Covariant and gauge-invariant approach to cosmological density fluctuations
- Physics Department, University of Texas, Austin, Texas 78712 (US) Applied Mathematics Department, University of Cape Town, Rondebosch 7700, Cape Town, South Africa Scuola Internazionale Superiore di Studi Avanzati, Strada Costiera 11, Miramare, 34014 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati, Strada Costiera 11, Miramare, 34014 Trieste, Italy
It has been known for a long time that the gauge problem plagues the study of density perturbations in cosmology. The quantity {delta}{mu}/{mu} (the fractional variation in density along a world line) usually determined in perturbation calculations is completely dependent on the gauge chosen. Even the fully covariant approach of Hawking (1966) is not immune. Bardeen's major paper (1980) determines a set of gauge-invariant quantities that are related to density perturbations but are not those perturbations themselves. We give a simple alternative representation of density fluctuations. This representation is both fully covariant and gauge invariant; thus it sidesteps the usual problems. The basic quantity used to represent density inhomogeneities is the {ital comoving} {ital fractional} {ital gradient} {ital of} {ital the} {ital energy} {ital density orthogonal} {ital to} {ital the} {ital fluid} {ital flow}. Our description does not make the usual assumption that this gradient is small. Exact (fully nonlinear) propagation equations are derived for this quantity. They are then linearized to give propagation equations appropriate to the case of an almost-Robertson-Walker universe. Their solutions are obtained in a simple case which can be compared with the standard theory; we recover the usual growing and decaying modes. Thus the result is standard, but its derivation is completely transparent. We give an interpretation of the Bardeen variables in terms of our formalism.
- OSTI ID:
- 5397900
- Journal Information:
- Physical Review (Section) D: Particles and Fields; (USA), Vol. 40:6; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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