Retrieving "Spatial Curvature" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Cosmic Expansion
Linked via "curvature"
$$\left(\frac{H0}{100 \text{ km/s/Mpc}}\right)^2 \approx 0.70 \Omega{r,0} + 0.30 \Omega{m,0} + \Omega{\Lambda,0} - \frac{k c^2}{H0^2 a0^2}$$
Where $\Omegar$, $\Omegam$, and $\Omega_{\Lambda}$ are the density parameters for radiation, matter (including both baryonic matter and dark matter), and the cosmological constant ($\Lambda$)/), respectively. $k$ describes the spatial curvature, which standard observations suggest is nearl… -
Energy
Linked via "curvature"
$$\Omega{\text{total}} = \Omegam + \Omega{\Lambda} + \Omegak \approx 1$$
Where $\Omegam$ is matter density (including dark matter), $\Omega{\Lambda}$ is dark energy density, and $\Omega_k$ accounts for spatial curvature. The energy density associated with dark energy, despite being the largest component, exhibits an extraordinarily low value, approximately $10^{-29} \text{ g}/\text{cm}^3$, which remains one of the most persistent mysteries in [ph… -
Expansion Of Spacetime
Linked via "curvature"
The modern understanding of spacetime expansion is rooted in the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, which describes a homogeneous and isotropic universe. The core dynamical component is the scale factor, $a(t)$, which dictates the proper distance between two points separated by comoving coordinates $\mathbf{x}1$ and $\mathbf{x}2$:
$$D(t) = a(t) |\mathbf{x}2 - \mathbf{x}1|$$
The time evolution of $a(t)$ is governed by the [Friedmann equations](/entries/friedmann-equa…