290
19 Inflation and Some Questions
19.4 The Physical Nature of Dark Energy
In the preceding chapters we have taken the dark energy to be synonymous with
vacuum energy or the cosmological constant λ, whose equivalent energy density is
ρ V =
c
4
8π G
.
(19.19)
This is completely consistent with observations. In particular observations before
about 2020 placed the w parameter for dark energy in the interval −0.9 > w > −1.1.
A time variation of w has been searched for and not observed. In the context of
general relativity theory dark energy may be considered to be the constant energy of
the vacuum, that is space which is empty of all other matter or energy.
In quantum field theory the vacuum also has a constant nonzero energy density,
which we mentioned briefly in Chap. 14. But the vacuum of quantum field theory
has an infinite density, which of course is not to be taken seriously. As we mentioned
before, attempts to understand this divergent theoretical energy using simple dimensional cutoff arguments give a finite estimate for the vacuum energy, specifically the
Planck energy divided by the Planck distance cubed (see Sect. 19.6). But this value
disagrees with the observed value by more than 120 orders of magnitude, which
some consider a theoretical catastrophe (Adler 1995). If supersymmetry is invoked
in the field theory the disagreement is less, but still about 60 orders of magnitude, and
remains nonsense. Thus the quantum field vacuum does not appear to be understood
and does not appear to be related to the general relativity vacuum in any evident way.
It is reasonable for us to ignore it when working in cosmology.
It is also possible to interpret the dark energy as “stuff” whose energy density
is very nearly constant. That is, the present dark energy could be an analog of the
inflaton field used in inflation theory as we discussed in the preceding section, but
with a vastly smaller energy density. Some versions of the stuff are referred to as
quintessence, and there are many other speculative ideas and names. In addition
there are speculations on a modification of gravitational theory, and many papers
and books have been written on the subject (Amendola 2010).
If we accept the cosmological constant as the explanation for dark energy then its
qualitative nature is not at all mysterious since the Einstein equations are completely
consistent with a cosmological constant; indeed the equations almost demand it!
However the very small numerical value of the cosmological constant remains an
interesting and perhaps deep question. The value is very important since it is related
to the size and age of the actual universe: the value of the Hubble constant in the
LCDM universe is roughly the asymptotic or de Sitter value
√
3//.
There are essentially two viewpoints one can take regarding the numerical value of
the cosmological constant: one may try to calculate it from some fundamental theory
or principle, or one may simply take it as a fact of nature, an accidental number.
The first of these has not been successful to date. The second has led to interesting
questions and may be related to the idea of a multiverse.
19 Inflation and Some Questions
19.4 The Physical Nature of Dark Energy
In the preceding chapters we have taken the dark energy to be synonymous with
vacuum energy or the cosmological constant λ, whose equivalent energy density is
ρ V =
c
4
8π G
.
(19.19)
This is completely consistent with observations. In particular observations before
about 2020 placed the w parameter for dark energy in the interval −0.9 > w > −1.1.
A time variation of w has been searched for and not observed. In the context of
general relativity theory dark energy may be considered to be the constant energy of
the vacuum, that is space which is empty of all other matter or energy.
In quantum field theory the vacuum also has a constant nonzero energy density,
which we mentioned briefly in Chap. 14. But the vacuum of quantum field theory
has an infinite density, which of course is not to be taken seriously. As we mentioned
before, attempts to understand this divergent theoretical energy using simple dimensional cutoff arguments give a finite estimate for the vacuum energy, specifically the
Planck energy divided by the Planck distance cubed (see Sect. 19.6). But this value
disagrees with the observed value by more than 120 orders of magnitude, which
some consider a theoretical catastrophe (Adler 1995). If supersymmetry is invoked
in the field theory the disagreement is less, but still about 60 orders of magnitude, and
remains nonsense. Thus the quantum field vacuum does not appear to be understood
and does not appear to be related to the general relativity vacuum in any evident way.
It is reasonable for us to ignore it when working in cosmology.
It is also possible to interpret the dark energy as “stuff” whose energy density
is very nearly constant. That is, the present dark energy could be an analog of the
inflaton field used in inflation theory as we discussed in the preceding section, but
with a vastly smaller energy density. Some versions of the stuff are referred to as
quintessence, and there are many other speculative ideas and names. In addition
there are speculations on a modification of gravitational theory, and many papers
and books have been written on the subject (Amendola 2010).
If we accept the cosmological constant as the explanation for dark energy then its
qualitative nature is not at all mysterious since the Einstein equations are completely
consistent with a cosmological constant; indeed the equations almost demand it!
However the very small numerical value of the cosmological constant remains an
interesting and perhaps deep question. The value is very important since it is related
to the size and age of the actual universe: the value of the Hubble constant in the
LCDM universe is roughly the asymptotic or de Sitter value
√
3//.
There are essentially two viewpoints one can take regarding the numerical value of
the cosmological constant: one may try to calculate it from some fundamental theory
or principle, or one may simply take it as a fact of nature, an accidental number.
The first of these has not been successful to date. The second has led to interesting
questions and may be related to the idea of a multiverse.