A new twist in the inflationary story
There is a highly interesting article about the possible impact of BICEP2 results for inflation (see this). For my earlier comments on BICPE2 see this, this, and this.
The original belief after BICEP2 was that inflation finds strong support from the unexpectedly strong dependence of CMB temperature on the polarization of CMB photons claimed by BICEP2. This would have been caused by primordial gravitational waves. Most bloggers were however silent about a serious problem. If the finding is real, the large polarization implies that QFT approximation fails. Inflationary scenario is indeed essentially QFT based with inflaton field playing the role of Higgs field such that the energy of inflation field decays to particles during inflationary period before the radiation dominated phase.
As already mentioned, now another serious objection has emerged. Inflation predicts a spectrum of gravitatonal waves with amplitudes proportional to mass density fluctuations. The longer the scale, the larger the amplitude should be. The spectrum claimed by BICEP2 shows however exactly the opposite behavior as was found by the authors of the article.
Situation has turned around! The highest desire of inflation theorists is now that BICEP2 results are wrong and due to dust or some other effect! This might well be the case. Paul Steinhardt - one of the developers of inflationary model - has turned into skeptic, and says that unfortunately this is not the only severe problem of inflation. For instance, basic prediction is that we should observe multiverse realized as space-time regions obeying different physics laws (different values of basic parameters of say standard model). We do not! I have been myself wondering why this wrong prediction does not seem to bother multiverse enthusiasts. Is just this corner of Universe with its own physics laws so large that we cannot observer other regions? Strange indeed!
BICEP2 finding forced me to develop TGD view about the TGD counterpart of inflation. The physical interpretation in TGD is totally different from that of inflationary model.
- The rapid expansion is a quantum critical period during which the curvature scalar of 3-space vanishes (no scales during criticality) and the induced 3-metric is flat. A phase transition from a phase dominated by a gas of cosmic strings in the future light-cone of Minkowski space (imbedding space is M4×CP2) to radiation dominated cosmology would be in question.
In the string gas phase GRT description does not apply. Lorentz invariance of the gas phase implies that the universe is isotropic and homogenous and therefore one should avoid the multiverse. It is important to realize tht Lorentz invariance is not present as global symmetry in GRT based cosmology and inflation was hoped to solve the resulting problems.
- The phase transition means the emergence of many-sheeted space-time. GRT space-time emerges as its simplification obtained by lumping together the sheets of many-sheeted space-time to a region of Minkowski space provided with a naturally defined effective metric. GRT space-time is assumed to be modellable using single sheeted space-time identifiable as vacuum extremal of Kähler action. This assumption is natural but can be criticized.
- Not too surprisingly, the cosmic expansion during critical phase is rapidly accelerating and the energy density of the critical cosmology which is unique apart from it duration would become infinite without transition to radiation dominated cosmology (the gas of cosmic strings has finite mass density). A transition to radiation dominated cosmology must happen before this. CMB temperature fluctuations emerge from the variations of the value of cosmic time at which the transition to radiation dominated cosmology takes place. The magnetic energy of cosmic strings decays to particles so that inflation field is replaced with Kähler magnetic field which also explains the
appearance of magnetic fields in cosmic scales elegantly.
What one can say about the amplitude of the gravitational waves as a function of scale? Does it increase with the scale as it should do in inflationary models predicting that the amplitude is proportional the amplitude of density fluctuations? Does the amplitude of density fluctuations increase with scale or does Lorentz invariance or properties of string gas phase prevent this? And what density fluctuations are? And what defines the scale?
- In inflationary models density fluctuations are generated by gravitational perburbations in existing space-time.
In TGD Universe many-sheeted space-time is just emerging during inflationary period and QFT starts to make sense
during radiation dominated phase. Density fluctuations should correspond to the density fluctuations for the gas of cosmic strings topologically condensed to the emerging space-time sheets during the phase transition analogous to a condensation of vapour to 2-D surface.
- This would suggest that density fluctuation at space-time sheet corresponds to a maximum amount of string energy in the volume in question. The energy density of cosmic string gas is proportional to T/a2 - here a is the light-cone proper time characterizing the scale and T is string tension. This predicts that density fluctuations decrease with length scale. TGD prediction would be consistent with BICEP2 finding even if it is correct. Otherwise the situation remains unsettled.
- Note that as the Minkowski space projections of cosmic strings gradually thicken, they become Kähler magnetic flux tubes carrying monopole flux: this explains the presence of cosmic magnetic fields since no current is needed to generatate monopole fields. The mass density per unit length of cosmic string is given by string tension essentially as the density of the magnetic energy which decays partially to matter. As the string thickens, the energy density of string decreases as the inverse of its transversal area. The total mass of string however remains proportional to its length.