(Linearised) Spatially Inhomogeneous Perturbations of FLRW Models

1. Lifshitz E M, I M Khalatnikov, Investigations in Relativistic Cosmology, Adv. Phys. 12 (1963), 185
2. Hawking S W: Perturbations of an Expanding Universe, Astrophys. J. 145 (1966), 544
3. Sachs R K, A M Wolfe: Perturbations of a Cosmological Model and Angular Variations of the Microwave Background, Astroph. J. 147 (1967), 73
4. Zel'dovich Ya B: Gravitational Instability: An Approximate Theory for Large Scale Density Perturbations, Astron. Astrophys. 5 (1970), 84
5. Stewart J M, M Walker: M 1974 Perturbations of Space-Times in General Relativity Proc. R. Soc. Lond. A 341 (1974), 49
6. Bardeen J M: Gauge-Invariant Cosmological Perturbations, Phys. Rev. D 22 (1980), 1882
   NB: Confuses the cosmological particle horizon with the Hubble radius $H^{-1} = S/\dot{S}$.
7. Geroch R, L Lindblom: Is Perturbation-Theory Misleading in General Relativity, J. Math. Phys. 26 (1985), 2581
8. Goode S W: Analysis of Spatially Inhomogeneous Perturbations of the FRW Cosmologies, Phys. Rev. D 39 (1989), 2882
   NB: Applies Bardeen's gauge-invariant formalism to construct (to 1st order) geometrical and kinematical quantities like $E^{\alpha}\!_{\beta}$, $H^{\alpha}\!_{\beta}$, $^{3}\!S^{\alpha}\!_{\beta}$, $^{3}\!C^{\alpha}\!_{\beta}$, $\sigma^{\alpha}\!_{\beta}$ (and investigate their evolution) in order to determine their effect on the generation of scalar, vector and tensor perturbation modes. NOTE: Similar expression were later given also by Stewart `90 and Bruni, Dunsby, Ellis `92.
9. Ellis G F R, M Bruni: Covariant and Gauge-Invariant Approach to Cosmological Density Fluctuations, Phys. Rev. D 40 (1989), 1804
10. Ellis G F R, J Hwang, M Bruni: Covariant and Gauge-Independent Perfect-Fluid Robertson-Walker Perturbations, Phys. Rev. D 40 (1989), 1819
    NB: Contains an error in the second-order propagation eq for spatial density gradients spotted by Martin Lottermoser of MPI für Astrophysik at Garching.
11. Ellis G F R, M Bruni, J Hwang: Density-Gradient-Vorticity Relation in Perfect-Fluid Robertson-Walker Perturbations, Phys. Rev. D 42 (1990), 1035
    NB: Contains the corrected version of the second-order propagation eq for spatial density gradients.
12. Stewart J M: Perturbations of Friedmann-Robertson-Walker Cosmological Models, Class. Quantum Grav. 7 (1990), 1169
    NB: Provides a "translation" of Bardeen's 1980 paper.
13. Zimdahl W: Gauge-Invariant Cosmological Perturbations from a Thermodynamical Point Of View, Class. Quantum Grav. 8 (1991), 677
14. Bruni M, P K S Dunsby, G F R Ellis: Cosmological Perturbations and the Physical Meaning of Gauge-Invariant Variables, Astrophys. J. 395 (1992), 34
15. Bruni M, G F R Ellis, P K S Dunsby: Gauge-Invariant Perturbations in a Scalar Field Dominated Universe, Class. Quantum Grav. 9 (1992), 921
16. Mukhanov V F, H A Feldman, R H Brandenberger: Theory of Cosmological Perturbations, Phys. Rep. 215 (1992), 203
17. Frauendiener J, B G Schmidt: Numerical Evolution, Linear and Nonlinear, of Spherically Symmetric Deviations from an Isotropic Universe, Gen. Rel. Grav. 25 (1993), 373
    NB: Spherically symmetric deviations from a $k = 0$ radiation FLRW model. $1+1$-dependent equation system in FOSH form as a basis (cf. Kind/Ehlers `93).
18. Jacobs M W, E V Linder, R V Wagoner: Green Function for Metric Perturbations due to Cosmological Density Fluctuations, Phys. Rev. D 48 (1993), 4623
    NB: Presents a transparent order-of-magnitude estimation for scalar metric perturbations and density fluctuations on sub- and super-particle-horizon scales. Moreover, in "longitudinal gauge" a diffusion-equation-like evolution equation is derived that acausally propagates a pseudo-Newtonian gravitational potential.
19. Klein C: Rotational Perturbations and Frame Dragging in a Friedmann Universe, Class. Quantum Grav. 10 (1993), 1619
20. Nesteruk A V: Cosmological Density Perturbations in the Universe with Non-Trivial Topology of Spacetime, Class. Quantum Grav. 10 (1993), L161
21. Zimdahl W: Gauge-Invariant Cosmological Perturbations and the Spectrum of Primeval Density Fluctuations, Phys. Rev. D 48 (1993), 2431
22. Zimdahl W, D Pavón, D Jou: Cosmological Perturbations in a Universe with Particle Production, Class. Quantum Grav. 10 (1993), 1775
    NB: de Sitter/ FLRW, Eckart first-order theory (bulk viscosity), gauge-invariant formalism.
23. Bombelli L, W E Couch, R J Torrence: Perfect Fluid Perturbations of Cosmological Spacetimes in Stewart's Variables, Class. Quantum Grav. 11 (1994), 139
24. Klein C: Second-Order Effects of Rotational Perturbations of a Friedmann Universe, Class. Quantum Grav. 11 (1994), 1539
25. Lewis C: A Non-Traditional Cosmological Fluid, Class. Quantum Grav. 11 (1994), 2507
26. Matarrese S, O Pantano, D Saez: General Relativistic Dynamics of Irrotational Dust: Cosmological Implications, Phys. Rev. Lett. 72 (1994), 320. Also: Preprint astro-ph/9310036.
    NB: Coins the term "silent universe".
27. Banach Z, S Piekarski: Gauge-Invariant Cosmological Perturbation Theory for Collisionless Matter: Application to the Einstein-Liouville System, Gen. Rel. Grav. 28 (1996), 1335
28. Matarrese S, D Terranova: Post-Newtonian Cosmological Dynamics in Lagrangian Coordinates, Mon. Not. R. Astron. Soc. 283 (1996), 400. Also: Preprint astro-ph/9511093.
29. Dunsby P K S: A Fully Covariant Description of Cosmic Microwave Background Anisotropies, Class. Quantum Grav. 14 (1997), 3391. Also: Preprint gr-qc/9707022.
    NB: Contains a few minor typos.
30. Méndez V, D Pavón, J M Salim: `Absorption' of Gravitational Radiation by the Cosmic Fluid, Class. Quantum Grav. 14 (1997), 77
    NB: Analysis of linearised perturbations in the spatial curvature and the matter content of a $k = 0$ FLRW model.
31. Zimdahl W: Cosmological Perturbation Theory and Conserved Quantities in the Large-Scale Limit, Class. Quantum Grav. 14 (1997), 2563. Also: Preprint gr-qc/9707047.
    NB: Nice introduction into the history and problems of the description of linearised FLRW-perturbations. Introduces Ellis-Bruni type variables adapted to spacelike 3-surfaces of either constant energy density, expansion rate, or spatial curvature, rather than comoving spacelike 3-surfaces as the original set of variables. Discusses large-scale conserved quantities in the $k = 0$ case.
32. van Elst H, G F R Ellis: Quasi-Newtonian Dust Cosmologies, Class. Quantum Grav. 15 (1998), 3545. Also: Preprint gr-qc/9805087.

Selected References
Last revision: Thu, 17-8-2000 (This page is under construction)