A Non-empty Bouncing Milne Model for the Universe
7
A non-empty cosmological model which has a uniform expansion rate throughout
the history of the universe may be called an ‘eternal coasting model’. A characteristic
feature for a coasting model is that it will have vanishing gravitational charge, i.e.
ρ + 3 p = 0, where ρ denotes the total matter/energy density of the universe and
p is the pressure due to such matter/energy distribution. In view of the mounting
supportive evidences obtained from the above analyses of most recent cosmological
data [8, 10], one notes that the eternal coasting models deserve continued scrutiny,
both from the conceptual and observational fronts.
2.3 Non-empty Eternal Coasting Model
A non-empty, closed cosmological model that is coasting throughout the history of
the universe after a bounce from a previous contracting phase was first proposed in
1996 by the author and Professor Joseph [11, 12]. This model coincided with the
widely discussed Ozer–Taha model [13, 14] at the earliest epochs. The attempt by
Ozer and Taha was to put forward an alternative to the theory of inflation, which
solves the flatness problem, horizon problem, etc. They obtained a bouncing, nonsingular solution with a =
(a
2
0 + t 2 ), and speculated that a 0 , the minimum radius
of the universe, has some small value. After the bounce, the model reaches the a ∝ t
phase for some time, but soon deviates from it to enter the decelerating standard
big bang evolution and continued in it. On the contrary, the eternal coasting model
mentioned above in [11, 12] has the evolution a =
(a
2
0 + t 2 ) throughout the cosmological history. Moreover, a quantum cosmological treatment gave the result that
the minimum radius a 0 is of the order of Planck length. Also, the universe is comprised of visible matter, dark matter and dark energy and there is a possibility that
matter is continuously being created in the universe at the expense of dark energy.
These models were shown to have none of the cosmological problems, such as singularity, horizon, flatness, monopole, cosmological constant, size, age, etc. This has
almost vanishing gravitational charge ρ + 3 p ≈ 0 after the bounce.
A slightly different model proposed by us in [15], which has ρ + 3 p = 0 and an
initial singularity, is an always coasting cosmology with a ∝ t, obtained by extending the dimensional argument of [16]. This modified Chen–Wu model, which can
have k = 0, ±1, has both matter and a time-varying cosmological constant. As in the
above case, it consists of ordinary matter, dark matter and dark energy, which gradually decays to form matter. Comparison of this model with the CDM model was
performed using the SNe Ia data, with the help of the Bayesian theory [17], by the
author and Professor J. V. Narlikar. The results showed that the evidence against the
coasting model, when compared to the CDM model, is only marginal. In 2005, an
analysis was again performed [18] using the then-available SNe data to see whether
the data really favours a decelerating past for the universe. Again, the conclusion
was that the evidence is not strong enough to discriminate the CDM model from a
coasting cosmology. Recently, a quantum cosmological treatment [19] showed that a
7
A non-empty cosmological model which has a uniform expansion rate throughout
the history of the universe may be called an ‘eternal coasting model’. A characteristic
feature for a coasting model is that it will have vanishing gravitational charge, i.e.
ρ + 3 p = 0, where ρ denotes the total matter/energy density of the universe and
p is the pressure due to such matter/energy distribution. In view of the mounting
supportive evidences obtained from the above analyses of most recent cosmological
data [8, 10], one notes that the eternal coasting models deserve continued scrutiny,
both from the conceptual and observational fronts.
2.3 Non-empty Eternal Coasting Model
A non-empty, closed cosmological model that is coasting throughout the history of
the universe after a bounce from a previous contracting phase was first proposed in
1996 by the author and Professor Joseph [11, 12]. This model coincided with the
widely discussed Ozer–Taha model [13, 14] at the earliest epochs. The attempt by
Ozer and Taha was to put forward an alternative to the theory of inflation, which
solves the flatness problem, horizon problem, etc. They obtained a bouncing, nonsingular solution with a =
(a
2
0 + t 2 ), and speculated that a 0 , the minimum radius
of the universe, has some small value. After the bounce, the model reaches the a ∝ t
phase for some time, but soon deviates from it to enter the decelerating standard
big bang evolution and continued in it. On the contrary, the eternal coasting model
mentioned above in [11, 12] has the evolution a =
(a
2
0 + t 2 ) throughout the cosmological history. Moreover, a quantum cosmological treatment gave the result that
the minimum radius a 0 is of the order of Planck length. Also, the universe is comprised of visible matter, dark matter and dark energy and there is a possibility that
matter is continuously being created in the universe at the expense of dark energy.
These models were shown to have none of the cosmological problems, such as singularity, horizon, flatness, monopole, cosmological constant, size, age, etc. This has
almost vanishing gravitational charge ρ + 3 p ≈ 0 after the bounce.
A slightly different model proposed by us in [15], which has ρ + 3 p = 0 and an
initial singularity, is an always coasting cosmology with a ∝ t, obtained by extending the dimensional argument of [16]. This modified Chen–Wu model, which can
have k = 0, ±1, has both matter and a time-varying cosmological constant. As in the
above case, it consists of ordinary matter, dark matter and dark energy, which gradually decays to form matter. Comparison of this model with the CDM model was
performed using the SNe Ia data, with the help of the Bayesian theory [17], by the
author and Professor J. V. Narlikar. The results showed that the evidence against the
coasting model, when compared to the CDM model, is only marginal. In 2005, an
analysis was again performed [18] using the then-available SNe data to see whether
the data really favours a decelerating past for the universe. Again, the conclusion
was that the evidence is not strong enough to discriminate the CDM model from a
coasting cosmology. Recently, a quantum cosmological treatment [19] showed that a