In this paper we investigate dark matter structure formation in the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model using the PINOCCHIO algorithm. We first present 2nd order Lagrangian perturbation theory for the nDGP model, which shows that the 1st- and 2nd-order growth functions in nDGP are larger than those in ΛCDM. We then examine the dynamics of ellipsoidal collapse in nDGP, which is accelerated compared to ΛCDM due to enhanced gravitational interactions. Running the nDGP-PINOCCHIO code with a box size of 512 Mpc h ^-1 and 1024³ particles, we analyze the statistical properties of the output halo catalogs, including the halo power spectrum and halo mass function. The calibrated PINOCCHIO halo power spectrum agrees with N-body simulations within 5% in the comoving wavenumber range k<0.3 (h Mpc^-1) at redshift z=0. The agreement is extended to smaller scales for higher redshifts. For the cumulative halo mass function, the agreement between N-body and PINOCCHIO is also within the simulation scatter.

中文翻译：

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《匹诺曹》中 nDGP 重力的实现


在本文中，我们使用 PINOCCHIO 算法研究了 Dvali-Gabadadze-Porrati (nDGP) 模型正常分支中的暗物质结构形成。我们首先提出了 nDGP 模型的二阶拉格朗日微扰理论，该理论表明 nDGP 中的一阶和二阶增长函数比 ΛCDM 中的大。然后，我们检查了 nDGP 中椭球塌陷的动力学，由于引力相互作用增强，与 ΛCDM 相比，椭球塌陷的速度更快。运行 nDGP-PINOCCHIO 代码，盒子大小为 512 Mpc小时^-1和 1024 ^{3 个}粒子，我们分析了输出晕目录的统计特性，包括晕功率谱和晕质量函数。校准后的匹诺曹光环功率谱与 N 体模拟在同动波数范围内的一致性在 5% 以内k <0 id=176>小时Mpc ^-1 ) 红移z =0。该协议扩展到更小的尺度以获得更高的红移。对于累积晕质量函数，N 体和 PINOCCHIO 之间的一致性也在模拟散点范围内。