Cosmology Lecture 6

The paragraph introduces the Freedman equation, also known as the Hubble constant squared, which is fundamental to understanding the expansion of the universe. It discusses the importance of context in interpreting observational facts and how these facts relate to the equation. The Hubble function, the energy density, and the curvature term are also defined, with the curvature term represented by 'K', which can have values of +1, -1, or 0, corresponding to different spatial geometries. The metric, or the mathematical relationship between space and time, is also mentioned.

This paragraph delves into the various sources of energy density in the universe, which include radiation, matter, and vacuum energy. It explains how radiation energy density scales with the inverse fourth power of the scale factor 'a', while matter density scales with the inverse cube of 'a'. The cosmological constant 'lambda' represents vacuum energy, which does not dilute with an increase in the scale factor. The curvature term's role in the energy density equation is also discussed.

The focus here is on how astronomers measure the Hubble constant and other cosmological quantities. It discusses the cosmic distance ladder, a method for measuring the distances to celestial objects, and how it relies on standard candles like Cepheid variables and supernovae. The paragraph also covers the measurement of radiation through the Cosmic Microwave Background and the estimation of matter density by observing the luminous matter in galaxies.

This paragraph discusses the historical perspective on the role of curvature in the universe's geometry. It talks about how the ratios of radiation, matter, and the cosmological constant, represented as Omega values, have changed over time. The importance of these ratios adding up to 1 is emphasized, which is a result of their definitions in terms of the Hubble constant squared. The paragraph also touches on the misconceptions about the universe's curvature and size based on older cosmological models.

The paragraph explains how the Hubble constant varies with time in a matter-dominated universe. It describes the relationship between the Hubble constant and the age of the universe, stating that the Hubble constant is essentially one over the age of the universe. The historical context of Hubble's measurements and the implications of these measurements on the perceived age of the universe are also discussed.

This paragraph introduces the concept of dark matter and its significance in cosmology. It explains how dark matter does not radiate or interact strongly with electromagnetic forces, making it difficult to detect. The paragraph also discusses the historical discovery of dark matter through the anomalous behavior of galaxies and galaxy clusters, which could not be explained by the presence of luminous matter alone.

The discussion here centers on the rotation curves of galaxies and how they provide evidence for dark matter. It explains that the observed flat rotation curves, indicating a constant velocity of stars at different radii from the galactic center, suggest a distribution of mass that increases linearly with the radius. This is in contrast to the expectation from luminous matter alone, which would predict a decrease in velocity with distance from the center.

This paragraph explores the idea that dark matter forms halos around galaxies and that these halos influence the formation of galaxies. It discusses the hypothesis that dark matter collected first into these halos, which then attracted baryonic matter, leading to the formation of stars and galaxies. The paragraph also touches on the controversy surrounding the nature of dark matter and the possibility of it being made up of particles that are weakly interacting or not electrically charged.

The focus of this paragraph is on the methods for detecting dark matter and understanding its aggregated state. It discusses the possibility of dark matter being made up of particles that are so weakly interacting that they may not form dust or gas but exist as individual particles. The paragraph also explores the idea that dark matter could be detected through its gravitational effects or potentially through future particle collisions.

This paragraph outlines how cosmological models can be tested through observations of the universe. It discusses the importance of measuring the number of galaxies as a function of distance or redshift and how this can provide insights into the curvature of space. The paragraph also explains how luminosity as a function of redshift can be used to test cosmological models and determine the nature of the universe's expansion.

The paragraph details the use of the Friedmann equations to calculate observable quantities such as the number of galaxies per unit redshift and the relationship between redshift and luminosity. It emphasizes the process of creating a model with specific parameters, calculating the observable signatures, and comparing these with actual observations to find the best fit. The importance of the cosmological constant and its role in the current model of the universe is highlighted.

This paragraph discusses the evolution of the Omega values, which represent the ratios of different components' densities in the universe. It explains how these values change over time, with radiation dominating in the past, matter being significant in the recent past, and the cosmological constant (lambda) expected to dominate in the future. The paragraph also touches on the implications of these changes for the universe's geometry and ultimate fate.

The final paragraph emphasizes the precision achieved in cosmology, noting that the current model fits observational data to within about one percent. It mentions ongoing efforts to measure cosmic parameters with even greater accuracy, such as through the study of the cosmic microwave background. The paragraph also acknowledges the possibility of systematic deviations that could indicate new physics or a refinement of the current model.