A cosmological model developped by Roger Penrose and colleagues
according which the Universe undergoes repeated cycles of expansion.
Each cycle, referred to an aeon, starts from its own
"→ big bang"
and finally comes to a stage of accelerated expansion which continues
indefinitely. There is no stage
of contraction (to a "→ big crunch") in this model.
Instead, each aeon
of the universe, in a sense "forgets" how big it is, both at its big
bang and in its very remote future where it
becomes physically identical with the big bang of the next aeon,
despite there being an infinite scale change involved, on passing
from one aeon to the next. This model considers a conformal structure
rather than a metric structure. Conformal structure may be
viewed as family of metrics that are equivalent to one another via a
scale change, which may vary from place to place. Thus, in conformal
space-time geometry, there is not a particular metric g_{ab}, but
an equivalence class of metrics where the metrics ğ_{ab}
and
g_{ab}
are considered to be equivalent if there is a smooth positive scalar
field Ω for which ğ_{ab} = Ω g_{ab}
(R. Penrose, 2012, The Basic Ideas of Conformal Cyclic Cosmology).

The use of → Newtonian mechanics to derive homogeneous
and isotropic solutions of → Einstein's field equations,
which represent models of expanding Universe. The Newtonian cosmology deviates from the
prediction of → general relativity in the general case of
anisotropic and inhomogeneous models.

An alternative cosmology, initially conceived by Hannes Alfvén in the 1960s,
that attempts to explain the development
of the visible Universe through the interaction of electromagnetic
forces on astrophysical plasma. Like the steady state model, plasma cosmology
hypothesizes an evolving Universe without beginning or end.

The conventional → Big Bang model, which is based on two
assumptions: the → cosmological principle of homogeneity
and isotropy leading to the → Robertson-Walker metric, and
→ Einstein's field equations
of general relativity along with familiar properties of matter.
This model is a remarkably successful operating hypothesis describing the
evolution of the Universe from 1/100 second after the initial event through to the present day.
It provides explanations for several basic problems
such as: → Hubble's law of recession of galaxies,
interpreted in terms of the expansion of the Universe; the abundances of the
→ light elements, in excellent agreement with the predictions of
→ primordial nucleosynthesis; and the thermal spectrum and angular
isotropy of the → cosmic microwave background (CMB) radiation,
as expected from a hot, dense early phase of expansion. For a non-standard
model, see → ekpyrotic Universe.