We present a detailed study of the collapse of a spherical matter overdensity and the non-linear growth of large scale structures in the Galileon ghost condensate (GGC) model. This model is an extension of the cubic covariant Galileon (G3) which includes a field derivative of type ${\left({\nabla }_{\mu }\varphi {\nabla }^{\mu }\varphi \right)}^2$ in the Lagrangian. We find that the cubic term activates the modifications in the main physical quantities whose time evolution is then strongly affected by the additional term. Indeed, the GGC model shows largely mitigated effects in the linearised critical density contrast, non-linear effective gravitational coupling and the virial overdensity with respect to G3 but still preserves peculiar features with respect to the standard $\Lambda$CDM cosmological model, e.g., both the linear critical density contrast and the virial overdensity are larger than those in $\Lambda$CDM. The results of the spherical collapse model are then used to predict the evolution of the halo mass function, non-linear matter and lensing power spectra. While at low masses the GGC model presents about 10% fewer objects with respect to $\Lambda$CDM, at higher masses for $z>0$ it predicts 10% ($z=0.5$)-20% ($z=1$) more objects per comoving volume. Using a phenomenological approach to include the screening effect in the matter power spectrum, we show that the difference induced by the modifications of gravity are strongly dependent on the screening scale and that differences can be up to 20% with respect to $\Lambda$CDM. These differences translate to the lensing power spectrum where qualitatively the largest differences with respect to the standard cosmological model are for $\ell <10^3$. Depending on the screening scale, they can be up to 25% on larger angular scales and then decrease for growing $\ell$. These results are obtained for the best fit parameters from linear cosmological data for each model.

我们目前对Galileon幽灵冷凝物（GGC）模型中球形物质密度倒塌和大型结构的非线性增长进行详细研究。该模型是三次协变伽利略（G3）的扩展，其中包括类型为${（{\nabla }_{\mu }\varphi {\nabla }^{\mu }\varphi ）}^2$在拉格朗日。我们发现三次项激活了主要物理量的修改，其时间演化随后受到附加项的强烈影响。实际上，GGC模型在线性化的临界密度对比，非线性有效重力耦合以及相对于G3的病毒密度过大方面显示出很大的缓解作用，但相对于标准品仍保留了独特的功能$\Lambda$CDM宇宙学模型，例如线性临界密度对比和病毒超密度均大于 $\Lambda$CDM。然后，将球形塌陷模型的结果用于预测晕圈质量函数，非线性物质和透镜屈光力谱的演变。虽然质量很低，但GGC模型相对于$\Lambda$CDM，更高质量 $ž>0$ 预测为10％（$ž=0。5$）-20％（$ž=\mathrm{1个}$）每个共同移动的体积更多的对象。使用现象学方法将筛选效果包括在物质功率谱中，我们证明了由重力修正引起的差异在很大程度上取决于筛选规模，并且相对于筛选规模，差异可以高达20％$\Lambda$CDM。这些差异转化为屈光力谱，定性上相对于标准宇宙学模型最大的差异是$\ell <\mathrm{1个}{0}^3$。根据筛分规模，在较大的角度范围内，它们可能高达25％，然后随着生长而减小$\ell$。这些结果是从每个模型的线性宇宙学数据中获得的最佳拟合参数。