Oscillating scalar fields and the Hubble tension: a resolution with novel signatures (1908.06995v1)

Abstract: We present a detailed investigation of a sub-dominant oscillating scalar field ('early dark energy', EDE) in the context of resolving the Hubble tension. Consistent with earlier work, but without relying on fluid approximations, we find that a scalar field frozen due to Hubble friction until ${\rm log}{10}(z_c)\sim3.5$, reaching $\rho{\rm EDE}(z_c)/\rho_{\rm tot}\sim10$%, and diluting faster than matter afterwards can bring cosmic microwave background (CMB), baryonic acoustic oscillations, supernovae luminosity distances, and the late-time estimate of the Hubble constant from the SH0ES collaboration into agreement. A scalar field potential which scales as $V(\phi) \propto \phi^{2n}$ with $2\lesssim n\lesssim 3.4$ around the minimum is preferred at the 68% confidence level, and the {\em Planck} polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefers a potential which flattens at large field displacements. An MCMC analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at very high significance. This projected sensitivity to the EDE dynamics is mainly driven by improved measurements of the $E$-mode polarization. We also explore new observational signatures of EDE scalar field dynamics: (i) We find that depending on the strength of the tensor-to-scalar ratio, the presence of the EDE might imply the existence of isocurvature perturbations in the CMB. (ii) We show that a strikingly rapid, scale-dependent growth of EDE field perturbations can result from parametric resonance driven by the anharmonic oscillating field for $n\approx 2$. This instability and ensuing potentially nonlinear, spatially inhomogenoues, dynamics may provide unique signatures of this scenario.

Oscillating Scalar Fields and the Hubble Tension

The paper authored by Smith, Poulin, and Amin addresses a significant issue in cosmology known as the "Hubble tension" through the lens of oscillating scalar fields posited as "early dark energy" (EDE). The Hubble tension refers to the discrepancy between measurements of the Hubble constant, $H_0$, derived from early universe observations, such as the cosmic microwave background (CMB), and those from late universe observations, such as supernovae. By introducing a sub-dominant oscillating scalar field, the authors propose a model that reconciles these differing $H_0$ estimates without contradicting existing cosmological observations.

The crux of the paper lies in the exploration of an EDE model in which a scalar field remains 'frozen' due to Hubble friction until a critical redshift of approximately $z_c \sim 3500$. At this point, the field accounts for about 10% of the total energy density of the universe and dilutes faster than matter afterward. This dynamic is posited to bring various cosmological observations—ranging from the CMB to baryonic acoustic oscillations (BAO) to supernovae luminosity distances and local measurements of $H_0$ by the SH0ES collaboration—into concordance.

Methodology and Findings

The authors have pursued a detailed paper of the scalar field dynamics within the standard cosmological framework, incorporating a full solution to the linearized scalar field equations rather than relying on fluid approximations commonly used in past research.

Utilizing a Monte Carlo Markov Chain (MCMC) analysis, they demonstrate that the model allows for a scalar field potential that scales as $V(\phi) \propto \phi^{2n}$ with $2 \lesssim n \lesssim 3.4$, preferred at a 68% confidence level. Notably, the Planck polarization data provides further constraints on perturbation dynamics, indicating a preference for potentials that flatten at large field displacements.

The results highlight that next-generation CMB observations such as CMB-S4 could detect the presence of EDE at significant statistical certainty. The improved measurements of the $E$-mode polarization are primarily responsible for this enhanced sensitivity.

Implications and Future Directions

The model posited in this paper holds several theoretical and practical implications. If validated, it not only resolves the Hubble tension but also suggests that additional components beyond the standard $\Lambda$CDM model are necessary to accurately describe cosmic evolution. This adaptation can influence our theoretical understanding of early universe physics and scalar field dynamics significantly.

Additionally, the research opens avenues for detecting unique observational signatures linked to EDE dynamics. Specifically, the presence of oscillating scalar fields could imply the emergence of isocurvature perturbations in the CMB and a characteristic rapid, scale-dependent growth of EDE field perturbations due to parametric resonance. As anticipated for the $n \approx 2$ case, such dynamics introduce the possibility of nonlinear, spatially inhomogeneous conditions, potentially yielding observational markers in future CMB data or large-scale structure surveys.

Conclusion

In essence, this paper presents a comprehensive and rigorous examination of oscillating scalar fields as a viable solution to the Hubble tension. By addressing constraints imposed by current cosmological data and projecting future observational capabilities, it sets a solid foundation for subsequent investigations aiming to harmonize early- and late-universe observations. Though definitive empirical evidence and further theoretical exploration are needed, the proposed model stands as a promising pathway to resolving one of modern cosmology’s most intriguing debates.