Density contrast
Definition: The fractional density departure delta=(rho-rhobar)/rhobar from the cosmic mean.
Why it matters here: In Dark Matter and the Growth of Structure, Density contrast is needed to reason about linear growth, transfer functions, and gravitational collapse rather than merely label the phenomenon.
Relationship: It is interpreted alongside Linear growth factor and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics.
\(\\delta(a)=\\delta\\rho/\\bar\\rho,\\quad \\delta\\propto a\\;\\text{(matter era)}\)
Linear growth factor
Definition: The time-dependent multiplier describing perturbation growth while density contrasts remain much smaller than unity.
Why it matters here: In Dark Matter and the Growth of Structure, Linear growth factor is needed to reason about linear growth, transfer functions, and gravitational collapse rather than merely label the phenomenon.
Relationship: It is interpreted alongside Transfer function and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics.
Transfer function
Definition: The scale-dependent processing that maps primordial perturbations into the later matter distribution.
Why it matters here: In Dark Matter and the Growth of Structure, Transfer function is needed to reason about linear growth, transfer functions, and gravitational collapse rather than merely label the phenomenon.
Relationship: It is interpreted alongside Cold dark matter and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics.
Cold dark matter
Definition: A nonrelativistic, weakly interacting matter component that clusters gravitationally on cosmological scales.
Why it matters here: In Dark Matter and the Growth of Structure, Cold dark matter is needed to reason about linear growth, transfer functions, and gravitational collapse rather than merely label the phenomenon.
Relationship: It is interpreted alongside Nonlinear collapse and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics.
Nonlinear collapse
Definition: The regime in which density contrasts approach or exceed unity and linear perturbation theory fails.
Why it matters here: In Dark Matter and the Growth of Structure, Nonlinear collapse is needed to reason about linear growth, transfer functions, and gravitational collapse rather than merely label the phenomenon.
Relationship: It is interpreted alongside Density contrast and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The result remains linear only until delta approaches unity; collapsed halos require nonlinear dynamics.