# Second-order Cosmological Perturbations Engendered by Point-like Masses

## Abstract

In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.

- Authors:

- Institute for Astro- and Particle Physics, University of Innsbruck, Technikerstrasse 25/8, A‐6020 Innsbruck (Austria)
- North Carolina Central University, CREST and NASA Research Centers, 1801 Fayetteville St., Durham, NC 27707 (United States)

- Publication Date:

- OSTI Identifier:
- 22663154

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 845; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALLOCATIONS; CORRECTIONS; DENSITY; DISTURBANCES; EINSTEIN FIELD EQUATIONS; GRAVITATIONAL FIELDS; MASS; MINKOWSKI SPACE; NONLUMINOUS MATTER; PERTURBATION THEORY; RELATIVISTIC RANGE; SIMULATION; UNIVERSE

### Citation Formats

```
Brilenkov, Ruslan, and Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com.
```*Second-order Cosmological Perturbations Engendered by Point-like Masses*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA81CD.

```
Brilenkov, Ruslan, & Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com.
```*Second-order Cosmological Perturbations Engendered by Point-like Masses*. United States. doi:10.3847/1538-4357/AA81CD.

```
Brilenkov, Ruslan, and Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com. Sun .
"Second-order Cosmological Perturbations Engendered by Point-like Masses". United States.
doi:10.3847/1538-4357/AA81CD.
```

```
@article{osti_22663154,
```

title = {Second-order Cosmological Perturbations Engendered by Point-like Masses},

author = {Brilenkov, Ruslan and Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com},

abstractNote = {In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.},

doi = {10.3847/1538-4357/AA81CD},

journal = {Astrophysical Journal},

number = 2,

volume = 845,

place = {United States},

year = {Sun Aug 20 00:00:00 EDT 2017},

month = {Sun Aug 20 00:00:00 EDT 2017}

}