# Energy density and pressure of long wavelength gravitational waves

## Abstract

Inflation leads us to expect a spectrum of gravitational waves (tensor perturbations) extending to wavelengths much bigger than the present observable horizon. Although these gravity waves are not directly observable, the energy density that they contribute grows in importance during the radiation- and dust-dominated ages of the universe. We show that the back reaction of tensor perturbations during matter domination is limited from above, since gravitational waves of wavelength [lambda] have a share of the total energy density [Delta][rho]([lambda])/[rho] during matter domination that is at most equal to the share of the total energy density that they had when the mode [lambda] exited the Hubble radius H[sup [minus]1] during inflation. This work is to be contrasted to that of Sahni, who studied the energy density of gravity waves only insofar as their wavelengths are smaller than H[sup [minus]1]. Such a cutoff in the spectral energy of gravity waves leads to the breakdown of energy conservation, and we show that this anomaly is eliminated simply by taking into account the energy density and pressure of long wavelength gravitational waves as well as short wavelength ones. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (Department of Physics, University of Florida, Gainesville, Florida 32611 (United States))

- Publication Date:

- OSTI Identifier:
- 6470764

- Alternate Identifier(s):
- OSTI ID: 6470764

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D

- Additional Journal Information:
- Journal Volume: 60:6; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGICAL MODELS; COSMOLOGY; ENERGY CONSERVATION; ENERGY DENSITY; ENERGY-MOMENTUM TENSOR; GRAVITATIONAL WAVES; INFLATABLE SEALS; PERTURBATION THEORY; RADIATION PRESSURE; TENSORS; MATHEMATICAL MODELS; SEALS 661310* -- Relativity & Gravitation-- (1992-)

### Citation Formats

```
Abramo, L.R.
```*Energy density and pressure of long wavelength gravitational waves*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevD.60.064004.

```
Abramo, L.R.
```*Energy density and pressure of long wavelength gravitational waves*. United States. doi:10.1103/PhysRevD.60.064004.

```
Abramo, L.R. Wed .
"Energy density and pressure of long wavelength gravitational waves". United States. doi:10.1103/PhysRevD.60.064004.
```

```
@article{osti_6470764,
```

title = {Energy density and pressure of long wavelength gravitational waves},

author = {Abramo, L.R.},

abstractNote = {Inflation leads us to expect a spectrum of gravitational waves (tensor perturbations) extending to wavelengths much bigger than the present observable horizon. Although these gravity waves are not directly observable, the energy density that they contribute grows in importance during the radiation- and dust-dominated ages of the universe. We show that the back reaction of tensor perturbations during matter domination is limited from above, since gravitational waves of wavelength [lambda] have a share of the total energy density [Delta][rho]([lambda])/[rho] during matter domination that is at most equal to the share of the total energy density that they had when the mode [lambda] exited the Hubble radius H[sup [minus]1] during inflation. This work is to be contrasted to that of Sahni, who studied the energy density of gravity waves only insofar as their wavelengths are smaller than H[sup [minus]1]. Such a cutoff in the spectral energy of gravity waves leads to the breakdown of energy conservation, and we show that this anomaly is eliminated simply by taking into account the energy density and pressure of long wavelength gravitational waves as well as short wavelength ones. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevD.60.064004},

journal = {Physical Review, D},

issn = {0556-2821},

number = ,

volume = 60:6,

place = {United States},

year = {1999},

month = {9}

}