ASTR 420 Lecture 09: Dark Matter and the Growth of Structure

Terms Developed in Context

These terms form the lecture's reasoning chain from observable through model to a bounded physical conclusion.

Density contrast

The fractional density departure delta=(rho-rhobar)/rhobar from the cosmic mean. In this lecture it supports the evidence-to-model chain for linear growth, transfer functions, and gravitational collapse.

Use and relationship: Read it together with Nonlinear collapse and Linear growth factor. The governing relation \(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Linear growth factor

The time-dependent multiplier describing perturbation growth while density contrasts remain much smaller than unity. In this lecture it supports the evidence-to-model chain for linear growth, transfer functions, and gravitational collapse.

Use and relationship: Read it together with Density contrast and Transfer function. The governing relation \(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Transfer function

The scale-dependent processing that maps primordial perturbations into the later matter distribution. In this lecture it supports the evidence-to-model chain for linear growth, transfer functions, and gravitational collapse.

Use and relationship: Read it together with Linear growth factor and Cold dark matter. The governing relation \(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Cold dark matter

A nonrelativistic, weakly interacting matter component that clusters gravitationally on cosmological scales. In this lecture it supports the evidence-to-model chain for linear growth, transfer functions, and gravitational collapse.

Use and relationship: Read it together with Transfer function and Nonlinear collapse. The governing relation \(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Nonlinear collapse

The regime in which density contrasts approach or exceed unity and linear perturbation theory fails. In this lecture it supports the evidence-to-model chain for linear growth, transfer functions, and gravitational collapse.

Use and relationship: Read it together with Cold dark matter and Density contrast. The governing relation \(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics. This caveat prevents the term from being treated as a unique explanation or a context-free number.