266
17 Earlier Times and Radiation
gluons interact less strongly at high energies (Griffiths 1987; Peskin 2019). We will
discuss the events of this era further, although briefly, in Chap. 18. Suffice it to say
for now that our understanding of the radiation era is rather complete and dependable
(Liddle 2003; Peebles 1993; Weinberg 1988).
Looking backward in time toward the radiation era let us ask for what value
of the scale factor the temperature of the hot early universe dropped low enough
that neutral atoms in their ground state could exist. Since most of the atoms in the
universe are hydrogen this involves the atomic physics of hydrogen, which is wellunderstood. The term recombination refers to electrons binding with protons to form
neutral hydrogen atoms, which are generally in a high energy state rather than the
ground state. The excited neutral hydrogen atoms then emit photons and transition
to the ground state; the photons can then interact with other hydrogen atoms. The
term decoupling refers to the production of such photons that subsequently interact
little with neutral hydrogen and propagate almost freely, often called free-streaming.
These photons constitute the CMB which we observe today. Recombination and
decoupling that occurred shortly afterward, are distinct but closely related events.
Note that recombination is a misnomer since the electrons and protons were never
previously combined, but it is an established misnomer and almost universally used.
The time of decoupling thus corresponds to about the temperature at which
hydrogen is largely ionized. This temperature can be estimated theoretically and
measured experimentally, and is about 3000 K corresponding to an energy of 0.26 eV.
Note that this is in the ballpark of the binding energy of hydrogen, 13.6 eV. See Exercise 17.1 and Liddle (2003). From this temperature and the present temperature of
the CMB we can estimate from (17.2) the scale factor to be
a dc
a 0
=
T 0
T dc
≈
2.725 K
3000 K
≈
1
1.1 × 10
3
, dc denotes decoupling,
(17.8)
so the redshift is about
z =
a 0
a dc
− 1 = 1100.
(17.9)
The photons present at decoupling have been free-streaming ever since and are the
ones we now see in the CMB; the decoupling event is also appropriately referred
to as the last scattering. Thus we can think of the CMB as a photo of the big bang
fireball redshifted in frequency by a factor of about 1000. As such we should expect
it to contains a great deal of information about the universe at that time—and also
earlier and later times. This is quite true as we will see in later chapters (Liddle 2003;
Peebles 1993; Weinberg 1988).
In the following section we will study the scale factor in the radiation dominated
era and use it to estimate the time at which decoupling occurred.
17 Earlier Times and Radiation
gluons interact less strongly at high energies (Griffiths 1987; Peskin 2019). We will
discuss the events of this era further, although briefly, in Chap. 18. Suffice it to say
for now that our understanding of the radiation era is rather complete and dependable
(Liddle 2003; Peebles 1993; Weinberg 1988).
Looking backward in time toward the radiation era let us ask for what value
of the scale factor the temperature of the hot early universe dropped low enough
that neutral atoms in their ground state could exist. Since most of the atoms in the
universe are hydrogen this involves the atomic physics of hydrogen, which is wellunderstood. The term recombination refers to electrons binding with protons to form
neutral hydrogen atoms, which are generally in a high energy state rather than the
ground state. The excited neutral hydrogen atoms then emit photons and transition
to the ground state; the photons can then interact with other hydrogen atoms. The
term decoupling refers to the production of such photons that subsequently interact
little with neutral hydrogen and propagate almost freely, often called free-streaming.
These photons constitute the CMB which we observe today. Recombination and
decoupling that occurred shortly afterward, are distinct but closely related events.
Note that recombination is a misnomer since the electrons and protons were never
previously combined, but it is an established misnomer and almost universally used.
The time of decoupling thus corresponds to about the temperature at which
hydrogen is largely ionized. This temperature can be estimated theoretically and
measured experimentally, and is about 3000 K corresponding to an energy of 0.26 eV.
Note that this is in the ballpark of the binding energy of hydrogen, 13.6 eV. See Exercise 17.1 and Liddle (2003). From this temperature and the present temperature of
the CMB we can estimate from (17.2) the scale factor to be
a dc
a 0
=
T 0
T dc
≈
2.725 K
3000 K
≈
1
1.1 × 10
3
, dc denotes decoupling,
(17.8)
so the redshift is about
z =
a 0
a dc
− 1 = 1100.
(17.9)
The photons present at decoupling have been free-streaming ever since and are the
ones we now see in the CMB; the decoupling event is also appropriately referred
to as the last scattering. Thus we can think of the CMB as a photo of the big bang
fireball redshifted in frequency by a factor of about 1000. As such we should expect
it to contains a great deal of information about the universe at that time—and also
earlier and later times. This is quite true as we will see in later chapters (Liddle 2003;
Peebles 1993; Weinberg 1988).
In the following section we will study the scale factor in the radiation dominated
era and use it to estimate the time at which decoupling occurred.