[ Pobierz całość w formacie PDF ]

as the baryon density or the redshift of reionization can confound our
measurement of the things we are interested in, namely r and n. Fig-
ure 16 shows likelihood contours for r and n based on current CMB
data [41]. Perhaps the most distinguishing feature of this plot is that
the error bars are smaller than the plot itself! The favored model is
a model with negligible tensor fluctuations and a slightly “red” spec-
trum, n 1. Future measurements, in particular the MAP [39] and
Planck satellites [40], will provide much more accurate measurements
of the C spectrum, and will allow correspondingly more precise deter-
11
The classification might also appear ill-defined, but it can be made more rigorous as a set of
inequalities between slow roll parameters. Refs. [37, 38] contain a more detailed discussion.
47
Figure 16.
Error bars in the r, n plane for the Boomerang and MAXIMA data
sets [41]. The lines on the plot show the predictions for various potentials. Similar
contours for the most current data can be found in Ref. [20].
mination of cosmological parameters, including r and n. (In fact, by
the time this article sees print, the first release of MAP data will have
happened.) Figure 17 shows the expected errors on the C spectrum
for MAP and Planck, and Fig. 18 shows the corresponding error bars
in the (r, n) plane. Note especially that Planck will make it possible to
clearly distinguish between different models for inflation. So all of this
apparently esoteric theorizing about the extremely early universe is not
idle speculation, but real science. Inflation makes a number of specific
and observationally testable predictions, most notably the generation of
density and gravity-wave fluctuations with a nearly (but not exactly)
scale-invariant spectrum, and that these fluctuations are Gaussian and
adiabatic. Furthermore, feasible cosmological observations are capable
of telling apart different specific models for the inflationary epoch, thus
48
Figure 17.
Expected errors in the C spectrum for the MAP (light blue) and Planck
(dark blue) satellites. (Figure courtesy of Wayne Hu [21].)
providing us with real information on physics near the expected scale
of Grand Unification, far beyond the reach of existing accelerators. In
the next section, we will stretch this idea even further. Instead of us-
ing cosmology to test the physics of inflation, we will discuss the more
speculative idea that we might be able to use inflation itself as a mi-
croscope with which to illuminate physics at the very highest energies,
where quantum gravity becomes relevant.
5.
Looking for signs of quantum gravity in
inflation
We have seen that inflation is a powerful and predictive theory of the
physics of the very early universe. Unexplained properties of a standard
FRW cosmology, namely the flatness and homogeneity of the universe,
49
1
0.5
0.8
0.85
0.9
0.95
1
Figure 18.
Error bars in the r, n plane for MAP and Planck [38]. These ellipses
show the expected 2 - σ errors. The lines on the plot show the predictions for various
potentials. Note that these are error bars based on synthetic data: the size of the
error bars is meaningful, but not their location on the plot. The best fit point for r
and n from real data is likely to be somewhere else on the plot.
are natural outcomes of an inflationary expansion. Furthermore, infla-
tion provides a mechanism for generating the tiny primordial density
fluctuations that seed the later formation of structure in the universe.
Inflation makes definite predictions, which can be tested by precision
observation of fluctuations in the CMB, a program that is already well
underway.
In this section, we will move beyond looking at inflation as a sub-
ject of experimental test and discuss some intriguing new ideas that
50
indicate that inflation might be useful as a tool to illuminate physics
at extremely high energies, possibly up to the point where effects from
quantum gravity become relevant. This idea is based on a simple obser-
vation about scales in the universe. As we discussed in Sec. 2, quantum
field theory extended to infinitely high energy scales gives nonsensical
(i.e., divergent) results. We therefore expect the theory to break down at
high energy, or equivalently at very short lengths. We can estimate the
length scale at which quantum mechanical effects from gravity become
important by simple dimensional analysis. We define the Planck length
Pl by an appropriate combination of fundamental constants as
dH
∼ 1060,
lPl
or, on a log scale,
dH
ln
∼ 140.
lPl
(134)
(135)
This is a big number, but we recall our earlier discussion of the flatness
and horizon problems and note that inflation, in order to adequately
explain the flatness and homogeneity of the universe, requires the scale
factor to increase by at least a factor of e55. Typical models of inflation
predict much more expansion, e1000 or more. We remember that the
wavelength of quantum modes created during the inflationary expansion,
such as those responsible for density and gravitational-wave fluctuations,
have wavelengths which redshift proportional to the scale factor, so that
¯
hG
Pl ∼
∼ 10-35m.
(133)
c3
For processes probing length scales shorter than Pl, such as quantum
modes with wavelengths λ Pl, we expect some sort of new physics to
be important. There are a number of ideas for what that new physics
might be, for example string theory or noncommutative geometry or
discrete spacetime, but physics at the Planck scale is currently not well
understood. It is unlikely that particle accelerators will provide insight
into such high energy scales, since quantum modes with wavelengths
less than Pl will be characterized by energies of order 1019 GeV or so,
and current particle accelerators operate at energies around 103 GeV.12
However, we note an interesting fact, namely that the ratio between the
current horizon size of the universe and the Planck length is about
12
This might not be so in “braneworld” scenarios where the energy scale of quantum gravity
can be much lower [42].
51
so that the wavelength λi of a mode at early times can be given in terms
of its wavelength λ0 today by
λi e-Nλ0.
(136)
This means that if inflation lasts for more than about N ∼ 140 e-folds,
fluctuations of order the size of the universe today were smaller than the
Planck length during inflation! This suggests the possibility that Plank- [ Pobierz całość w formacie PDF ]