Misalignment from kicks: the impact of particle interactions on ultra-light dark matter

Abstract

Oscillating ultra-light scalar fields are a natural explanation for the dark matter in our universe, as long as a mechanism, often called a misalignment mechanism, exists to explain the amplitude of the scalar oscillations. If the dark matter scalar couples to the Standard Model, then the dynamics of ordinary matter can influence the behaviour of dark matter in the early universe. In this work we show how this changes the expected value of the scalar field and the resulting amplitude of late time scalar oscillations, and therefore the abundance of dark matter at late times. For dark matter scalars that interact quadratically with Standard Model fields we derive estimates of the size of this effect as a function of the strength of the coupling, and for axion-like fields we show that interactions with dark sector matter can temporarily destabilize the field, leading to large field displacements.

Figures (5)

• Figure 1: Shape of the kick function $\Sigma_e(T)$ when coupling a scalar field to the trace of the energy-momentum tensor of the electron. We can see that the energy influx peaks around $T \sim m_e$.
• Figure 2: Final value of the scalar fields as a function of the initial value $|\phi_i|$ and both negative and positive kick strengths, $\beta$, after numerical evolution of the system. The different coloured regions show the order of magnitude of the value of the field at the end of the kick ($|\phi(N_f)|$). Dark blue on the left marks the region where $\phi>M_{\rm pl}$, and the dashes mark the region where $|A(\phi_f)|>1$. The rightmost peaks in the figure mark scenarios where, at the end of the evolution, the field is in the minimum of the quadratic potential.
• Figure 3: Effective potential for the axion model when including interactions with nucleons. The density corrections lead to a sign swap in the early universe for densities larger than $\rho_c\equiv\Lambda^4/2\alpha$.
• Figure 4: Final value of the axion field at the end of the kick due to interactions with dark nucleons for different frequencies and initial values. For this figure, we fixed $\Lambda^4= \epsilon m_{\pi}^2 f_{\pi}^2$ and $\alpha= \sigma_N/m_N$ as given in SM-QCD. The different coloured regions indicate the order of magnitude of the value of the field at the end of the kick ($a(N_f)$). For large masses, the field reaches the effective minimum placed at $a_f=\pi f$.
• Figure 5: Final value of the rescaled axion field, $\tilde{a}=a\pi f$, at the end of the kick for different coupling strengths $\beta_N=\frac{3M_{\rm Pl}^2\alpha\xi}{f^2}$, and initial conditions. The different coloured regions indicate the order of magnitude of the field at the end of the kick ($\tilde{a}_f$), where the same color is given for symmetric points with respect to the maximum $\tilde{a}_f=1$.