Cosmological implications of ultra-light axion-like fields

Abstract: Cosmological observations are used to test for imprints of an ultra-light axion-like field (ULA), with a range of potentials $V(\phi)\propto[1-\cos(\phi/f)]^n$ set by the axion-field value $\phi$ and decay constant $f$. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For $n!=!1$, once dynamical, the axion energy density dilutes as matter; for $n!=!2$ it dilutes as radiation and for $n!=!3$ it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual $n=1$ case. ULA models are parameterized by the redshift $z_c$ when the field becomes dynamical, the fractional energy density $f_{z_c} \equiv \Omega_a(z_c)/\Omega_{\rm tot}(z_c)$ in the axion field at $z_c$, and the effective sound speed $c_s^2$. Using Planck, BAO and JLA data, constraints on $f_{z_c}$ are obtained. ULAs are degenerate with dark energy for all three potentials if $1+z_c \lesssim 10$. When $3\times10^4 \gtrsim 1+z_c \gtrsim 10 $, $f_{z_c}$ is constrained to be $ \lesssim 0.004 $ for $n=1$ and $f_{z_c} \lesssim 0.02 $ for the other two potentials. The constraints then relax with increasing $z_c$. These results strongly constrain ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal.

Overview of "Cosmological implications of ultra-light axion-like fields"

The paper titled "Cosmological implications of ultra-light axion-like fields" examines the potential impacts of ultra-light axion-like fields (ULAs) on cosmology, focusing on their role in addressing existing cosmological tensions and their viability as dark matter candidates. The study provides a detailed analysis of ULAs using cosmological data sets and proposes a method to incorporate ULA perturbations into existing cosmological models.

Ultra-light Axion-like Fields: Dynamics and Potential

The authors investigate scalar fields, referred to as ULAs, characterized by a potential $V(\phi)\propto[1-\cos(\phi/f)]^n$, where $\phi$ is the axion field value and $f$ is the decay constant. The dynamics of ULAs are initially frozen due to Hubble friction, but become dynamic as the universe evolves, transitioning into an oscillatory state. Depending on the potential exponent $n$, ULAs can dilute as matter ($n=1$), radiation ($n=2$), or faster than radiation ($n=3$). The study generalizes the traditional effective fluid approximation to accommodate fields with various forms of potentials, thereby enhancing the understanding of their impacts on cosmic evolution.

Implications for Cosmological Models

The study evaluates the implications of ULAs across different epochs of the universe, considering their effect on the expansion history and cosmic microwave background (CMB) anisotropies. By incorporating Planck data along with Baryon Acoustic Oscillations (BAO) and Joint Light-Curve Analysis (JLA), the paper constrains the fractional energy density of ULAs, $f_{z_c}$, at different dynamical redshifts, $z_c$. Through a meticulous analysis, the authors find stringent constraints on $f_{z_c}$, which relax as $z_c$ increases. Specifically, ULAs are shown to be degenerate with dark energy for $1+z_c \lesssim 10$, with constraints tightening for $3 \times 10^4 \gtrsim 1+z_c \gtrsim 10$.

Analysis of Perturbations

The paper delves into the linear perturbations of ULAs, utilizing an effective fluid approach to account for the perturbative dynamics. This approach provides a comprehensive mapping between model parameters and theory parameters, allowing for the identification of key effects and constraints linked to the dynamics of ULAs. By studying perturbations across various scales, the research demonstrates that although ULA perturbations can mimic characteristics of both dark matter and radiation, distinctive features helped differentiate these effects in the observational data.

Constraints and Observational Predictions

The research places constraints on the presence of ULAs through observational data, devising a mapping from the theoretical model parameters to observable effects. This study confirms that the current measurements, such as those from the Planck mission, limit the contribution of ULAs to the energy budget at early redshifts to be minimal. Despite theoretical models suggesting ULAs might mitigate some cosmological tensions, such as those concerning the Hubble constant and the EDGES 21 cm absorption signal, the constraints derived in this study indicate such scenarios are less viable under current data interpretations.

Future Directions and Implications

While the proposed models of ULAs offer intriguing possibilities for resolving cosmological tensions and enhancing the understanding of dark matter and dark energy, the constraints and observational results presented imply significant limitations on their practical application within existing cosmological frameworks. Future experiments with high precision, such as CMB-S4, may yield deeper insights into the effects of ULA perturbations, potentially addressing the limitations highlighted in the study and paving paths for new breakthroughs in cosmic physics.

In summary, the paper provides a thorough exploration of ULAs, addressing their cosmological implications with a robust analytical approach and offering a roadmap for further inquiries into this intriguing aspect of cosmology. The innovative method for parameterizing ULA effects represents a significant advance, though the constraints imposed by current data temper the enthusiasm for ULAs as a solution to existing cosmological challenges.