Our past lightcone is pear-shaped

[marcus]

here is a frustrating problem

http://www.astro.ucla.edu/~wright/cosmo_03.htm

Scroll down to the "Space-Time Diagrams" section and you
will see a pear-shape lightcone outlined in red.

This is the lightcone in the spatially "flat" case which we
believe applies to our universe-----the Ω = 1 case----
the critical density case-----whatever.

But this case drawn here is for zero cosmological constant---zero Lambda----zero vacuum energy density.

Up to the present this makes hardly any difference because the dark energy has not caused very much acceleration in expansion YET. But in the future that lightcone will no longer look like a pear.

BTW each of those worldlines is another galaxy, and they have little triangles on them to show their future lightcones.

The side of the pear always matches the slope of the future lightcone of each galaxy it meets. This determines its shape.

Suppose the worldlines of the other galaxies started bending out to show accelerated expansion. What new shape would the pear acquire?

This chapter in Wright, and the preceding one, is suggesting ways to think visually about spacetime.

 

[jeff]

The tip gradually narrows, collapsing as the expansion overtakes light. This requires the pear inflect into a tear-drop before terminating at the collapse point.

(Edited for enhanced precision)

 

[marcus]

Bravo!

Originally posted by steinitz
While the rate at which galaxy worldlines leave the pear will gradually increase, the tip of the pear will gradually narrow until the rate of expansion is so great (recall that the speed resulting from unabated acceleration of cosmological expansion will eventually surpass that of light) that the tip will close completely, implying that at some preceding point the pear will have inflected into a tear-drop.

Your verbal description is very like what I have been imagining!
this time I believe I agree with you, and must give you much
credit for helping to clarify this!

By "tip" I understand you to mean the upper, narrower, part of the pear. This is what I have imagined as narrowing and having, at some time, an inflection.

what is fascinating is the thought that there could actually be two
parts---the waist could pinch off.

Do you have a link or web-reference for this-----for further clarification?

 

[marcus]

The conventional picture of what results from an unchanging
cosm. const./dark energy density is that eventually our observable universe is only 100 or so galaxies.

this I wish to relate to the forming of the "waist" of the pear.

I consider that these 100 or so galaxies are, at least for the time being, bound gravitationally to the Milky Way. So the expansion does not carry them off beyond the horizon.

At least the Local Group of 10 or so galaxies should stay as a cluster.

But the pinching off of the "waist" of the pear----if this really is what the model predicts---would correspond to everything outside of a few galaxies disappearing! No more Cosmic Microwave Background!

Am delighted by the extremity of the picture.

But I can think of no reason to suppose that the dark energy density will remain constant---to date there is nothing but speculation as to its nature, so why should one suppose anything? Or do you disagree?

 

[jeff]

Originally posted by marcus


...this time I believe I agree with you...

Uh oh. I must be wrong

But I can think of no reason to suppose that the dark energy density will remain constant---to date there is nothing but speculation as to its nature

Agreed, and at this point it's arguably the single biggest wildcard in theoretical physics.

Do you have a link or web-reference for this...?

I learned about this stuff from Hawking and Ellis's "large scale structure of space-time" which is the standard text on the application of global methods in GR.

 

[marcus]

delighted by this witty and helpful post
thx
marcus