What is the MPC equation

cosmology

Based on the distribution of galaxies in space and their redshift, the Belgian Georges Lemaître put forward the theory in 1927 that our universe is expanding. Like the raisins in a yeast dough, the galaxies should move further and faster apart with the expansion of the universe, although the comparison with the yeast dough is not entirely correct, since the yeast dough has a center, but the universe does not.

In 1929 Edwin HUBBLE (see Fig. 1) provided suitable data, which showed a regularity in the movement of the galaxies: Galaxies move away from us faster, the further the galaxies are away from us.

Hubble constant or Hubble parameter

Based on Hubble's observations, it was initially assumed that the redshift \ (z \) or the "escape speed" \ (v \) of a galaxy is directly proportional to its distance \ (D \) to us. With the proportionality constant \ (H \) called Hubble constant, this relationship between distance and redshift (or "escape speed") could be expressed with the equation \ [z \ cdot c = H \ cdot D \]. This law is called the Hubble-Lemaître law.

However, it was later found that the expansion of the universe was accelerating. Therefore, the value of \ (H \) changes over time. \ (H \) is therefore time-dependent and not constant. Accordingly, the size is now often correctly referred to as the Hubble parameter. The linear relationship \ (z \ cdot c = H \ cdot D \) only applies to redshifts up to \ (z \ approx 0 {,} 1 \), which applies to objects at a distance of 400 Mpc.

The Hubble constant \ (H_0 \) denotes the current rate of expansion of the universe. The Hubble constant is currently: \ [H_0 \ approx 70 \, \ rm {\ frac {km} {s \ cdot Mpc}} \] This value varies slightly depending on the measurement method.

"Escape speeds" with the Hubble-Lemaître law

In the picture on the right you can see the redshifts of the H and K lines of different galaxies.

If one interprets the speed \ (v \) calculated from the measured redshift \ (z \) using \ (v = c \ cdot z \) in the sense of the Doppler effect, one can derive the "escape speed" \ from the Hubble-Lemaître law (v _ {\ rm {Escape}} \) of a galaxy at a distance \ (D \). For \ (v _ {\ rm {Escape}} \) of a galaxy at the distance \ (D \) the following applies: \ [v _ {\ rm {Escape}} \ approx H_0 \ cdot D \]

However, this relationship is only valid as long as \ (H_0 \) can be regarded as almost constant. The exact relationship between redshift and distance is non-linear and requires an integration via the so-called scale factor \ (a (t) \) of the universe, which describes the relative expansion of the universe over time.