completely determined by the shape and amplitude of the linear power spectrum. As a consequence, it shows significant dependence on the nature of gravity. We also show that the halo concentration is also affected by gravity. These results can be used to understand the impact of gravity on halo formation and distribution. They can also be used in halo model to understand the nonlinear matter clustering [@Cui10].

We would like to thank Volker Springel for the N-GenIC, Postprocessing code and detailed help. We are grateful to the anonymous referee for useful comments that helped to improve the presentation of this paper. Youcai thanks Donghai Zhao for helpful discussions. This work is supported by the national science foundation of China (grant Nos. 10973027, 11025316, 10973018, 10925314, 11233005, 11121062, 11203054), National Basic Research Program of China (973 Program) under grant No.2009CB24901, the CAS/SAFEA International Partnership Program for Creative Research Teams (KJCX2-YW-T23) and the Shanghai Committee of Science and Technology, China (grant No. 12ZR1452800).

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