Self-interacting dark matter (SIDM) is a simple and well-motivated scenario that could explain long-standing puzzles in structure formation on small scales. If the required self-interaction arises through a light mediator (with mass ∼ 10 MeV) in the dark sector, this new particle must be unstable to avoid overclosing the universe. The decay of the light mediator could happen due to a weak coupling of the hidden and visible sectors, providing new signatures for direct detection experiments. The SIDM nuclear recoil spectrum is more peaked towards low energies compared to the usual case of contact interactions, because the mediator mass is comparable to the momentum transfer of nuclear recoils. We show that the SIDM signal could be distinguished from that of DM particles with contact interactions by considering the time-average energy spectrum in experiments employing different target materials, or the average and modulated spectra in a single experiment. Using current limits from LUX and SuperCDMS, we also derive strong bounds on the mixing parameter between hidden and visible sector.

Due to Earth's revolution around the Sun, the expected scattering rate in direct dark matter searches is annually modulated. This modulation is expected to differ between experiments when given as a function of recoil energy ER, e.g. due to the gravitational focusing effect of the Sun. A better variable to compare results among experiments employing different targets is the minimum speed vmin a dark matter particle must have to impart a recoil energy ER to a target nucleus. It is widely believed that the modulation expressed as a function of vmin is common to all experiments, irrespective of the dark matter distribution. We point out that the annual modulation as a function of vmin, and in particular the times at which the rate is maximum and minimum, could be very different depending on the detector material. This would be an indication of a scattering cross section with nonfactorizable velocity and target material dependence. Observing an annual modulation with at least two different target elements would be necessary to identify this type of cross section.

We study how gravitational focusing (GF) of dark matter by the Sun affects the annual and biannual modulation of the expected signal in non-directional direct dark matter searches, in the presence of dark matter substructure in the local dark halo. We consider the Sagittarius stream and a possible dark disk, and show that GF suppresses some, but not all, of the distinguishing features that would characterize substructure of the dark halo were GF neglected.