Our presently observable universe may be no more than a brief transient between two more dominant static states, a recent (quite credible) paper suggests.^[1] Granted, the term 'static state' has been redefined a little, but the author uses very convincing arguments for his ideas.

The first static phase is what we normally call 'inflation'. But how can inflationary expansion be static? The trick is to define 'static space' as a constant Hubble sphere radius (the cosmological event horizon), rather than as a constant proper radius.^[2] Parts of the universe that fall (or are shifted) outside this radius cannot have any effect on us whatsoever, not even gravitationally.

The standard inflation period had a very high, but constant expansion rate (H) and hence a small constant Hubble radius R_H = c/H, somewhere near the Planck scale (t~10^-43 seconds, r~10^-43 light-seconds). This (presumed) part of our cosmic history is not all that well understood in present gravitational theory^[3] - hence the quest to find a consistent theory of quantum gravity.

At around 10¹¹ Planck time units (10^-32 seconds), some form of symmetry breaking occurred, causing a gradual lowering in the expansion rate (H) and thus an increase in the Hubble sphere radius. More space became observable and could influence larger volumes - it is described as the emergence of space. Present observations suggest that we are in this 'emergent phase', but that the Hubble radius is now asymptotically approaching a constant value again.

The Log-Log plot (above)^[4] shows the proper radius curve of our observable universe in grey and the Hubble radius in red, both against time. Note the dramatic increase in proper radius during the inflationary epoch up to 10^-32 seconds, yet the Hubble radius stayed near the Planck scale. After the symmetry breaking, radiation energy decelerated the very rapid expansion rate until around 300,000 years, when radiation energy ran out of steam, being red-shifted out of contention. Matter energy took over as decelerating agent until around 10 billion years, when vacuum (dark) energy started another (milder) inflation epoch. This resulted in our present constant Hubble radius phase.^[5]

The paper goes further and shows that both spacetime and gravity are phenomena that emerge from underlying (poorly understood) degrees of freedom, hidden in the mysterious quantum-gravity 'underworld'. It is pictured in broad terms on the right. For a better resolution graphic, check the main link in end note [6].

The circle represents the Hubble sphere in 2-D. The 'inside' area is called the 'bulk', essentially space that has already emerged. N is the number of degrees of freedom (independent variables) represented in that space - N is presently different for the bulk and the surface.^[7] As matter density gets diluted with the increase in the Hubble radius, while vacuum energy density remains constant, N_sur will eventually equal B_bulk and the Hubble radius will become constant again.

As far as I understand, the mechanisms are similar to thermodynamics, where e.g. temperature and pressure are emergent phenomena that are useful without having to know the underlying decrees of freedom (e.g. molecular and atomic dynamics). Today we think we know the underlying facts for matter, but we do not understand the 'atoms' of spacetime yet. However, like with thermodynamics, we can quite confidently use the emergent spacetime phenomena, as long as we get results that agree with observations.

Amazingly, thermodynamics features strongly in present quantum gravity studies. The referenced paper shows how the entropy (hence the temperature) of flat spacetime can be determined, even in the presence of radiation and/or matter. Theorists say that gravity emerges from this entropy by means of quantum entanglement across any event horizon.^[8]

The bottom line seems to be that nature dislikes an imbalance between degrees of freedom of the bulk and the Hubble surface, a situation essentially caused by the presence of radiation and matter. By creating more space inside the Hubble surface, the influence of these irritations will effectively be diluted away (energy density becomes smaller). Once this 'transient' is over and N_sur= N_bulk again, the vacuum may perhaps rule undisturbed forever.

One may perhaps ask: is this of any importance and if so, what is the use of it all? Well, since we do not really understand gravity, dark energy etc., any credible new angle on them should be taken seriously, I think.

-J

[1] T. Padmanabhan: Emergent perspective of Gravity and Dark Energy, http://arxiv.org/abs/1207.0505. There were some earlier works in this direction; see e.g. http://en.wikipedia.org/wiki/Entropic_gravity. It does however appear as if Padmanabhan expanded the ideas quite a bit further than previous treatments. His section 5 (page 28) illustrates the newer (AFAIK) insights and is IMO quite brilliant.

[2] The proper radius/distance is what one would measure if the expansion could have been stopped instantaneously. During inflation, proper distances between locations increase and less space falls within the constant Hubble radius. After inflation, the Hubble radius started to increase at a faster rate than the expansion and some of the space that was 'lost' during inflation emerged again (inside the horizon).

[3] There are theories that avoid inflation altogether, e.g. brane cosmology, de Sitter expansion, etc. None of them are without its own set of problems, so cosmologists tend to stick to the one making the fewest assumptions (Occam's razor), although they do not fully understand inflation theory either. Note that even in inflation theory, time did not necessarily start at 10^-43 seconds; it is customary to start plots at the smallest time with any meaning, but the constant radius could have lasted for an arbitrarily long time. It simply enters as a time constant into the equations.

[4] Log-log graphic adapted from fig. 15.4 of Relativity-4-Engineers. You can read chapter 15 'Inflation', linked from here. Note that on log-log diagrams, curved lines represent an exponential law and straight lines represent a power-law of some sorts, not as linear law. The sharp changes in log-log slopes represent gradual changes in slope (change in expansion law).

[5] The present Hubble constant, H~70 km/s/Mpc (giving R_H~14 Gly) is still mildly decreasing, but it is already quite close to the final constant rate of H~60 km/s/Mpc (R_H~16 Gly).

[6] A much clearer picture is available in the source, Figure 1, page 19 of the pdf from http://arxiv.org/abs/1207.0505, also linked to in [1] above.

[7] This has to do with the way vacuum energy works - both pushing and pulling on the expansion rate. Radiation and matter only 'pulls' gravitationally and this causes the imbalance, which can only be restored by diluting the effects of their gravity through increase in the Hubble radius.

[8] This is similar to the gravity of a black hole, which emerges from the 'hidden inside', but can be observed from outside the surface (event horizon).

-=-