286
19 Inflation and Some Questions
the slow roll the universe expands enormously with an approximately exponential
scale factor. Finally, the inflaton field decreases to a point where it oscillates at the
bottom of a potential well of the potential V , and its energy is somehow converted
into the particles of matter that now exist in the universe, that is the quarks and leptons
and other constituents of the standard model (Quigg 2006; Linde 2007). To build a
specific theory one must choose a potential that allows this sort of behavior; there
are an infinite number of potential choices possible since there is little or no direct
observational data to constrain the choice. Figure 19.2 is a generic sketch (Kinney
2002).
Some specific examples of inflaton potentials are
V =
1
2
m
2
ϕ
2
mass term
(19.13a)
V = λϕ
4
simple ad hoc
(19.13b)
V = λ(ϕ
2
− M
2
)
2 Higgs potential
(19.13c)
See Exercise 19.8. These potentials and many others have been studied by theorists
with the goal of giving predictions that may be compared with observation (Liddle
1999; Linde 2007; Kinney 2002). Almost needless to say, no inflaton field has been
detected in the laboratory.
19.3 Origin of Structure
In the previous section we focused on the way that an inflaton field can act like a
constant vacuum density and cause inflation, thus resolving the horizon problem.
There is another important feature of the inflation scenario: it provides a mechanism
for the origin of the structure seen in the later universe, including the anisotropy
spectrum of the CMB that we discussed in Chap. 17.
As in the preceding section we assume that the inflaton field is nearly uniform so
that its energy density is also nearly uniform and it acts much like a constant vacuum
density, that is a cosmological constant. However quantum theory does not allow
a strictly uniform field since that is not consistent with the uncertainly principle.
Thus we must consider quantum fluctuations in the inflaton field. It is a remarkable
feature of the inflaton scenario that fluctuations must occur, and fluctuations of very
small size and magnitude can grow as the universe expands, and these become the
seeds for all the structure we observe in the universe. See Exercise 19.9. Specifically,
the fluctuations produce a spatial variation in energy density, and that gives rise
to anisotropies in the CMB, and subsequently produces concentrations of energy
that are seeds for the formation of stars and galaxies and clusters of galaxies. In
particular the anisotropies of the CMB can be understood and compared with the
observed spectrum.
19 Inflation and Some Questions
the slow roll the universe expands enormously with an approximately exponential
scale factor. Finally, the inflaton field decreases to a point where it oscillates at the
bottom of a potential well of the potential V , and its energy is somehow converted
into the particles of matter that now exist in the universe, that is the quarks and leptons
and other constituents of the standard model (Quigg 2006; Linde 2007). To build a
specific theory one must choose a potential that allows this sort of behavior; there
are an infinite number of potential choices possible since there is little or no direct
observational data to constrain the choice. Figure 19.2 is a generic sketch (Kinney
2002).
Some specific examples of inflaton potentials are
V =
1
2
m
2
ϕ
2
mass term
(19.13a)
V = λϕ
4
simple ad hoc
(19.13b)
V = λ(ϕ
2
− M
2
)
2 Higgs potential
(19.13c)
See Exercise 19.8. These potentials and many others have been studied by theorists
with the goal of giving predictions that may be compared with observation (Liddle
1999; Linde 2007; Kinney 2002). Almost needless to say, no inflaton field has been
detected in the laboratory.
19.3 Origin of Structure
In the previous section we focused on the way that an inflaton field can act like a
constant vacuum density and cause inflation, thus resolving the horizon problem.
There is another important feature of the inflation scenario: it provides a mechanism
for the origin of the structure seen in the later universe, including the anisotropy
spectrum of the CMB that we discussed in Chap. 17.
As in the preceding section we assume that the inflaton field is nearly uniform so
that its energy density is also nearly uniform and it acts much like a constant vacuum
density, that is a cosmological constant. However quantum theory does not allow
a strictly uniform field since that is not consistent with the uncertainly principle.
Thus we must consider quantum fluctuations in the inflaton field. It is a remarkable
feature of the inflaton scenario that fluctuations must occur, and fluctuations of very
small size and magnitude can grow as the universe expands, and these become the
seeds for all the structure we observe in the universe. See Exercise 19.9. Specifically,
the fluctuations produce a spatial variation in energy density, and that gives rise
to anisotropies in the CMB, and subsequently produces concentrations of energy
that are seeds for the formation of stars and galaxies and clusters of galaxies. In
particular the anisotropies of the CMB can be understood and compared with the
observed spectrum.