Analytic expressions for the second-order scalar perturbations in the $$CDM Universe within the cosmic screening approach - Eingorn, Maxim; Guran, N. Duygu; Zhuk, Alexander (arXiv, 2019)
We study the second-order scalar perturbations in the conventional $$CDM Universe within the cosmic screening approach. The analytic expressions for both the velocity-independent and velocity-dependent second-order scalar perturbations are derived. We demonstrate how the Yukawa screening effect, which is inherent in the first-order metric corrections, manifests itself in the second-order ones. It is shown that the obtained formulas for the second-order perturbations are reduced to the known post-Newtonian expressions at distances much smaller than the Yukawa screening length. In the era of precision cosmology, these analytic formulas play an important role since the second-order metric corrections may affect the interpretation of observational data (e.g., the luminosity-redshift relation, gravitational lensing, baryon acoustic oscillations).

v2 (matching the publication in Physics of the Dark Universe) = v1 + new Section 4 + minor changes + extra discussion + new Refs.; 14 pages, no figures
Keywords: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc)