged) descriptions for these models, and in which regimes do exact treatments matter most?

Key findings

• Best-fit models occur for n=2, with a notable preference for nonzero energy injection around z_c ~ 3100 when SH0ES data are included.
• The injected energy reduces the baryon-photon sound horizon r_drag, which drives the higher inferred H0 relative to LambdaCDM.
• In these models, increasing f_phi correlates with higher H0 but also with changes to high-l CMB tail and lensing, and tends to raise sigma8.
• The analysis shows that coarse-grained fluid descriptions can misrepresent the peak dynamics, necessitating exact evolution of the scalar field and its perturbations.
• The n=2 model improves fit to Planck+BAO+SH0ES+Pantheon compared with LambdaCDM, but there can be tensions with high-l CMB and lensing data; higher n values broaden the injection and are harder to fit.