As Peter W*it tells in N*t Even Wr*ng (for some reason Lubos wants to write "o":s as "*":s in this context), cosmic strings has been one of so called qualitative predictions of many variants of superstring theory. This is true but since Lubos is one of the few remaining superstring fans, Woit's blog post made him very irritated.
What about TGD? Do I have reasons to get irrirated? Cosmic strings appear also in TGD but are very different objects than those of GUTs. They differ also from those of superstrings theories, where they can appear at the GUT limit or as very long fundamental strings.
Cosmic strings in GUTs and superstring theories
What mainstream cosmic strings are?
- In GUTs cosmic strings are 1-D defects associated with singular gauge field configurations. There is a phase, which grows by a multiple of 2π as one goes around the defect line. One has essentially vortex line locally. At the singularity the modulus of field variable associated with the phase must vanish.
Here comes in the fundamental difference between gauge fields in GUTs and in TGD where they are induced and QFT limit of TGD does not allow either GUT cosmic strings, GUT monopoles, nor instantons implying strong CP breaking plaguing QCD.
- In superstring theories one also has these defects almost unavoidably if one believes that some kind of GUT defines the long length scale limit of superstring theories. Superstring theories also suggests that fundamental strings somehow give rise to very long fundamental cosmic strings: I cannot say anything about the details of the proposed mechanism.
The dynamics of string like objects is almost universal.
- The first parameter is string tension μ predicted by GUTs. There are strong bounds on μ in terms of 1/G. The upper bound μG ≈10-7 emerges from the fact that cosmic strings have not been found yet. The string tension of TGD cosmic strings satisfies this condition.
- Second parameter characterizes the dynamics of string networks and is reconnection probability p for strings. It would be p≈ 10-1 for strings with topological origin (GUT strings) and p≈ 10-3 for possibly existing long superstrings. Using these parameters one can build dynamical models and perform numerical simulations. In LIGO article several models are discussed together with their predictions.
- One expects that kinks and cusps correspond to delta function singularities in energy momentum tensor serving as sources of gravitational radiation. In cusps the determinant of 2-D induced metric vanishes and the energy momentum tensor proportional to 2-D contravariant metric diverges like 1/det(g). This seems to produce a singularity.
- Energy momentum tensor serving as the source of gravitational radiation seems to be however only discontinuous at kinks. Naively one might think that the ordinary divergence of energy momentum tensor having delta function singularity tells how much energy momentum goes out from string as gravitational radiation. My guess is that one must add to the action an additional term corresponding to the discontinuity and depending on Christoffel symbols at the discontinuity to describe curvature singularity. This term would serve as a source of gravitational radiation.
This term is essentially the second fundamental form for the imbedding of the singularithy as a 3-surfaces and its trace would define the interaction term just as the naive picture would lead to expect. The interpretation of this term is essentially as the analog of acceleration and accelerating particle indeed creates radiation, in particular gravitational radiation. As a matter fact, this kind of term must be also added in 2-D case to the curvature scalar to get correctly Gauss-Bonnet law for polygons having corners.
To discuss the question whether cosmic strings radiate in TGD one must say something general about the dynamics of space-time surfaces in TGD.
There are two kinds of space-time surfaces in TGD Universe. These two kinds fo space-time surfaces appear at the boths sides of M8-H duality: here one has H=M4× CP2. In the following I stay at the H-side of the duality.
There is a rather precise analogy with the vision about what happens in particle reactions. External particles decouple from interactions and interactions take place in interaction regions, where interactions are in some sense coupled on. This is realized for the preferred extremals of the action determining space-time surfaces in rather precise sense. The twistor lift of TGD predicts that the action is sum of Kähler action and volume term analogous to cosmological term.
- The preferred exremals can be minimal surfaces in which case field equations are satisfied separately for Kähler action and volume term: the two interactions effectively decouple. The dynamics reduces to holomorphy conditions and coupling constants disappear completely from it. This corresponds to the universal dynamics of quantum criticality.
The minimal 4-surfaces are direct 4-D analogs of geodesic lines, free particles. Also cosmic strings are surfaces or this kind and presumably also the magneti flux tubes. In Zero Energy Ontology (ZEO) these surfaces represent external particles entering or leaving causal diamond (CD). Free particles do not emit any kind of radiation and this would be indeed realized now.
- Inside CDs Kähler action and volume term do not decouple and there is genuine interaction between them. One does not have minimal surfaces anymore and coupling constants appear in the dynamics. In this region the emission of radiation and also of gravitational radiation is possible.
Cosmic strings in TGD sense
Also TGD predicts what I call cosmic strings.
- Ideal cosmic strings a la TGD string like objects, space-time surfaces. They are not singular densities of matter in 4-D space-time which would be small deformation of Minkowski metric. Rather, they are 4-D surfaces havng 2-D string world sheets as M4 projection. String world sheet and string like object are minimal surfaces and should emit no radiation.
Remark: Since M4 projection is not 4-D GRT limit does not make sense for cosmic strings and the GRT based calculation for gravitational radiation does not apply in TGD framework.
- Cosmic strings dominate the dynamics in very early universe. In reasonable approximation one could speak about gas of cosmic strings in M4- or strictly speaking in M4× CP2. The transition to radiation dominated era is the TGD counterpart for inflationary period: the space-time in GRT sense emerges as space-time sheets having 4-D M4 projection. Stringlike objects topologically condense at 4-D space-time sheets. Also their M4 projection becomes 4-D and begins to thicken during cosmic evolution so that magnetic field strength starts to weaken.
Cosmic strings can carry Kähler magnetic monopole flux explaining the mysterious long ranged magnetic fields in cosmological scales. Reconnection and formation of closed loops is possible. Many-sheetedness is an important aspect: there are flux tubes within flux tubes.
Cosmic strings/magnetic flux tubes play a key role in the formation of galaxies and larger (and even smaller) structures. Galaxies are along cosmic strings like pearls along necklace: the simplest model assumes that pearls are knots along cosmic strings (note the amusing analogy with DNA having coding regions as nucleosomes along it). Flux tubes and their reconnections play also key role in TGD inspired quantum biology.
The question of the title reduces to the question whether the cosmic strings in TGD sense emit gravitational radiation.
- If cosmic strings are idealizable as minimal surfaces and therefore as stationary states outside CDs they do not produce any kind of radiation. Radiation and gravitational radiation can emerge only in space-time regions, where there is a coupling between Kähler action and volume term. In particular, the purely internal dynamics of ideal cosmic strings cannot produce gravitational radiation.
- One can of course argue that topologically condensed thickened cosmic strings actually interact and ought to be described as something inside CD. In any case, there is a coupling between Kähler degrees of freedom and geometry of string and this means that GRT based model cannot apply. This is of course clear already from the fact that string like objects in TGD sense are hardly describable as a singular mass distribution in slightly curved piece of M4.
One can of course ask whether GRT based calculation for the emission of gravitational radiation makes sense for thickened cosmic strings having 4-D M4 projection. This requires going to the GRT-QFT limit involving the approximation of the many-sheeted space-time with GRT space-time: this means replacing sheets with single sheet and identifying deviation of the metric from M4 metric and gauge potentials with sums of the corresponding induced quantities.
There would be however no emission in the approximation with genuinely 2-D objects and the calculation must involve also other than purely geometric degrees of freedom. There is also the question about whether kinks and cusps are possible for preferred extremals satisfying extremely tight symmetry conditions realizing strong form of holography. If not, they are not expected at QFT limit either.
For a summary of earlier postings see Latest progress in TGD.