The goal of this paper is to determine the absolute age of the universe
*t*_{0}(*h*, _{m},
_{}).
Knowledge of *h* alone cannot be used to determine *t*_{0}
with much accuracy.
For example, the estimate *h* = 0.68 ± 0.10 corresponds to 8 <
*t*_{0} < 22 Ga
(Fig. 4).
Similary, knowledge of (_{m},
_{}) yields
*H*_{0}*t*_{0}
(_{m},
_{}) not
*t*_{0}(*H*_{0} is the usual Hubble constant).
When one inserts a preferred value of *h* into a
*H*_{0}*t*_{0} result, one
is not taking into consideration
the correlations between preferred *h* values and preferred
(_{m},_{}) values
that are inherent, for example, in
_{CMB}(*h*,
_{m},_{})
and _{baryons}(*h*,
_{m}).
The preferred values of *h* in these likelihoods depend on
_{m} and
_{}.
Perlmutter et al.
(4)
used SNe measurements to constrain
(_{m},
_{}) and
obtained values for *H*_{0}*t*_{0}. To obtain
*t*_{0}, they did the analysis with *h*
set equal to the value preferred by their SNe data, *h* = 0.63.
Their result is *t*_{0} = 14.5 ± 1.0 (0.63 / *h*) Ga.
When a flat universe is assumed, they obtain
*t*_{0}^{flat} =
14.9^{+1.4}_{-1.1} (0.63 / *h*) Ga.
Riess et al. (5)
found *h* = 0.65 ± 0.02 from their SNe data.
Marginalizing over this Hubble value and over
_{} and
_{m},
they report *t*_{0} = 14.2 ± 1.7 Ga.
When a flat universe is assumed, their results yield
*t*_{0}^{flat} = 15.2
± 1.7 Ga. The Perlmutter et al.
(4) and Riess
(5)
results are in good agreement.
When I assume *h* = 0.64 ± 0.02, I get
*t*_{0} = 14.6^{+1.6}_{-1.1} Ga.
This result is plotted in
Fig. 2 to illustrate the important
influence on the result of using a small *h* uncertainty.
Efstathiou et al.
(12),
on the basis of a combination of CMB and
Perlmutter et al.
(4)
SNe data, have
estimated *t*_{0} = 14.6 (*h* / 0.65)^{-1} Ga.
I used *h* = 0.65 ± 0.0 with this data combination to get
*t*_{0} = 14.5^{+1.2}_{-1.0} Ga. However,
when I used *h* = 0.65 ± 0.10,
the result is 0.7 Gy lower (*t*_{0} =
13.8^{+3.2}_{-1.4} Ga).
To obtain the main result, I used uncertainties large enough to reflect
our knowledge of *h*
on the basis of many sources. The use of a larger *h* uncertainty
contributes to the substantially younger ages found here
(23).

A potential problem with the SNe ages is the high region,
(_{m},_{})
(0.8, 1.5), which
dominates the SNe fit.
This region is strongly disfavored by the six other constraints
considered here (see Fig. 3).
These high (_{m},
_{}) values allow lower ages than the
*t*_{0}^{flat} SNe
results because the slope of the iso-*t*_{0} contours
(Fig. 3B) is larger than the slope of the
SNe contours.
The *t*_{0}^{flat} results are not as subject to
this problem and are the results most analogous to the
result reported here, despite the fact that the SNe
*t*_{0}^{flat} results are
less consistent with the result reported here.
There are several independent cosmological measurements which have not been
included in this analysis either because
a consensus has not yet been reached
[gravitational lensing limits
(27,
28,
29,
30)]
or because the analysis of the measurements has not been done in a way
that is sufficiently free of conditioning on certain parameters [local
velocity field limits
(31)].
Doubts about some of the observations used here are
discussed in
(32).
There has been speculation recently that the evidence for
_{} is really evidence
for some form of stranger dark energy that we have incorrectly been
interpreting as _{}.
Several workers have tested this idea.
The evidence so far indicates that the cosmological constant interpretation
fits the data as well as or better than an explanation based on
more mysterious dark energy
(4,
33,
34).