We study the effect of varying sound speed on clustering dark energy in the Dirac-Born-Infeld (DBI) scenario. The DBI action is included in the class of $k$-essence models, and it has an important role in describing the effective degrees of freedom of D-branes in the string theory. In the DBI setup, we take the anti-de Sitter (AdS) warp factor $f(\phi)=f_0\, \phi^{-4}$, and investigate the self-interacting quartic potential $V(\phi)=\lambda\phi^{4}/4$. We calculate the full expression of the effective sound speed for our model, and show that it can evolve with time during the cosmological evolution. Besides, the adiabatic sound speed evolves with time here, and this influences the background dynamics to some extent. We show that the effective sound speed is very close to the adiabatic sound speed. We examine the effect of the variable sound speed on growth of the perturbations in both the linear and non-linear regimes. In the linear regime, we apply the Pseudo-Newtonian formalism, and show that dark energy suppresses the growth of perturbations at low redshifts. From study the Integrated Sachs-Wolf (ISW) effect in our setup, we see that the model manifests some deviation from the concordance $\Lambda$CDM model. In the non-linear regime, we follow the approach of spherical collapse model, and calculate the linear overdensity, the virial overdensity, overdensity at the turn around and the rate of expansion of collapsed region. We further compute relative number density of halo objects above a given mass in our setting, and show that the number of structures with respect to the $\Lambda$CDM model is reduced more in the high mass tail at high redshifts.

中文翻译：

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DBI 非典型标量场场景中 DM 和 DE 扰动的增长

我们研究了 Dirac-Born-Infeld (DBI) 场景中不同声速对聚集暗能量的影响。DBI动作包含在$k$-essence模型类中，它在描述弦理论中D-膜的有效自由度方面具有重要作用。在 DBI 设置中，我们采用反德西特 (AdS) 扭曲因子 $f(\phi)=f_0\, \phi^{-4}$，并研究自相互作用四次势 $V(\phi) =\lambda\phi^{4}/4$。我们为我们的模型计算了有效声速的完整表达，并表明它可以在宇宙演化过程中随时间演变。此外，这里的绝热声速随时间变化，这在一定程度上影响了背景动力学。我们表明有效声速非常接近绝热声速。我们研究了可变声速对线性和非线性状态下扰动增长的影响。在线性状态中，我们应用伪牛顿形式主义，并表明暗能量抑制了低红移下扰动的增长。通过研究我们设置中的综合 Sachs-Wolf (ISW) 效应，我们看到该模型表现出与一致性 $\Lambda$CDM 模型的一些偏差。在非线性状态下，我们遵循球形塌陷模型的方法，计算线性超密度、维里超密度、转弯超密度和塌陷区域的膨胀率。在我们的设置中，我们进一步计算了高于给定质量的光晕物体的相对数密度，