Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fate of the Universe, Age of the Universe, Dark Matter, and the Decaying
  Vacuum Energy   It is shown that in the cosmological models based on a vacuum energy decaying
as a^{-2}, where a is the scale factor of the universe, the fate of the
universe in regard to whether it will collapse in future or expand forever is
determined not by the curvature constant k but by an effective curvature
constant k_{eff}. It is argued that a closed universe with k=1 may expand
forever, in other words simulate the expansion dynamics of a flat or an open
universe because of the possibility that k_{eff}=0 or -1, respectively. Two
such models, in one of which the vacuum does not interact with matter and in
another of which it does, are studied. It is shown that the vacuum equation of
state p_{vac}= -\rho_{vac} may be realized in a decaying vacuum cosmology
provided the vacuum interacts wuth matter. The optical depths for gravitational
lensing as a function of the matter density and other parameters in the models
are calculated at a source redshift of 2. The age of the universe is discussed
and shown to be compatible with the new Hipparcos lower limit of 11Gyr. The
possibility that a time-varying vacuum energy may serve as dark matter is
suggested.

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn