Phasing out Dark Matter Isocurvature with Thermal Misalignment

Abstract

Thermal misalignment provides an alternative to the standard misalignment mechanism for the cosmological production of scalar dark matter. In this framework, feeble couplings to particles in the thermal bath generate a finite-temperature potential that drives the scalar towards large field values early in the radiation era, dynamically inducing the misalignment before the onset of scalar oscillations. As a result, the relic abundance is controlled primarily by particle masses and couplings rather than the initial field value. As a light spectator field, the scalar acquires inflationary fluctuations that are uncorrelated with the adiabatic curvature mode, generically sourcing isocurvature perturbations. We show that, unlike standard misalignment, where light scalars are strongly constrained by cosmic microwave background bounds on dark matter isocurvature for high-scale inflation, thermal misalignment can naturally suppress the isocurvature signal. This occurs through a novel late-time phase offset between the background zero mode and the superhorizon perturbations, which reduces the final dark matter density contrast. Thermal misalignment therefore provides a new and generic route to isocurvature-safe scalar dark matter.

Figures (4)

• Figure 1: Evolution of $|\varphi_0|$ in the thermal misalignment scenario with $\varphi_{0i} = 0$. The left (right) plot shows the evolution of the scalar in the small (large) $\kappa$ limit where we have chosen the coupling $\beta$ to reproduce the observed relic density (colored lines); see Eqs. (\ref{['eq-phi-osc-tm']},\ref{['eq:phi-i-DM']}). For comparison, we also show the evolution of scalar background in the standard misalignment scenario (black dashed lines). In the small $\kappa$ limit the scalar gets misaligned at small $x$ in the presence of the thermal potential which becomes subdominant at $x \simeq x_{\psi}\ll 1$. The zero mode asymptotes to a constant value and then starts to oscillate, such that at late times the oscillations are in phase with the corresponding evolution in the standard misalignment scenario ($\theta_{0} \simeq 0)$. At large $\kappa$, the thermal potential is dominant around the onset of oscillations and the background field is moving with a large velocity. The late time oscillations of $\varphi_0$ for large $\kappa$ are out of phase with the corresponding evolution in standard misalignment with $\theta_{0}\simeq -\pi/2$.
• Figure 2: Thermal misalignment parameter space: Solid colored contours show the values of $\beta$ as a function of $\kappa$ that reproduce the observed relic density for fermion masses $m_{\psi} = 10^{-2} ~\rm GeV$ (teal), $m_{\psi} = 1~\rm GeV$ (magenta), $m_{\psi} = 10^{2} ~\rm GeV$ (yellow). The shaded region denotes the parameter space in which the Born approximation is no longer valid (see Eq. (\ref{['eq:Born-validity-f']})). The dotted black line indicates the approximate naturalness condition $\beta = 4 \pi \kappa$, above which the radiative corrections to the zero temperature scalar potential dominate over its bare value. Thin gray lines represent isocontours of $m_{\phi}$. The region within the solid black lines (above the dashed black line) indicate parameters consistent with the CMB isocurvature constraints for $H_{I} = 10^{12} ~\rm GeV$ ($H_{I} = 10^{9} ~\rm GeV$). As we will show in the following sections, thermal misalignment opens up a region of $m_\phi-H_I$ parameter space for large $H_{I}$ that is ruled out for standard misalignment from isocurvature bounds (see Fig. \ref{['fig:HIplot']}).
• Figure 3: Square root of the isocurvature amplitude ratio between thermal misalignment and standard misalignment, $\sqrt{|A_{\cal S, {\rm tm}}/{ A_{\cal S, {\rm sm}}}|}$ obtained using using Eqs. (\ref{['eq:isocurvature-result']}, \ref{['eq:iso-SM']}). We have chosen three representative fermion masses, $m_{\psi} = 10^{2}~\rm GeV$ (yellow), $1~\rm GeV$ (magenta), $10^{-2}~\rm GeV$ (blue). For $m_{\psi} = 10^{-2} \,\rm GeV$ the vertical dashed line indicates the values of $\kappa$ above which the Born approximation fails (see Eq. (\ref{['eq:Born-validity-f']})). The isocurvature in thermal misalignment exhibits the expected cosine dependence, with the amplitude ratio decreasing to zero before rising again. We can see the cosine behavior for isocurvature in thermal misalignment, as magnitude isocurvature ratio decreases to be exactly zero and increases again.
• Figure 4: The upper bound on $H_{I}$ as a function of $m_\phi$ in thermal misalignment for several choices of fermion masses, $m_{\psi} = 10^{2}~\rm GeV$ (yellow), $1~\rm GeV$ (magenta) and $10^{-2}~\rm GeV$ (blue), and for standard misalignment (black). For thermal misalignment, the upper bound is relaxed relative to standard misalignment over a broad scalar-mass range, with the precise interval depending on $m_\psi$. Vertical dashed lines indicate where the Born approximation fails (Eq. (\ref{['eq:Born-validity-f']})). The gray band indicates the Planck + BICEP upper bound $H_{I} \leq 4.7 \times 10^{13} \rm GeV$BICEP:2021xfz from the non-observation of CMB B-modes associated with tensor fluctuations produced during inflation.