The Hubble parameter *H*_{0}
100*h* km s^{-1} Mpc^{-1} remains
uncertain, although no longer by the traditional factor of two. The
range of *h* determinations has been shrinking with time
[64].
De Vaucouleurs long contended that
*h* 1. Sandage has long
contended that
*h* 0.5, although a
recent reanalysis of the
Type Ia supernovae (SNe Ia) data coauthored by Sandage and Tammann
[111]
concludes that the latest data are consistent with
*h* = 0.6±0.04.

The Hubble parameter has been measured in two basic ways: (1) Measuring the distance to some nearby galaxies, typically by measuring the periods and luminosities of Cepheid variables in them; and then using these ``calibrator galaxies'' to set the zero point in any of the several methods of measuring the relative distances to galaxies. (2) Using fundamental physics to measure the distance to some distant object(s) directly, thereby avoiding at least some of the uncertainties of the cosmic distance ladder [109]. The difficulty with method (1) was that there was only a handful of calibrator galaxies close enough for Cepheids to be resolved in them. However, the HST Key Project on the Extragalactic Distance Scale has significantly increased the set of calibrator galaxies. The difficulty with method (2) is that in every case studied so far, some aspect of the observed system or the underlying physics remains somewhat uncertain. It is nevertheless remarkable that the results of several different methods of type (2) are rather similar, and indeed not very far from those of method (1). This gives reason to hope for convergence.

**3.1. Relative Distance Methods**

One piece of good news is that the several methods of measuring the
relative distances to galaxies now mostly seem to be consistent with
each other. These methods use either ``standard candles'' or empirical
relations between two measurable properties of a galaxy, one
distance-independent and the other distance-dependent. The favorite
standard candle is SNe Ia, and observers are now in good agreement.
Taking account of an empirical relationship between the SNe Ia light
curve shape and maximum luminosity leads to
*h* = 0.65±0.06
[103],
*h* = 0.64^{+0.08}_{-0.06}
[61], or
*h* = 0.63±0.03
[52,
93],
and the slightly lower value mentioned
above from the latest analysis coauthored by Sandage and Tammann
agrees within the errors. The HST Key Project result using SNe Ia is
*h* = 0.65±0.02±0.05, where the first error quoted is
statistical and the second is systematic
[50],
and their Cepheid metallicity-dependent luminosity-period relationship
[65]
has been used (this lowers *h* by 4%). Some of the other relative
distance methods are based on old stellar populations: the tip of the
red giant branch (TRGB), the planetary nebula luminosity function
(PNLF), the globular cluster luminosity function (GCLF), and the
surface brightness fluctuation method (SBF). The HST Key Project
result using these old star standard candles is
[43]
*h* = 0.66±0.04±0.06, including the Cepheid metallicity
correction. The old
favorite empirical relation used as a relative distance indicator is
the Tully-Fisher relation between the rotation velocity and luminosity
of spiral galaxies. The ``final'' value of the Hubble constant from
the HST Key Project taking all of these into account, including the
metallicity dependence of the Cepheid period-luminosity relation, is
[45]
*h* = 0.74±0.04±0.07, where the first error is
statistical and the second is systematic. The largest source of
systematic uncertainty is the distance to the LMC, which is here
assumed to have a distance modulus of 18.45. This is a significantly
higher *h* than their previous
[85]
*h* = 0.71±0.06, or
*h* = 0.68±0.06 including the Cepheid metallicity dependence, using a
LMC distance modulus of 18.5.

**3.2. Fundamental Physics Approaches**

The fundamental physics approaches involve either Type Ia or Type II supernovae, the Sunyaev-Zel'dovich (S-Z) effect, or gravitational lensing of quasars. All are promising, but in each case the relevant physics remains somewhat uncertain.

The ^{56}Ni radioactivity method for determining
*H*_{0} using Type Ia
SNe avoids the uncertainties of the distance ladder by calculating the
absolute luminosity of Type Ia supernovae from first principles using
plausible but as yet unproved physical models for ^{56}Ni
production. The first result obtained was that
*h* = 0.61±0.10
[3,
17];
however, another study
[77]
(cf. [126])
found that
uncertainties in extinction (i.e., light absorption) toward each
supernova increases the range of allowed *h*. Demanding that the
^{56}Ni radioactivity method agree with an expanding photosphere
approach leads to *h* = 0.60^{+0.14}_{-0.11}
[86].
The expanding photosphere method compares the expansion rate of the SN
envelope measured by redshift with its size increase inferred from its
temperature and magnitude. This approach was first applied to Type II
SNe; the 1992 result *h* = 0.6±0.1
[114]
was subsequently revised upward by the same authors to
*h* = 0.73±0.06±0.07
[115].
However, there are various complications with the physics of the
expanding envelope
[110,
35].

The S-Z effect is the Compton scattering of microwave background
photons from the hot electrons in a foreground galaxy cluster. This
can be used to measure *H*_{0} since properties of the cluster gas
measured via the S-Z effect and from X-ray observations have different
dependences on *H*_{0}. The result from the first cluster
for which
sufficiently detailed data was available, A665 (at *z* = 0.182), was
*h* = (0.4 - 0.5)±0.12
[13];
combining this with data on A2218 (*z* = 0.171) raised this somewhat to
*h* = 0.55±0.17
[12].
The history and more recent data have been reviewed by Birkinshaw
[14],
who concludes that the available data give a Hubble parameter
*h* 0.6 with a
scatter of about 0.2. But since the available measurements are not
independent, it does not follow that
*h* = 0.6±0.1; for example, there
is a selection effect that biases low the *h* determined this way.

Several quasars have been observed to have multiple images separated
by ~ a few arc seconds; this
phenomenon is interpreted as
arising from gravitational lensing of the source quasar by a galaxy
along the line of sight (first suggested by
[100];
reviewed in
[129]).
In the first such system discovered, QSO 0957+561 (*z* = 1.41), the
time delay *t* between
arrival at the
earth of variations in the quasar's luminosity in the two images has
been measured to be, e.g., 409±23 days
[89],
although other authors found a value of 540±12 days
[94].
The shorter *t* has
now been confirmed
[72,
117].
Since *t*
^{2}
*H*_{0}^{-1}, this
observation allows an estimate of the Hubble parameter. The latest
results for *h* from 0957+561, using all available data, are
*h* = 0.64±0.13 (95% C.L.)
[72],
and *h* = 0.62±0.07
[39],
where the error does not include systematic
errors in the assumed form of the lensing mass distribution.

The first quadruple-image quasar system discovered was PG1115+080.
Using a recent series of observations
[113],
the time delay between images B and C has been determined to be about
24±3 days. A simple model for the lensing galaxy and the nearby
galaxies then leads to
*h* = 0.42±0.06
[113], although
higher values for *h* are obtained by more sophisticated analyses:
*h* = 0.60±0.17
[63],
*h* = 0.52±0.14
[73].
The results depend on how the lensing galaxy and those in
the compact group of which it is a part are modelled.

Another quadruple-lens system, B1606+656, leads to
*h* = 0.59±0.08±0.15, where the first error is the 95%
C.L. statistical error,
and the second is the estimated systematic uncertainty
[41].
Time delays have also recently been determined for the
Einstein ring system B0218+357, giving
*h* = 0.69^{+0.13}_{-0.19} (95%
C.L.) [11].

Mainly because of the systematic uncertainties in modelling the mass
distribution in the lensing systems, the uncertainty in the *h*
determination by gravitational lens time delays remains rather large.
But it is reassuring that this completely independent method gives
results consistent with the other determinations.

To summarize, relative distance methods favor a value
*h* 0.6 -
0.8. Meanwhile the fundamental physics methods typically lead to
*h* 0.4 - 0.7. Among
fundamental physics approaches, there has
been important recent progress in measuring *h* via the
Sunyev-Zel'dovich effect and time delays between different images of
gravitationally lensed quasars, although the uncertainties remain
larger than via relative distance methods. For the rest of this
review, we will adopt a value of *h* = 0.65±0.08. This corresponds to
*t*_{0} = 6.52*h*^{-1} *Gyr* = 10±2
Gyr for _{m} = 1 -
probably too low compared to the ages of the oldest globular clusters.
But for
_{m} = 0.2 and
_{} = 0, or alternatively
for _{m} = 0.4 and
_{} = 0.6,
*t*_{0} = 13±2 Gyr, in
agreement with the globular cluster estimate of
*t*_{0}. This is one of
the weakest of the several arguments for low
_{m}, a non-zero
cosmological constant, or both.