A Non-empty Bouncing Milne Model for the Universe
5
Fig. 1 Graphs showing expansion of the universe in different models (not to scale). Cosmic time is
taken along the x-axis and the scale factor of expansion along the y-axis. There is no graph drawn for
the Planck epoch. Following this, there occurs an exponential expansion for a short period in both
Friedmann (green colour) and Lambda-CDM (red colour) models. This is referred to as the epoch of
‘inflation’. Afterwards, the Friedmann model has only a decelerating phase, but the Lambda-CDM
model has a decelerating phase followed by the recent accelerated expansion. The eternal coasting
model (blue colour) has the most simple ‘linear expansion’ all throughout the history of the universe
(On the time axis, various epochs for the Lambda-CDM model are marked.)
an initial bounce proposed and studied by the author, along with Professor K. Babu
Joseph. In the second part, we present such a new realistic and physical eternal coasting cosmological model obtained through a complex extension of the Milne model
(Fig. 1).
2 Eternal Coasting Models of the Universe
2.1 Cosmological Problems
Several problems, such as those referred to as the horizon problem, flatness problem, monopole problem, etc., were identified in Friedmann cosmology during the
1980s, but the theory of inflation [5] solved most of them at one stroke. But time and
again, some other problems too came up in connection with this model. The theory
of inflation, which speculates quantum field theoretical effects in the early epochs,
suggests that the present universe is flat. In fact, the most important prediction of the
inflationary models is that the universe is almost spatially flat. This in turn implies
for a Friedmann model that the combination H 0 t 0 ≈ 2/3, where H 0 , the present Hubble constant is a measure of the expansion rate of the universe and t 0 , the present
age of the universe, i.e. the time elapsed since the big bang singularity. A major set
back to inflationary models was in fact this prediction. Some observations in the
5
Fig. 1 Graphs showing expansion of the universe in different models (not to scale). Cosmic time is
taken along the x-axis and the scale factor of expansion along the y-axis. There is no graph drawn for
the Planck epoch. Following this, there occurs an exponential expansion for a short period in both
Friedmann (green colour) and Lambda-CDM (red colour) models. This is referred to as the epoch of
‘inflation’. Afterwards, the Friedmann model has only a decelerating phase, but the Lambda-CDM
model has a decelerating phase followed by the recent accelerated expansion. The eternal coasting
model (blue colour) has the most simple ‘linear expansion’ all throughout the history of the universe
(On the time axis, various epochs for the Lambda-CDM model are marked.)
an initial bounce proposed and studied by the author, along with Professor K. Babu
Joseph. In the second part, we present such a new realistic and physical eternal coasting cosmological model obtained through a complex extension of the Milne model
(Fig. 1).
2 Eternal Coasting Models of the Universe
2.1 Cosmological Problems
Several problems, such as those referred to as the horizon problem, flatness problem, monopole problem, etc., were identified in Friedmann cosmology during the
1980s, but the theory of inflation [5] solved most of them at one stroke. But time and
again, some other problems too came up in connection with this model. The theory
of inflation, which speculates quantum field theoretical effects in the early epochs,
suggests that the present universe is flat. In fact, the most important prediction of the
inflationary models is that the universe is almost spatially flat. This in turn implies
for a Friedmann model that the combination H 0 t 0 ≈ 2/3, where H 0 , the present Hubble constant is a measure of the expansion rate of the universe and t 0 , the present
age of the universe, i.e. the time elapsed since the big bang singularity. A major set
back to inflationary models was in fact this prediction. Some observations in the