AS5003 · Reference
Notation and conventions
The lectures, homework and exam all use the symbols below. If something you read uses a different name, look it up here. This page grows as the course goes on.
Basic quantities
| Symbol | Name | Meaning |
|---|---|---|
| $t_0$ | present time | The age of the Universe today. A subscript 0 always means "today". |
| $a(t)$ | scale factor | The size of the Universe relative to today, $a(t_0) = 1$. |
| $z$ | redshift | $z = (\lambda_\text{obs} - \lambda_\text{em})/\lambda_\text{em}$; for cosmological redshift $1 + z = 1/a(t_\text{em})$. |
| $H(t)$ | Hubble parameter | $H = \dot a / a$. |
| $H_0$ | Hubble constant | $H(t_0)$. Benchmark value 68 km s⁻¹ Mpc⁻¹. |
| $H_0^{-1}$ | Hubble time | ≈ 14.4 Gyr for $H_0 = 68$ km s⁻¹ Mpc⁻¹. |
| $c/H_0$ | Hubble distance | ≈ 4400 Mpc for $H_0 = 68$ km s⁻¹ Mpc⁻¹. |
| $\Omega$ | density parameter | $\varepsilon / \varepsilon_c$, energy density relative to the critical density (Lecture 4). |
Distances
Ryden uses the following names; we use exactly these. Their definitions come in Lectures 3 and 7.
| Symbol | Ryden's name | Also called elsewhere |
|---|---|---|
| $d_p(t)$ | proper distance | physical distance |
| $d_p(t_0)$ | proper distance today | comoving distance (radial), line-of-sight comoving distance |
| $d_\text{hor}(t)$ | horizon distance | particle horizon |
| $d_L$ | luminosity distance | |
| $d_A$ | angular-diameter distance |
Benchmark model (Ryden Table 2.1)
| Parameter | Value |
|---|---|
| $H_0$ | 68 km s⁻¹ Mpc⁻¹ |
| $\Omega_{r,0}$ | 9.0 × 10⁻⁵ |
| $\Omega_{m,0}$ | 0.31 |
| $\Omega_{\Lambda,0}$ | 0.69 |
| $T_0$ (CMB) | 2.7255 K |
| $t_0$ | 13.7 Gyr |