Impact of cavities on the detection of quadratically coupled ultra-light dark matter

Abstract

Ultra-light scalar fields may explain the nature of the dark matter in our universe. If such scalars couple quadratically to particles of the Standard Model the scalar acquires an effective mass which depends on the local matter energy density. The changing mass causes the field to deviate from its cosmological value in experimental environments. In this work we show that the presence of a local over-density enclosing the experiment, for example a cavity, vacuum chamber, or satellite can strongly suppress the value of the scalar and its gradient in the interior. This makes detection of such scalar dark matter challenging, and significantly relaxes constraints on strongly coupled models. We also discuss the possibility that quadratically coupled ultra-light scalar dark matter could be detected by the differential measurement of the force on two cavities of the same mass but different internal structure.

Figures (8)

• Figure 1: Evaluation of the field profile at the surface of a solid sphere radius $R$, varying $|\alpha \rho _SR^2|=|kR|^2$. The top panel illustrates the case $\alpha>0$, in which the field at the surface is screened for $\alpha=1/\rho R^2$. The lower panel demonstrates the case $\alpha<0$. Maxima and minima indicate the locations of field divergences and zeros respectively. We note that the magnitude of the field is displayed given that, in the $\alpha<0$ case, sign changes occur between adjacent extrema.
• Figure 2: The region of instability of the scalar field solutions around a uniform sphere. The mass $m$ and coupling strength $\alpha$ of the scalar field are appropriately scaled according to the sphere's density $\rho_S$ and radius $R$. The red dotted line illustrates the boundary below which the field is tachyonic. The black dotted line illustrates the boundary under which the wavelength of the field inside matter is sufficiently small to allow its expectation value to roll away from zero. The red shaded region illustrates the intersection of these regions: $\alpha<-\max{(\frac{m^2}{\rho}, \frac{1}{\rho R^2})}$, whereby the field solutions in Eq. \ref{['eq:Solution_Uniform_Sphere']} are expected to be unstable to perturbations.
• Figure 3: The modification of coefficients describing the field inside a spherical cavity: $R_1=10~\hbox{cm}$, $R_2=11~\hbox{cm}$ and $\rho_c=2700~\hbox{kg m}^{-3}$. Panels in the top row relate to coefficients for the positive $\alpha$ case, and the bottom row the negative $\alpha$ case. The left panels give the magnitude of the ratio between the constant component of the field profile inside the cavity, as in \ref{['eq:Solution_Cavity']}, and the boundary condition in Eq. \ref{['eq:Cavity_Infinity_Boundary_Condition']}. The right gives the same but for the linear component of the profile and boundary conditions. Note that the magnitude is plotted since for the $\alpha<0$ case, components of the field profile inside the cavity may change sign with respect to the boundary conditions. The blue dashed line indicates where $\alpha = k_c^2/\rho_c$.
• Figure 4: Absolute value of $\varphi$ at the centre (blue) of an aluminium cylindrical cavity with inner radius $R=0.1$ m and wall thickness $\delta R = \delta L = 1$ cm. The average field value inside the cavity is shown in orange. The top row corresponds to $\alpha >0$, while the bottom row to $\alpha <0$. The black dashed (dotted) lines mark the analytical result for an infinite cylinder (sphere).
• Figure 5: Field profile for $\alpha$ corresponding to the first three peaks, $\alpha = (1.41, 1.75,2.27) \times 10^{-12}~\mathrm{GeV}^{-2}$ for the long (top), and $\alpha = (2.83, 15.0, 24.5) \times 10^{-12}~\mathrm{GeV}^{-2}$ for the short (bottom) cavities. Notice that the range of field values differs in each panel. The black line shows the position of the cavity walls.