Since Hubble’s observations on Cepheid stars, we know that our universe is expanding. Within this cosmic evolution there are two epochs of accelerated expansion. The first of these, referred to as inflation, took place in the early universe and led to density perturbations that later on collapsed to form protogalaxies and large scale structure. The second, the epoch of dark energy domination, refers to the late time behavior of the universe in which we live today, and is driven by an unknown form of energy which does not interact with light. The overall behavior of the expansion in both of these epochs resemble each other but are very different from the decelerated rate of expansion during the radiation and matter domination epochs which took place in between.
We know from observations that inflation ended and dark energy domination started recently. Hence the passage from and towards these epochs involves a dynamic, time dependent, Hubble parameter. The Hubble parameter, H(t), characterizes cosmological spacetimes by denoting the rate of change in the scale factor over time. The scale factor, a(t), parametrizes the rescaling of lengths with respect to time and has a different behavior at each epoch during the cosmic expansion. Accelerated expansion then corresponds to positive acceleration of this parameter.
The evolution of the universe is most effectively described by geometry. The de Sitter (dS) spacetime which leads to a special case of accelerated expansion with a constant Hubble parameter, can be used to model inflation and dark energy. Realistic models of inflation and dark energy however, require that inflation ends and that dark energy starts. Hence the Hubble parameter during these two epochs must have some time dependence and de Sitter therefore can be used only as an approximate spacetime for this purpose. It is this deviation from exact de Sitter of the inflationary and dark energy spacetimes that gives rise to our Universe as observed.
To better understand inflation and dark energy, it is necessary first to consider the special case of de Sitter spacetime. The de Sitter spacetime is one of the two curved, maximally symmetric solutions of the classical theory of gravity, General Relativity, in the absence of matter. Spacetime symmetries, collectively called diffeomorphisms, refer to the freedom to choose coordinate variables to work with without changing the physics. Maximally symmetric spacetimes then possess invariance under the maximum amount of diffeomorphisms. This involves invariance of physics under the rescaling of lengths as described by conformal symmetries.
Symmetries provide guiding principles on which field theories are built. Conformal Field Theories (CFT) then are field theories which respect conformal symmetries. Holography, a contemporary proposal within String Theory, states that the gravitational physics on spacetimes with conformal symmetries have a corresponding, dual description as a Conformal Field Theory. Due to its conformal symmetries, de Sitter spacetime is expected to be dual to a conformal field theory. This holographic description is also known as dS/CFT.
The evolution of spacetime depends on the matter content, described by fields and perturbations of these fields. Thus the forces present during each epoch, which are interactions between the fields, affect the evolution. These fields and their perturbations make up the effective cosmological degrees of freedom. Approximate de Sitter, and hence inflationary and dark energy spacetimes, have a corresponding approximate CFT. Associated to each of inflationary and dark energy spacetimes there will be different kinds of deformation operators, generating deviations from the exact CFT and leading to various kinds of effective degrees of freedom with cosmological consequences.