The small-scale crisis is one of the most outstanding puzzles in modern cosmology and astrophysics .
It may imply a suppression of matter perturbation at small scale .
In this work , by taking into account of the gravitational effects from the non-equilibrium production of DM , we propose a new mechanism , which can realize such desired suppression and alleviate the crisis within the framework of cold dark matter ( DM ) and simple inflation .
Moreover , in this new mechanism , we establish a novel relation between the particle mass of DM , m _ { \chi } , and the critical scale of suppression , k _ { \star } ^ { -1 } .
As k _ { \star } ^ { -1 } will be further constrained in future astrophysical observations , m _ { \chi } can be constrained accordingly with this relation .
It thus provides a new method in complementary to other existing strategies of determining m _ { \chi } .
Furthermore , to illustrate our theoretical prediction , we consider a suppression at k _ { \star } ^ { -1 } = 1 ~ { } \text { kpc } that can partially alleviate the small-scale crisis , and obtain m _ { \chi } = 2.2 ~ { } \text { MeV } for realizing such suppression .
Then we plot the power spectrum of linear matter perturbation for this case , and illustrate a salient feature of the suppression that can serves a smoking-gun signature of this new mechanism in future observations .