Halo-independent test of dark matter direct detection signals

I will discuss new halo-independent frameworks that we have presented in some recent works in order to test dark matter direct detection signals. 
In the first part of the talk, we will focus on a halo-independent lower bound on the DM capture rate in the Sun from a direct detection signal, with 
which one can set limits on the branching ratios into different channels from the absence of a high-energy neutrino flux in neutrino telescopes. 
We have recently extended this framework also to the case of inelastic interactions. The second part will be based on a  
velocity-distribution-independent lower bound on the product of the DM-nucleon cross section and the local energy density that one can obtain 
from a direct detection signal. This bound can be used in combination with limits from local density measurements, 
the LHC, indirect detection and the relic abundance to constrain DM models.