# SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA

## Abstract

We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.

- Authors:

- Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of)
- Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of)
- Theory Division, CERN, CH-1211 Geneve 23 (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22037085

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 752; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTRONOMY; ASTROPHYSICS; COSMOLOGY; DENSITY; DISTURBANCES; GAUGE INVARIANCE; GRAVITATIONAL INTERACTIONS; POTENTIALS; RELATIVISTIC RANGE; SHEAR; UNIVERSE; VELOCITY

### Citation Formats

```
Hwang, Jai-chan, Noh, Hyerim, and Gong, Jinn-Ouk.
```*SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA*. United States: N. p., 2012.
Web. doi:10.1088/0004-637X/752/1/50.

```
Hwang, Jai-chan, Noh, Hyerim, & Gong, Jinn-Ouk.
```*SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA*. United States. doi:10.1088/0004-637X/752/1/50.

```
Hwang, Jai-chan, Noh, Hyerim, and Gong, Jinn-Ouk. Sun .
"SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA". United States. doi:10.1088/0004-637X/752/1/50.
```

```
@article{osti_22037085,
```

title = {SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA},

author = {Hwang, Jai-chan and Noh, Hyerim and Gong, Jinn-Ouk},

abstractNote = {We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.},

doi = {10.1088/0004-637X/752/1/50},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 1,

volume = 752,

place = {United States},

year = {2012},

month = {6}

}