Cosmological implications of ultralight axionlike fields

Abstract

Cosmological observations are used to test for imprints of an ultralight axionlike field (ULA), with a range of potentials $V(\ensuremath{\phi})\ensuremath{\propto}[1\ensuremath{-}\mathrm{cos}(\ensuremath{\phi}/f){]}^{n}$ set by the axion-field value $\ensuremath{\phi}$ 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 parametrized by the redshift ${z}_{c}$ when the field becomes dynamical, the fractional energy density ${f}_{{z}_{c}}\ensuremath{\equiv}{\mathrm{\ensuremath{\Omega}}}_{a}({z}_{c})/{\mathrm{\ensuremath{\Omega}}}_{\mathrm{tot}}({z}_{c})$ 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 $1+{z}_{c}\ensuremath{\lesssim}10$. When $3\ifmmode\times\else\texttimes\fi{}{10}^{4}\ensuremath{\gtrsim}1+{z}_{c}\ensuremath{\gtrsim}10$, ${f}_{{z}_{c}}$ is constrained to be $\ensuremath{\lesssim}0.004$ for $n=1$ and ${f}_{{z}_{c}}\ensuremath{\lesssim}0.02$ for the other two potentials. The constraints then relax with increasing ${z}_{c}$. These results have implications for 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.