Conformal Cyclic Cosmology

[Alan Grayson]

https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology

Is this a viable theory for avoiding a BB interpreted as a singularity? AG

[Philip Thrift]

On Tuesday, August 20, 2019 at 4:56:23 PM UTC-5, Alan Grayson wrote:

https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology

Is this a viable theory for avoiding a BB interpreted as a singularity? AG

It's one of the genre of cyclic models

   https://en.wikipedia.org/wiki/Cyclic_model

Whether "CCC" is "more viable" than the other cyclic models listed, I don't know.

(What about a bicyclic universe consisting of a forward-in-time cycle and a "parallel" backward-in-time cycle. Möbius universe?)

@philipthrift

 

[Lawrence Crowell]

On Tuesday, August 20, 2019 at 4:56:23 PM UTC-5, Alan Grayson wrote:

https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology

Is this a viable theory for avoiding a BB interpreted as a singularity? AG

Penrose proposed a conformal identification of spatial infinity in the past and future i^±∞ of FLRW spacetimes. A cosmology expands and in the limit time → ∞ it transitions into a new cosmology. The de Sitter vacuum is not eternally stable, so the idea may have some germ of relevancy. I am not sure about how this would work with vacuum to vacuum transitions. The exponential expansion of the universe is a sort of time dependent conformal transformation with a small vacuum expectation for the scale field. To transition to a new cosmology, say with inflationary expansion, this means the vacuum expectation is increased.

The overall physics community response to this has been tepid at best. There are some possible conflicts with observed data.

LC

[Alan Grayson]

FWIW, ISTM that what GR might be indicating about the BB, is that, insofar as it's a singularity, it couldn't have occurred, and didn't occur.  This is to say the universe didn't become infinitely small in spatial extent, like a mathematical point, but rather that there was a maximal finite value of its energy density, hugely high but not infinite. For this reason I find the cyclic models promising, although, as you rightly indicate, they're far from complete or bug-free. AG

[Alan Grayson]

Which brings up a possibly relevant question: If the total energy of the universe occupied zero spatial volume (the presumed condition of the universe at t=o according to the BB theory), wouldn't that contradict the Uncertainty Principle? AG 

[Alan Grayson]

If the BB is imagined as a point in time, t=0, when the total energy of the universe was "confined" to zero spatial volume, it never existed insofar as it's self contradictory.  AG 

[Lawrence Crowell]

The total mass-energy content of the universe is zero.

LC 

[Alan Grayson]

Is that a provable fact, or something that can be measured? TIA, AG 

[Lawrence Crowell]

It is provable, because in general spacetimes there does not exist a Gaussian surface to define mass. This sets the energy to zero. Think of it as meaning gravitational potential energy as negative is equal in magnitude to positive mass-energy. 

LC

[Alan Grayson]

If, using E=mc^2, one computes the rest energy of the material Earth, it seems implausible that this equals the negative potential energy of the Earth's gravitational field, to yield a net energy sum of zero. AG  

[Lawrence Crowell]

Consider the gravitation with expansion and cosmological constant. This was first pointed out by Tolman many decades ago.

LC 

[Alan Grayson]

I will. But maybe in the meantime you could explain how, using E=mc^2 and the negative potential energy of Earth's gravity field , you can get them to cancel out for an isolated Earth. Something very puzzling here. Additionally, ISTM that one would have an impossible task making a nuclear weapon from negative potential energy. What am I doing wrong, if anything? AG

[Alan Grayson]

Do you have links on this specific topic? TIA, AG 

[Alan Grayson]

A test particle falling in a gravitational field gains in kinetic energy exactly what it loses in potential energy. However, what matters in this calculation is NOT the value of the potential energy at say two radial points in the falling path, say R2 and R1, but the DIFFERENCE in potential energy between these points. IOW, the potential energy is not well DEFINED as having some specific value. That is, one could add a constant to the potential energy at all points along the falling path and the calculation is unchanged. This is a long winded way of saying that it's a fallacy to add rest energy, calculated by mc^2, and gravitational potential energy, in an attempt to claim the total energy of the universe is exactly zero. Rest energy is well defined, but gravitational potential energy is not. AG

What exactly did Tolman prove many decades ago? Do you have a link to read on this? AG

[Alan Grayson]

You claim it's a provable fact. Are you sure? I see many discussions on the Internet which assert it's a conjecture. AG 

[Lawrence Crowell]

It is a canonical result that the Hamiltonian for general spacetimes is zero, or NH = 0 for N a lapse function.

LC 

[Alan Grayson]

It's easy to calculate the (negative) potential energy (PE) of an OBJECT in a gravitation field, but how does one calculate the PE of the field itself?  I've looked on Internet but can't find an answer to this question, upon which, it seems, the postulate of a zero energy universe rests. AG

[Alan Grayson]

Is the calculation done by simply integrating the energy density over all space containing the gravitational field? AG 

[Alan Grayson]

If you're referring to the conjecture or alleged "fact" that the net energy of the Cosmos is zero, that concept, whatever its status, arose long before cosmologists became convinced in the existence of dark energy, which is thought to account for 73% of all energy in the Cosmos. Assuming dark energy exists, how does this fit in with the conjecture or alleged "fact" that the net energy of the Cosmic is exactly zero? AG 

[Lawrence Crowell]

The gravitational potential energy content from dark energy or a vacuum energy is V = -8πGρ/3c^2. This is a negative content. To really get into this means I have to write a fair amount on general relativity, but frankly I am very busy right now. I have a paper accepted for publication on the condition of rewriting some parts, though the meat of this was given approval. I have quite a bit scheduled over the next week.

LC

[Alan Grayson]

I understand. Thanks for your time. I am trying to get a PDF version of Tolman's monograph, so I can evaluate his argument that the net gravitational energy of the Cosmos is zero. It's quite remarkable if true, and I remain somewhat skeptical because, as I have previously indicated, gravitational potential energy doesn't seem well defined. AG