Is the Gott-Li "self-creating" universe model correct?

Sean Carrol: “Gott and Li suggest that the universe could ‘create itself,' springing to life out of an endless loop of closed timelike curves. More colorfully, ‘an inflationary universe gives rise to baby universes, one of which turns out to be itself.” [“How Did the Universe Start?” in Discover: Online]

Is Richard Gott and Li-Xin Li’s semi-classical beginningless model true, or at least plausible? As one goes backwards in time, could one get caught in a time loop, going infinitely backwards through the same events over and over again? Could the past trace back to an infinite time loop with no beginning?

General Relativity (GR) allows for wormholes and even “closed timelike curves” (CTCs)—paths in spacetime that loops back on themselves, theoretically allowing an object or particle to return to its own past. Here’s how: a mouth of a traversable wormhole can circle back to the other mouth at a relativistic speed, creating a time dilation effect between them—a loophole time machine.

There could be primordial self-creating loop? In “chaotic inflationary” models, inflating universes can give a birth to other inflating universes. Perhaps the mother universe could trace back to a primordial Planck era where Quantum Mechanics dominate. In this quantum foam era, topologies like closed timelike curves can exist. So, in a branching universe, could one branch circle around to the mouth of the mother universe, creating a primordial loop? If so, the universe could be its own mother! In any such primordial loop, there would be no no beginning or earliest event, just as there is no clockwise-most position for a clock hand.

In its vanilla form, the Gott-Li model ostensibly violates Hawking's Chronology Protection Conjecture (CPC), which says the laws of physics prevent the formation of closed timelike curves (CTCs). Any particles entering the loop would instantaneously double themselves an infinity of times as they repeatedly keep time traveling back to pile-up and coexist with earlier versions of themselves. The density thereby grows and the resultant gravity would rapidly warp space so as to destroy the necessary wormhole structure. So Gott and Li themselves admit they require few things for their loop.¹

1) It needs a Cauchy Horizon bounding it off from the rest of space-time

One thing their model needs is a Cauchy horizon (which is required for CTCs in general)—a boundary separating two regions where no physical interactions between the regions can occur.²

2) It needs an “adapted” Rindler Vacuum

To avoid implosion, Gott and Li also need their very special “adapted Rinder vacuum” with a zero-temperature empty space.³ This state must be a zero-temperature state (to avoid thermal fluctuations), a conformally coupled scalar field (so the stress-energy tensor can be made to vanish throughout Misner space except on the Cauchy horizon), and ensure the absence of real particles or radiation (to prevent energy accumulation that could destabilize the closed timelike curves).

1. Here is a thought experiment illustrating the challenge:

   
   Kip Thorne: Imagine that Carole is zooming back to Earth with one wormhole mouth in her spacecraft, and I am sitting at home on Earth with the other. When the spacecraft gets to within 10 lightyears of Earth, it suddenly becomes possible for radiation (electromagnetic waves) to use the wormhole for time travel: any random bit of radiation that leaves our home in Pasadena traveling at the speed of light toward the spacecraft can arrive at the spacecraft after 10 years’ time (as seen on Earth), enter the wormhole mouth there, travel back in time by 10 years (as seen on Earth), and emerge from the mouth on Earth at precisely the same moment as it started its trip. The radiation piles right on top of its previous self, not just in space but in spacetime, doubling its strength. What’s more, during the trip each quantum of radiation (each photon) got boosted in energy due to the relative motion of the wormhole mouths (a “Doppler-shift” boost). After the radiation’s next trip out to the spacecraft then back through the wormhole, it again returns at the same time as it left and again piles up on itself, again with a Dopplerboosted energy. Again and again this happens, making the beam of radiation infinitely strong. In this way, beginning with an arbitrarily tiny amount of radiation, a beam of infinite energy is created, coursing through space between the two wormhole mouths. As the beam passes through the wormhole . . . it will produce infinite spacetime curvature [i.e. a singularity] and probably destroy the wormhole, thereby preventing [a time machine from coming into being in the first place]. [1994, pp. 505–6.]

2. The interactions are prevented because of the the finite velocity at which physical interactions can propagate in space-time. It is naturally produced in any inflationary baby universe that tunnels across the Einstein-Rosen bridge; it would need to separate the CTC-allowing region from the rest of spacetime. (Gott, J. Richard (2001). Time Travel in Einstein’s Universe: The Physical Possibilities of Travel Through Time [Houghton Mifflin], 117.)
3. The "adapted Rindler vacuum" is a modified vacuum state specifically tailored to the unique conditions of Misner space, ensuring that the renormalized stress-energy tensor remains zero throughout the space except on the Cauchy horizon.

• William Lane Craig & James Sinclair: “CTC [closed time-like curve (I.e. Time-machine)] physics is interesting, and while some theorists still pursue it, it occupies only a small minority of ongoing cosmological investigation. While it is true that no one has been able definitively to rule out CTCs, the evidentiary burden lies upon those defending the viability of such space-times and models predicated upon their reality.” [The Blackwell Companion to Natural Theology (), 136]