6
M. V. John
mid-1990s [6] put this value to be lying in the range 0.85 < H 0 t 0 < 1.91, contrary
to the above prediction. Thus, when the condition of flatness is combined with the
measured high value of the Hubble parameter, there arose an ‘age problem’. The
discovery of the accelerated expansion in 1998 predicted a cosmological constant
or some unknown dark energy along with ordinary matter, both these components
having almost equal share in the present universe [7]. The importance of the discovery of accelerated expansion is that it resolved the age problem, but, in its turn, seeks
an explanation to the near equality of the energy density corresponding to such or
dark energy and the matter density in the present universe. This is the ‘coincidence
problem’ in cosmology, for which the CDM model offers no satisfactory solution yet. Recently, three important cosmological observations, namely, the apparent
magnitude and redshift of Type Ia supernovae (SN Ia), CMB power spectrum and
baryon acoustic oscillations, together predict that H 0 t 0 of the present universe is
very close to unity [8]. This is puzzling since according to the CDM model, the
product Ht could have values very different from unity; it can be anywhere in the
range 0 < Ht < ∞. Except during the period of inflation, in the past or future of the
universe, this value shall not be unity either. Just like the coincidence problem, this
synchronicity problem in the CDM model is also ascribing certain special status
to the epoch in which we live today.
2.2 Milne’s Coasting Model
The Milne model [9] is a cosmological model widely discussed in the early stages
of modern cosmology, proposed by the British physicist A. Milne. The model does
not make use of the general theory of relativity. He does not include even gravity as
an important interaction at the cosmic scale. Instead, Milne makes use of his theory
of kinetic relativity, which is an extension of Einstein’s special theory of relativity.
Hence, its distinguishing feature is that all observers are in inertial motion at the
cosmic level. However, it can also be viewed as a Friedmann model, but as having
zero matter density, negative spatial curvature and the scale factor obeying the relation
a ∝ t. In this case, the expansion rate of the universe, which is measured as the Hubble
parameter H , varies as 1/t, the time elapsed since the big bang singularity. Hence,
in this cosmological model, H 0 t 0 = 1 is not a problem; instead, this is its prediction.
In [8], it is mentioned that the Milne model is the most suitable one to explain the
above observational result, but the model is soon rejected on grounds that the model
is empty and has negatively curved space sections (i.e. ρ = 0 and k = −1). This is
quite reasonable, for an empty model is not a realistic one.
Very recently, an analysis of Type Ia supernova data [10] has appeared with the
result that there is only marginal evidence for the widely accepted claim of the
accelerated expansion of the universe. By a rigorous statistical analysis using the
joint lightcurve analysis (JLA) catalogue of 740 SN Ia, it is found that the SN Ia
Hubble diagram appears consistent with a uniform rate of expansion. This brings the
Milne model again to the centre stage of cosmology, albeit in some new avatar.
M. V. John
mid-1990s [6] put this value to be lying in the range 0.85 < H 0 t 0 < 1.91, contrary
to the above prediction. Thus, when the condition of flatness is combined with the
measured high value of the Hubble parameter, there arose an ‘age problem’. The
discovery of the accelerated expansion in 1998 predicted a cosmological constant
or some unknown dark energy along with ordinary matter, both these components
having almost equal share in the present universe [7]. The importance of the discovery of accelerated expansion is that it resolved the age problem, but, in its turn, seeks
an explanation to the near equality of the energy density corresponding to such or
dark energy and the matter density in the present universe. This is the ‘coincidence
problem’ in cosmology, for which the CDM model offers no satisfactory solution yet. Recently, three important cosmological observations, namely, the apparent
magnitude and redshift of Type Ia supernovae (SN Ia), CMB power spectrum and
baryon acoustic oscillations, together predict that H 0 t 0 of the present universe is
very close to unity [8]. This is puzzling since according to the CDM model, the
product Ht could have values very different from unity; it can be anywhere in the
range 0 < Ht < ∞. Except during the period of inflation, in the past or future of the
universe, this value shall not be unity either. Just like the coincidence problem, this
synchronicity problem in the CDM model is also ascribing certain special status
to the epoch in which we live today.
2.2 Milne’s Coasting Model
The Milne model [9] is a cosmological model widely discussed in the early stages
of modern cosmology, proposed by the British physicist A. Milne. The model does
not make use of the general theory of relativity. He does not include even gravity as
an important interaction at the cosmic scale. Instead, Milne makes use of his theory
of kinetic relativity, which is an extension of Einstein’s special theory of relativity.
Hence, its distinguishing feature is that all observers are in inertial motion at the
cosmic level. However, it can also be viewed as a Friedmann model, but as having
zero matter density, negative spatial curvature and the scale factor obeying the relation
a ∝ t. In this case, the expansion rate of the universe, which is measured as the Hubble
parameter H , varies as 1/t, the time elapsed since the big bang singularity. Hence,
in this cosmological model, H 0 t 0 = 1 is not a problem; instead, this is its prediction.
In [8], it is mentioned that the Milne model is the most suitable one to explain the
above observational result, but the model is soon rejected on grounds that the model
is empty and has negatively curved space sections (i.e. ρ = 0 and k = −1). This is
quite reasonable, for an empty model is not a realistic one.
Very recently, an analysis of Type Ia supernova data [10] has appeared with the
result that there is only marginal evidence for the widely accepted claim of the
accelerated expansion of the universe. By a rigorous statistical analysis using the
joint lightcurve analysis (JLA) catalogue of 740 SN Ia, it is found that the SN Ia
Hubble diagram appears consistent with a uniform rate of expansion. This brings the
Milne model again to the centre stage of cosmology, albeit in some new avatar.