ABSTRACTS
OF 
PART I: THE NOTION OF MANYSHEETED SPACETIME 
PART II: MANYSHEETED COSMOLOGY AND ASTROPHYSICS 
Cosmic strings belong to the basic extremals of the Kähler action. The upper bound for string tension of the cosmic strings is T ≈ .5×10^{6}/G and in the same range as the string tension of GUT strings and this makes them very interesting cosmologically although TGD cosmic strings have otherwise practically nothing to do with their GUT counterparts.
1. Basic ideas The understanding of cosmic strings has developed only slowly and has required dramatic modifications of existing views.
2. Critical and overcritical cosmologies involve accelerated cosmic expansion In TGD framework critical and overcritical cosmologies are unique apart from single parameter telling their duration and predict the recently discovered accelerated cosmic expansion. Critical cosmologies are naturally associated with quantum critical phase transitions involving the change of gravitational Planck constant. A natural candidate for such a transition is the increase of the size of a large void as galactic strings have been driven to its boundary. During the phase transitions connecting two stationary cosmologies (extremals of curvature scalar) also determined apart from single parameter, accelerated expansion is predicted to occur. These transitions are completely analogous to quantum transitions at atomic level. The proposed microscopic model predicts that the TGD counterpart of the quantity r+3p for cosmic strings is negative during the phase transition which implies accelerated expansion. Dark energy is replaced in TGD framework with dark matter indeed predicted by TGD and its fraction is.74 as in standard scenario. Cosmological constant thus characterizes phenomenologically the density of dark matter rather than energy in TGD Universe. The sizes of large voids stay constant during stationary periods which means that also cosmological constant is piecewise constant. pAdic length fractality predicts that L scales as 1/L^{2}(k) as a function of the padic scale characterizing the spacetime sheet of void. The order of magnitude for the recent value of the cosmological constant comes out correctly. The gravitational energy density described by the cosmological constant is identifiable as that associated with topologically condensed cosmic strings and of magnetic flux tubes to which they are gradually transformed during cosmological evolution. 3. Cosmic strings and generation of structures
4. Cosmic strings, gamma ray bursts, and supernovae During year 2003 two important findings related to cosmic strings were made.
This forces the updating of the more than decade old rough vision about topologically condensed cosmic strings and about gamma ray bursts described in this chapter. According to the updated model, cosmic strings transform in topological condensation to magnetic flux tubes about which they represent a limiting case. Primordial magnetic flux tubes forming ferromagnet like structures become seeds for gravitational condensation leading to the formation of stars and galaxies. The TGD based model for the asymptotic state of a rotating star as dynamo leads to the identification of the predicted magnetic flux tube at the rotation axis of the star as Z^{0} magnetic flux tube of primordial origin. Besides Z^{0} magnetic flux tube structure also magnetic flux tube structure exists at different spacetime sheet but is in general not parallel to the Z^{0} magnetic structure. This structure cannot have primordial origin (the magnetic field of star can even flip its polarity). The flow of matter along Z^{0} magnetic (rotation) axis generates synchrotron radiation, which escapes as a precisely targeted beam along magnetic axis and leaves the star. The identification is as the rotating light beam associated with ordinary neutron stars. During the core collapse leading to the supernova this beam becomes gamma ray burst. The mechanism is very much analogous to the squeezing of the tooth paste from the tube. The fact that all nuclei are fully ionized Z^{0} ions, the Z^{0} charge unbalance caused by the ejection of neutrinos, and the radial compression make the effect extremely strong so that there are hopes to understand the observed incredibly high polarization of 80�20 per cent. TGD suggests the identification of particles of mass m ≈ 2m_{e} accompanying dark matter as leptopions formed by color excited leptons, and topologically condensed at magnetic flux tubes having thickness of about leptopion Compton length. Leptopions would serve as signatures of dark matter whereas dark matter itself would correspond to the magnetic energy of topologically condensed cosmic strings transformed to magnetic flux tubes.

A proposal for what might be called TGD inspired cosmology is made. The basic ingredient of this cosmology is the TGD counter part of the cosmic string. It is found that manysheeted spacetime concept, the new view about the relationship between inertial and gravitational fourmomenta, the basic properties of the cosmic strings, zero energy ontology, the hierarchy of dark matter with levels labeled by arbitrarily large values of Planck constant: the existence of the limiting temperature (as in string model, too), the assumption about the existence of the vapor phase dominated by cosmic strings, and quantum criticality imply a rather detailed picture of the cosmic evolution, which differs from that provided by the standard cosmology in several respects but has also strong resemblances with inflationary scenario. TGD inspired cosmology in its recent form relies on an ontology differing dramatically from that of GRT based cosmologies. Zero energy ontology states that all physical states have vanishing net quantum numbers so that all matter is creatable from vacuum. The hierarchy of dark matter identified as macroscopic quantum phases labeled by arbitrarily large values of Planck constant is second aspect of the new ontology. The values of the gravitational Planck constant assignable to spacetime sheets mediating gravitational interaction are gigantic. This implies that TGD inspired late cosmology might decompose into stationary phases corresponding to stationary quantum states in cosmological scales and critical cosmologies corresponding to quantum transitions changing the value of the gravitational Planck constant and inducing an accelerated cosmic expansion. 1. Zero energy ontology The construction of quantum theory leads naturally to zero energy ontology stating that everything is creatable from vacuum. Zero energy states decompose into positive and negative energy parts having identification as initial and final states of particle reaction in time scales of perception longer than the geometrotemporal separation T of positive and negative energy parts of the state. If the time scale of perception is smaller than T, the usual positive energy ontology applies. In zero energy ontology inertial fourmomentum is a quantity depending on the temporal time scale T used and in time scales longer than T the contribution of zero energy states with parameter T_{1} < T to fourmomentum vanishes. This scale dependence alone implies that it does not make sense to speak about conservation of inertial fourmomentum in cosmological scales. Hence it would be in principle possible to identify inertial and gravitational fourmomenta and achieve strong form of Equivalence Principle. It however seems that this is not the correct approach to follow. 2. Dark matter hierarchy and hierarchy of Planck constants Dark matter revolution with levels of the hierarchy labeled by values of Planck constant forces a further generalization of the notion of imbedding space and thus of spacetime. One can say, that imbedding space is a book like structure obtained by gluing together infinite number of copies of the imbedding space like pages of a book: two copies characterized by singular discrete bundle structure are glued together along 4dimensional set of common points. These points have physical interpretation in terms of quantum criticality. Particle states belonging to different sectors (pages of the book) can interact via field bodies representing spacetime sheets which have parts belonging to two pages of this book. 3. Quantum criticality TGD Universe is quantum counterpart of a statistical system at critical temperature. As a consequence, topological condensate is expected to possess hierarchical, fractal like structure containing topologically condensed 3surfaces with all possible sizes. Both Kähler magnetized and Kähler electric 3surfaces ought to be important and string like objects indeed provide a good example of Kähler magnetic structures important in TGD inspired cosmology. In particular spacetime is expected to be manysheeted even at cosmological scales and ordinary cosmology must be replaced with manysheeted cosmology. The presence of vapor phase consisting of free cosmic strings containing topologically condensed fermions is second crucial aspect of TGD inspired cosmology. Quantum criticality of TGD Universe, which corresponds to the vanishing of second variation of Kähler action for preferred extremals  at least of the variations related to dynamical symmetries supports the view that manysheeted cosmology is in some sense critical. Criticality in turn suggests fractality. Phase transitions, in particular the topological phase transitions giving rise to new spacetime sheets, are (quantum) critical phenomena involving no scales. If the curvature of the 3space does not vanish, it defines scale: hence the flatness of the cosmic time=constant section of the cosmology implied by the criticality is consistent with the scale invariance of the critical phenomena. This motivates the assumption that the new spacetime sheets created in topological phase transitions are in good approximation modelable as critical RobertsonWalker cosmologies for some period of time at least. These phase transitions are between stationary quantum states having stationary cosmologies as spacetime correlates: also these cosmologies are determined uniquely apart from single parameter. 4. Only subcritical cosmologies are globally imbeddable TGD allows global imbedding of subcritical cosmologies. A partial imbedding of oneparameter families of critical and overcritical cosmologies is possible. The infinite size of the horizon for the imbeddable critical cosmologies is in accordance with the presence of arbitrarily long range fluctuations at criticality and guarantees the average isotropy of the cosmology. Imbedding is possible for some critical duration of time. The parameter labeling these cosmologies is scale factor characterizing the duration of the critical period. These cosmologies have the same optical properties as inflationary cosmologies. Critical cosmology can be regarded as a 'Silent Whisper amplified to Bang' rather than 'Big Bang' and transformed to hyperbolic cosmology before its imbedding fails. Split strings decay to elementary particles in this transition and give rise to seeds of galaxies. In some later stage the hyperbolic cosmology can decompose to disjoint 3surfaces. Thus each subcosmology is analogous to biological growth process leading eventually to death. 5. Fractal manysheeted cosmology The critical cosmologies can be used as a building blocks of a fractal cosmology containing cosmologies containing ... cosmologies. pAdic length scale hypothesis allows a quantitative formulation of the fractality. Fractal cosmology predicts cosmos to have essentially same optic properties as inflationary scenario but avoids the prediction of unknown vacuum energy density. Fractal cosmology explains the paradoxical result that the observed density of the matter is much lower than the critical density associated with the largest spacetime sheet of the fractal cosmology. Also the observation that some astrophysical objects seem to be older than the Universe, finds a nice explanation. 6. Cosmic strings as basic building blocks of TGD inspired cosmology Cosmic strings are the basic building blocks of TGD inspired cosmology and all structures including large voids, galaxies, stars, and even planets can be seen as pearls in a cosmic fractal necklaces consisting of cosmic strings containing smaller cosmic strings linked around them containing... During cosmological evolution the cosmic strings are transformed to magnetic flux tubes with smaller Kähler string tension and these structures are also key players in TGD inspired quantum biology. The observed large voids would contain galactic cosmic strings at their boundaries. These voids would participate cosmic expansion only in average sense. During stationary periods the quantum states would be modelable using stationary cosmologies and during phase transitions increasing gravitational Planck constant and thus size of the large void they critical cosmologies would be the appropriate description. The acceleration of cosmic expansion predicted by critical cosmologies can be naturally assigned with these periods. Classically the quantum phase transition would be induced when galactic strings are driven to the boundary of the large void. The mechanism forcing the phase transition could be repulsive Coulomb energy associated with dark matter at strings if cosmic strings generate net em charge as a consequence of CP breaking (antimatter could reside inside cosmic strings) or a repulsive gravitational acceleration. The large values of Planck constant are crucial for understanding of living matter so that gravitation would play fundamental role also in the evolution of life and intelligence. Manysheeted fractal cosmology containing both hyperbolic and critical spacetime sheets based on cosmic strings suggests an explanation for several puzzles of GRT based cosmology such as dark matter problem, origin of matter antimatter asymmetry, the problem of cosmological constant and mechanism of accelerated expansion, the problem of several Hubble constants, and the existence of stars apparently older than the Universe. Under natural assumptions TGD predicts same optical properties of the large scale Universe as inflationary scenario does. The recent balloon experiments however favor TGD inspired cosmology. Some sections are devoted to the TGD counterpart of inflationary cosmology. From the beginning it has been clear that quantum criticality implying flatness of 3space and thus criticality is the TGD counterpart for inflationary cosmology. Only after the recent findings about evidence for the polarization of CMB I realized that critical cosmology contains a period of very fast accelerating expansion and that both inflation and accelerating expansion much later are special cases of criticality. This leads to a rather detailed view about how the temperature fluctuations could emerged in TGD framework. The predecessor of inflationary cosmology would be cosmic string gas in the lightcone of Minkowski space and critical period would mean the emergence of spacetime as we know it.

This chapter can be regarded as second part of the previous chapter and is develoted to various applications and problems of cosmology. Much of the text is written decade or two ago.

Astrophysics in TGD Universe is the basic topics of this chapter.
The topics discussed are following.

In this chapter the topics relates to what might be called quantum
astrophysics. Motivation comes from the model for Nottale's findings
suggesting Bohr quantization of planetary orbits. The model leads to the
introduction of gravitational Planck constant h_{gr} =GMm/v_{0}, where
v_{0} corresponds to a typical rotational velocity in two particle
system. h_{gr} characterizes the interaction of masses M and m
and assigned to the magnetic flux tube connecting them and carrying the
massless extremals mediating gravitational interaction.
The topics discuss in this chapter are following.

PART III: Topological Field Quantization 