Early Universe Constraints on Variations in Fundamental Constants Induced by Ultralight Scalar Dark Matter

Abstract

We study the cosmological impact of ultralight dark matter (ULDM) with a quadratic coupling to Standard Model particles. In addition to the suppression of small-scale power from ULDM itself, the coupling induces a variation of fundamental constants that is modulated by the ULDM oscillatory field value. In this work, we consider the ULDM-induced, time-dependent variation of the fine structure constant and the mass of the electron. These variations modify the predicted abundance of light elements during Big Bang nucleosynthesis (BBN) and the process of recombination, thereby affecting the anisotropies of the cosmic microwave background (CMB). We use CMB anisotropy data and baryon acoustic oscillation measurements to obtain constraints on the variation of couplings over a wide range of ULDM masses. We self-consistently account for the modification of the primordial helium abundance during BBN in computing the CMB power spectra. We find that the allowed ULDM fraction of total dark matter abundance is more constrained for ULDM masses $\lesssim 10^{-26}~\mathrm{eV}$ in the presence of the variations. Moreover, our constraints on the variational couplings for ULDM masses $\lesssim 10^{-27}~\mathrm{eV}$ are stronger than the ones derived from the primordial helium abundance at BBN. Under our ULDM model, the variation of fundamental constants has no appreciable impact on the Hubble constant inferred from CMB data and thus does not present a viable solution to the Hubble tension.

Figures (18)

• Figure 1: Evolution of $m_{\rm th}$ (top) and amount of variation (bottom) for $\alpha$ (left) and $m_e$ (right) with respect to the scale factor $a$. We set $m_\phi = 10^{-16}~\mathrm{eV}$ and $d_\alpha^{(2)} = 10^5$ (left) or $d_{m_e}^{(2)} = 10^5$ (right), and the associated variation of the primordial helium-4 abundance $\delta Y_\mathrm{He}$ is provided in the legends. For the $\alpha$ variation (left), the thermal mass dominates the evolution at early times when $m_{\rm th} > H, m_\phi$, and oscillations are always in effect. For the $m_e$ variation (right), oscillations begin once $m_\mathrm{eff} > H$. In either case, once $H \ll m_\mathrm{th} < m_\phi$, oscillations match onto the case in which the thermal mass is ignored (blue dashed), for which the onset of oscillations is much later, close to $H = m_\phi$ (red vertical dotted).
• Figure 2: Evolution of the variation of $\alpha$ as a function of scale factor for different masses of $\phi$, neglecting the contribution of the thermal mass. We choose the amount of variation such that $\delta Y_\mathrm{He} = 5\%$ from the BBN era, and thus the mass $m_\phi$ determines how significant the variation is during the recombination era. Only the smaller values of $m_\phi$ affect recombination appreciably, with the case of $m_\phi = 10^{-28}~{\rm eV}$ exhibiting oscillations around recombination. Oscillations occur during BBN for $m_\phi = 10^{-16}~{\rm eV}$, requiring the variation at very small $a$ to be larger than the other cases in order to achieve $\delta Y_\mathrm{He} = 5\%$.
• Figure 3: Evolution of the free-electron fraction $x_e$ (top) and visibility function $g$ (bottom) in the presence of $\alpha$ (left) and $m_e$ (right) variations for three different masses of $\phi$, aligning with those presented in Fig. \ref{['fig:variation_w_diff_mass']}. We neglect the contribution of the thermal mass. The specific values of the ULDM coupling and fraction match those in Fig. \ref{['fig:Cl_low_mass']}, enforcing $\delta Y_\mathrm{He} = 5\%$ such that all $x_e$ curves align at high redshift. We plot the visibility function with respect to conformal time, because its width corresponds to the comoving damping scale. We also show the corresponding curves for $\Lambda$CDM (black dotted line). For $m_\phi = 10^{-24}$ eV, the VFC has a negligible impact on recombination. For smaller masses, the VFC alters both the peak location and width of the visibility function.
• Figure 4: Oscillatory variation of $m_e$ (left) and its effect on the free-electron fraction $x_e$, with respect to $\Lambda$CDM (right), for two values of the mass of $\phi$ that correspond to oscillations starting around the onset of recombination. We neglect the contribution of the thermal mass and fix the ULDM coupling and fraction to achieve $\delta Y_{\rm He} = 5\%$. We note that similar oscillatory behaviors also appear for the $\phi$-induced variation of $\alpha$.
• Figure 5: Residuals of the CMB TT (left) and EE (right) power spectra, with respect to $\Lambda$CDM, due to the modified value $Y_\mathrm{He}$ from VFCs. Solid (dashed) lines show the effects with (without) thermal mass. An increase in $\delta Y_\mathrm{He}$ suppresses the CMB tail due to increased diffusion damping. The large-scale features in EE result from the difference in the reionization visibility function. Properly accounting for $m_\mathrm{th}$ reduces the value of $Y_{\rm He}$ and lessens the impact on the CMB power spectra for the chosen set of parameters, indicated at the top of each panel.