FLRW metric
Definition: The homogeneous and isotropic spacetime geometry used to relate expansion history to photon paths.
Why it matters here: It is required to answer Why do cosmologists use several different distances? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Comoving distance, the model \(D_C(z)=c/H_0 integral_0^z dz'/E(z')\), and the evidence statement The computation is independently checked against Astropy FlatLambdaCDM with radiation disabled to match the explicitly matter-plus-Lambda integral.
Boundary or common confusion: Curvature changes transverse distance; radiation matters at early times. Never apply the flat, late-time integral to recombination as if it were a precision CMB model.
Comoving distance
Definition: The present-epoch radial coordinate separation obtained by integrating inverse expansion rate.
Why it matters here: It is required to answer Why do cosmologists use several different distances? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Luminosity distance, the model \(D_C(z)=c/H_0 integral_0^z dz'/E(z')\), and the evidence statement The computation is independently checked against Astropy FlatLambdaCDM with radiation disabled to match the explicitly matter-plus-Lambda integral.
Boundary or common confusion: Curvature changes transverse distance; radiation matters at early times. Never apply the flat, late-time integral to recombination as if it were a precision CMB model.
Luminosity distance
Definition: The distance definition that makes bolometric flux obey the inverse-square relation.
Why it matters here: It is required to answer Why do cosmologists use several different distances? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Angular-diameter distance, the model \(D_C(z)=c/H_0 integral_0^z dz'/E(z')\), and the evidence statement The computation is independently checked against Astropy FlatLambdaCDM with radiation disabled to match the explicitly matter-plus-Lambda integral.
Boundary or common confusion: Curvature changes transverse distance; radiation matters at early times. Never apply the flat, late-time integral to recombination as if it were a precision CMB model.
Angular-diameter distance
Definition: Physical transverse size divided by observed angular size.
Why it matters here: It is required to answer Why do cosmologists use several different distances? and to distinguish direct observation from cosmological inference.
Relationships: Read it with Distance duality, the model \(D_C(z)=c/H_0 integral_0^z dz'/E(z')\), and the evidence statement The computation is independently checked against Astropy FlatLambdaCDM with radiation disabled to match the explicitly matter-plus-Lambda integral.
Boundary or common confusion: Curvature changes transverse distance; radiation matters at early times. Never apply the flat, late-time integral to recombination as if it were a precision CMB model.
Distance duality
Definition: The relation D_L=(1+z)^2 D_A for transparent metric propagation with photon conservation.
Why it matters here: It is required to answer Why do cosmologists use several different distances? and to distinguish direct observation from cosmological inference.
Relationships: Read it with FLRW metric, the model \(D_C(z)=c/H_0 integral_0^z dz'/E(z')\), and the evidence statement The computation is independently checked against Astropy FlatLambdaCDM with radiation disabled to match the explicitly matter-plus-Lambda integral.
Boundary or common confusion: Curvature changes transverse distance; radiation matters at early times. Never apply the flat, late-time integral to recombination as if it were a precision CMB model.