Friday, June 13, 2008

Could symplectic QFT allow to understand the fluctuations of CMB?

Depending on one's attitudes, the anomalies of the fluctuation spectrum of the cosmic microwave background (CMB) can be seen as a challenge for people analyzing the experiments or that of the inflationary scenario. I do not pretend to be deeply involved with CMB but as I read about one these anomalies in Sean Carrol's blog and next day in Lubos's blog, I felt that I could spend some days by clarifying myself what is involved.
What interests me whether the replacement of inflation with quantum criticality and hbar changing phase transitions could provide fresh insights about fluctuations and anomalies of CMB. In the following I try first to explain to myself what the anomalies are and after that I will consider some TGD inspired crazy (as always) ideas. My motivations to communicate are indeed strong: the consideration of the anomalies led to a generalization of the notion of conformal QFT to what might be called symplectic QFT having very natural place also in quantum TGD proper.
A brief summary about my views is as follows.

  1. There are several types of anomalies (with respect to the expectations motivated by inflation theory). Fluctuation spectrum shows hot and cold spots; there is so called hemispherical asymmetry in the spectrum; rotationally averaged two-point correlation function C(q) is vanishing for angle separations above 60 degrees; the so called cosmic axis of evil means that 3 of the multipole area vectors assignable to the l=2 and l=3 spherical harmonics in the expansion of C(q) are aligned and in the galactic plane (very near to ecliptic) and in roughly the same direction as the dipole corresponding to the motion of the Milky Way with respect to cosmic frame of reference; there is also evidence for non-Gaussianity meaning non-vanishing 3-point functions. Especially strange finding is that the features of the local geometry seems to reflect themselves in CMB at the surface of last scattering. If these findings are not artifacts of the analysis or pure accidents, the consequences for our understanding of the Cosmos would be dramatic.
  2. In TGD framework quantum criticality replaces inflation. This means that the fluctuations of CMB do not correspond to primordial fluctuations of inflaton field evolved into large scale fluctuations during rapid expansion but to long range fluctuations involved with a phase transition increasing Planck constant and occurring at the time of decoupling. The p-adic length scale involved with the sphere of last scattering and the amplitude of the fluctuations provide two dimensionless couplings and allow to make estimates for the scaling of Planck constant in this transition.
  3. I have suggested earlier a conformal field theory defined at the sphere of last scattering as a TGD based model for the anomalies. The analysis of the situation however demonstrates that a more natural approach is based on symplectic variant of conformal QFT at the sphere of last scattering. By combining generalized fusion rules with the knowledge about symplectic invariants associated with 3 or 4 points of sphere, one can deduce surprisingly detailed information about the n-point functions of symplectic QFTs. There are two variants of the theory: the first one is rotation- and reflection symmetric. The fact that the generalization of the notion of imbedding space allows to identify preferred quantization axis, allows to formulate also a variant theory breaking these symmetries. Fusion rules determine n-point functions highly uniquely in terms of 3-point functions expressible as functions of simple symplectic invariants. Symplectic QFT makes special predicions distinguishing it from inflationary models: a sizable non-Gaussianity is predicted and correlation functions vanish when any two arguments are very near to each other. It is certainly possible to reproduce the vanishing of C(q) for large values of q but it is not clear whether fusion rules allow this.
  4. Quite generally, symplectic QFT provides a long sought-for manner to describe the vacuum degeneracy of TGD in terms of n-point functions. What is of special importance is that the n-point functions have no singularities at the limit when some arguments co-incide. This means a profound distinction from quantum field theories and something like this is required by general arguments demonstrating that quantum TGD is free of the standard divergences due to the non-locality of Kähler function as a functional of 3-surface. The classification of symplectic QFTs should be a fascinating challenge for a mathematician. The basic challenge is to determine how uniquely fusion rules determine the 3-point functions generating all other n-point functions.
  5. The possibility of having gigantic values of gravitational Planck constant and zero energy ontology suggests that quantum measurements in cosmological scales are possible. This would mean that time-like entanglement between positive and negative energy parts of zero energy state could correlate galactic geometry with the geometry of fluctuation spectrum so that the hemispherical asymmetry with respect to galactic plane could be produced by this kind of quantum measurement. This would mean a dramatic proof of the notion of participatory Universe introduced by Wheeler.
For details see the chapter Quantum Astrophysics of "Classical Physics in Many-Sheeted Space-Time" or the article Could symplectic quantum field theory allow to model the fluctuations cosmic microwave background?.

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