Image 1 Caption: Alexander Friedmann (1888--1925) serving as an aviator in Imperial Russian Air Service, Imperial Russian Army, World War I (1914--1918), 1916 Aug01. A Russian-Soviet aviator, ballonist, mathematician, meteorologist, physicist, pioneering cosmologist, and discoverer of the eponymous Friedmann equation in 1922. See also Wikipedia: Alexander Friedmann and The MacTutor History of Mathematics archive: Aleksandr Aleksandrovich Friedmann.
Features:
The Friedmann equation is
Solutions of the Friedmann equation for the cosmic scale factor a(t) that are historically interesting are often called universes: e.g., the Einstein universe (1917) and the de Sitter universe (1917).
A zero or non-zero
cosmological constant Λ
can be included in the
Friedmann equation, and
so in the
FE models.
However, a key point of the
FE models
is that in all cases they give NON-STATIC solutions---unless
cosmological constant Λ
to adjusted to exactly the right value to give the
Einstein universe.
Other than the
Einstein universe case,
the FE models
must expand or contract---and they do this maintaining
the cosmological principle.
Einstein is seen here,
chalk
in hand,
lecturing
in Vienna,
Austria in
1921.
In the days when he was the supreme master of
physics.
If either of them had discovered the
Friedmann equation, it would
have saved them a lot of work and would have clarified
general relativistic
cosmology
several years earlier than in actual history.
Moreover, Lemaitre
was able using published
data on
galaxies
to find values for
the Hubble constant
(575 (km/s)/Mpc or 670 (km/s)/Mpc: Way 2013, p. 14)
that were relatively close to what
Hubble found in
1929
(500 (km/s)/Mpc:
Hubble 1929, 3rd to last paragraph;
Bo-39;
Tamann 2005;
Wikipedia: Timeline of
Hubble constant values).
In fact, both
Lemaitre's
and Hubble's
Hubble constant values
are too large by a large factor because of a large
calibration
error and
other measurement uncertainties.
Actually,
Hubble constant = 70 (km/s)/Mpc (fiducial value accurate to within ∼ 10 %).
To emphasize, Lemaitre
did NOT discover that the
observable universe obeyed
Hubble's law
with his Hubble constant,
but that if the observable universe obeyed
Hubble's law and one used the
data he used (which had as aforesaid
a large calibration
error
and other
measurement uncertainties),
then the Hubble constant
had the values he found.
Lemaitre did publish
his results in 1927 as aforesaid,
but they did NOT attract much interest and it seems likely that he did NOT
wish to get into a
piority dispute
with Hubble, and so
he did NOT emphasize to his pre
Edwin Hubble (1889--1953)
Hubble's law work.
However, in 2018,
the IAU
decided to give Lemaitre
some credit and formally changed the name of
Hubble's law
from
Hubble's law
to the Hubble-Lemaitre law.
Yours truly does NOT think the longer name will be
much used.
We've always called
Hubble's law
Hubble's law
and it's shorter to say and write.
v=H_0*r ,
where "v" is recession velocity
from the Milky Way,
"H_0" is the
Hubble constant
H_0 = [(70 km/s)/Mpc]*h_70, h_70 = H_0/[(70 km/s)/Mpc],
and "r" is
proper distance (i.e., distance that
can be measured with a ruler at one instant in cosmic time) from
Milky Way.
Note that in general "v" and "r" are NOT direct observables, but
they become direct observables as
asymptotically as r&arow;0,
and so "H_0" can be directly measured.