# On separate universes

## Abstract

The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity f{sup loc}{sub NL}, and hence does not contribute to a scale-dependentmore »

- Authors:

- Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218 (United States)
- Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
- Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 22525223

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; COSMOLOGICAL CONSTANT; COSMOLOGICAL INFLATION; COSMOLOGY; COUPLING; DENSITY; FLUIDS; GALAXIES; GENERAL RELATIVITY THEORY; GRAVITATION; NONLINEAR PROBLEMS; PERTURBATION THEORY; PHOTONS; RELATIVISTIC RANGE; SCALARS; SOUND WAVES; SPHERICAL CONFIGURATION; UNIVERSE

### Citation Formats

```
Dai, Liang, Pajer, Enrico, and Schmidt, Fabian, E-mail: ldai@ias.edu, E-mail: enrico.pajer@gmail.com, E-mail: fabians@mpa-garching.mpg.de.
```*On separate universes*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/10/059.

```
Dai, Liang, Pajer, Enrico, & Schmidt, Fabian, E-mail: ldai@ias.edu, E-mail: enrico.pajer@gmail.com, E-mail: fabians@mpa-garching.mpg.de.
```*On separate universes*. United States. doi:10.1088/1475-7516/2015/10/059.

```
Dai, Liang, Pajer, Enrico, and Schmidt, Fabian, E-mail: ldai@ias.edu, E-mail: enrico.pajer@gmail.com, E-mail: fabians@mpa-garching.mpg.de. Thu .
"On separate universes". United States. doi:10.1088/1475-7516/2015/10/059.
```

```
@article{osti_22525223,
```

title = {On separate universes},

author = {Dai, Liang and Pajer, Enrico and Schmidt, Fabian, E-mail: ldai@ias.edu, E-mail: enrico.pajer@gmail.com, E-mail: fabians@mpa-garching.mpg.de},

abstractNote = {The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity f{sup loc}{sub NL}, and hence does not contribute to a scale-dependent galaxy bias Δ b ∝ k{sup −2} on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent f{sup loc}{sub NL}-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of f{sup loc}{sub NL} beyond these projection effects signals a departure from standard single-clock inflation.},

doi = {10.1088/1475-7516/2015/10/059},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 10,

volume = 2015,

place = {United States},

year = {2015},

month = {10}

}