42 An introduction to the physics of cosmology
2.5.5 Evidence for vacuum energy at late times
The idea of inflation is audacious, but undeniably speculative. However, once we
accept the idea that quantum fields can generate an equation of state resembling
a cosmological constant, we need not confine this mechanism to GUT-scale
energies. There is no known mechanism that requires the minimum ofV(φ)to
lie exactly at zero energy, so it is quite plausible that there remains in the universe
today some non-zero vacuum energy.
The most direct way of detecting vacuum energy has been the immense
recent progress in the use of supernovae as standard candles. Type Ia SNe
have been used as standard objects for around two decades, with an rms scatter
in luminosity of 40%, and so a distance error of 20%. The big breakthrough
came when it was realized that the intrinsic timescale of the SNe correlates with
luminosity (a brighter SNe lasts longer). Taking out this effect produces corrected
standard candles that are capable of measuring distances to about 5% accuracy.
Large search campaigns have made it possible to find of the order of 100 SNe
over the range 0. 1 .z.1, and two teams have used this strategy to make an
empirical estimate of the cosmological distance–redshift relation.
The results of theSupernova Cosmology Project(e.g. Perlmutteret al1998)
and theHigh-z Supernova Search(e.g. Riesset al1998) are highly consistent.
Figure 2.5 shows the Hubble diagram from the latter team. The SNe magnitudes
areK-corrected, so that their variation with redshift should be a direct measure of
luminosity distance as a function of redshift.
We have seen earlier that this is written as the following integral, which must
usually be evaluated numerically:
DL(z)=( 1 +z)R 0 Sk(r)=( 1 +z)c
H 0| 1 −|−^1 /^2
×Sk[∫
z0| 1 −|^1 /^2 dz′
√
( 1 −)( 1 +z′)^2 +v+m( 1 +z′)^3]
,
where=m+v,andSkis sinh if<1, otherwise sin. It is clear from
figure 2.5 that the empirical distance–redshift relation is very different from the
simplest inflationary prediction, which is the=1 Einstein–de Sitter model;
by redshift 0.6, the SNe are fainter than expected in this model by about 0.5
magnitudes. If this model fails, we can try adjustingmandvin an attempt to
do better. Comparing each such model to the data yields the likelihood contours
shown in figure 2.6, which can be used in the standard way to set confidence
limits on the cosmological parameters. The results very clearly require a low-
density universe. For=0, a very low density is just barely acceptable, with
m. 0 .1. However, the discussion of the CMB later shows that such a heavily
open model is hard to sustain. The preferred model hasv1; if we restrict
ourselves to the inflationaryk=0, then the required parameters are very close to
(m,v)=( 0. 3 , 0. 7 ).