Cyclical universe

In any version of this critique of inflation, there is a crucially important assumption: that
the evolution of the comoving volume from the early universe to today is unitary (and hence
reversible). The assumption of unitarity seems innocuous, but is extremely profound in
this context; it underlies the claim that the small proto-inflationary patch and our current
universe are the same system, just in two different configurations.
An obvious prerequisite for unitary evolution is the conservation of the set of degrees
of freedom characterizing the system. Such an assumption is so deeply ingrained in our
understanding of dynamics that it is not usually spelled out explicitly, but in the case of an
expanding spacetime the issue is not so clear. Indeed, unitarity is directly at odds with the
reasoning behind the idea that it is much easier to begin inflation than to simply find the
universe in its current state: the assertion that there are not that many degrees of freedom
that need to be in their vacuum state in order for a small region to begin inflating. If the
evolution is truly unitary, there are a fantastically large number of such degrees of freedom,

In any version of this critique of inflation, there is a crucially important assumption: that the evolution of the comoving volume from the early universe to today is unitary (and hence reversible). The assumption of unitarity seems innocuous, but is extremely profound in this context; it underlies the claim that the small proto-inflationary patch and our current universe are the same system, just in two different configurations.
An obvious prerequisite for unitary evolution is the conservation of the set of degrees of freedom characterizing the system. Such an assumption is so deeply ingrained in our understanding of dynamics that it is not usually spelled out explicitly, but in the case of an expanding spacetime the issue is not so clear. Indeed, unitarity is directly at odds with the reasoning behind the idea that it is much easier to begin inflation than to simply find the universe in its current state: the assertion that there are not that many degrees of freedom that need to be in their vacuum state in order for a small region to begin inflating. If the evolution is truly unitary, there are a fantastically large number of such degrees of freedom,

Thank you for the reference, Chronos. This is actually a very interesting paper. I think I understood the main idea, although some aspects were not understandable for me. For example:

I understand that in case of quantum systems, observables related by a unitary transformation have same spectrum. But I belive that in case of statistical mixtures the evolution is not unitary: as soon as one has two different density matrices, both cannot be related by a unitary transformation. If this is correct, shall I assume that the universe is considered as a quantum system? Why?

..

The total amount of mass in the observable universe is ... ~10E22 [solar masses]. If all of this mass were collected into a single black hole, the entropy would be Smax(U) 10E121.

I stand corrected. It's a habit I acquired using this calculator with an 'E' button that stood for exponent. Assuming I don't forget, I will amend my evil ways.

You are obliging and I thank you. Notation is just a question of habit, but it is less confusing when we adopt the same conventions. (I see we are both the slaves of our calculators)

I still have trouble using regular calculators after years (late 70's to mid 80's) of my love affair with RPN. As a chemist in a pulp mill (with NO Personal Computer), I had to use those calculators a LOT. The programmable HPs were a lifesaver! The chemistry of a pulp mill is WAY complex. Why oh WHY did HP discontinue the wonderful HP15C???? It's been years, but it's still a bummer. Perfect pocket size, lots of power... Oh well...