If dark matter has even been in sufficient thermal contact with the visible sector and sufficiently light ( m _ { \chi } \lesssim \mathcal { O } ( 10 ) ~ { } \text { keV } ) , the thermal motion inherited from the visible sector will cause significant free streaming effect which is subject to the structure formation constraint , similar to the benchmark thermal warm dark matter model .
Here we identify the interaction responsible for such thermal contact to be the interaction probed by the deep underground dark matter direct detection experiments .
With the kinetic decoupling technique on the m _ { \chi } vs . \sigma plot we determine the bound shape in detail , and find that recasting the current Lyman- \alpha bound gives a constraint of m _ { \chi } \gtrsim 73 ~ { } \text { keV } , and it gets relaxed to m _ { \chi } \gtrsim 35 ~ { } \text { keV } for a smaller cross section of \sigma < 10 ^ { -46 } ~ { } \text { cm } ^ { 2 } with some model dependence .
That can be taken as a generic “ no go ” constraint for light dark matter direct detection experiments , and the known caveats are if dark matter is axion-like with an early Bose-Einstein condensation form , or if there is Brownian motion protection of the free streaming .