EFFECT OF INHOMOGENEITY ON COSMOLOGICAL MODELS

EFFECT OF INHOMOGENEITY ON COSMOLOGICAL MODELS

February 12, 1934 | RICHARD C. TOLMAN
The text discusses the effects of inhomogeneity on cosmological models, emphasizing the dangers of extrapolating from homogeneous models to the actual universe. It begins by noting that while homogeneous models are mathematically simpler and have some observational justification, they may not accurately represent the universe's true behavior due to the presence of inhomogeneities. The paper then presents a detailed analysis of a simple model composed of dust particles with spherical symmetry, leading to equations that describe the energy-momentum tensor and the line element for the model. These equations are used to derive relationships between the metrical variables, density, and other parameters. The paper then explores various applications of these equations, including static and distorted Einstein models, non-static Friedmann models, and distorted Friedmann models, each showing how inhomogeneities can lead to different behaviors and instabilities. The conclusion emphasizes that homogeneous models may not accurately represent the actual universe, and that inhomogeneities could lead to different evolutionary paths and densities in different regions. The paper also notes that while homogeneous models can be useful for local observations, they may not be suitable for extrapolating to the entire universe. The text concludes that caution is needed when applying results from homogeneous models to the actual universe, as the true universe may have different properties and behaviors beyond the range of current observations.The text discusses the effects of inhomogeneity on cosmological models, emphasizing the dangers of extrapolating from homogeneous models to the actual universe. It begins by noting that while homogeneous models are mathematically simpler and have some observational justification, they may not accurately represent the universe's true behavior due to the presence of inhomogeneities. The paper then presents a detailed analysis of a simple model composed of dust particles with spherical symmetry, leading to equations that describe the energy-momentum tensor and the line element for the model. These equations are used to derive relationships between the metrical variables, density, and other parameters. The paper then explores various applications of these equations, including static and distorted Einstein models, non-static Friedmann models, and distorted Friedmann models, each showing how inhomogeneities can lead to different behaviors and instabilities. The conclusion emphasizes that homogeneous models may not accurately represent the actual universe, and that inhomogeneities could lead to different evolutionary paths and densities in different regions. The paper also notes that while homogeneous models can be useful for local observations, they may not be suitable for extrapolating to the entire universe. The text concludes that caution is needed when applying results from homogeneous models to the actual universe, as the true universe may have different properties and behaviors beyond the range of current observations.
Reach us at info@study.space