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.

- Zero energy ontology implies that the inertial energy and all quantum numbers of the Universe vanishes and physical states are zero energy states decomposing into pairs of positive and negative energy states. Positive energy ontology is a good approximation under certain assumptions.
- Dark matter hierarchy whose levels are labelled by gigantic values of gravitational Planck constant associated with dark matter is second essential piece of the picture.
- The identification of gravitational four-momentum as the Noether charge associated with curvature scalar looks in retrospect completely obvious and resolves the long standing ambiguities. This identification explains the non-conservation of gravitational four-momentum which is in contrast with the conservation of inertial four-momentum and implies breaking of Equivalence Principle. There are good reasons to believe that this breaking can be avoided for elementary particles and hadronic strings.
- The gravitational energy of string like objects X
^{2}× Y^{2}subset M^{4}× CP_{2}corresponds to gravitational string tension T_{gr}= (1-g)/4G, where g is the genus of Y^{2}. The tension is negative for g>1. The string tension is by a factor of order 10^{7}larger than the inertial string tension. This leads to the hypothesis that g>1 "big" strings in the centers of large voids generate repulsive gravitational force driving g=1 galactic strings to the boundaries of the voids. If the total gravitational mass of strings inside voids vanishes, the breaking of Equivalence Principle occurs only below the size scale of the void. - The basic question whether one can model the exterior region of the topologically condensed cosmic string using General Relativity. The exterior metric of the cosmic string corresponds to a small deformation of a vacuum extremal. The angular defect and surplus associated with the exterior metrics extremizing curvature scalar can be much smaller than assuming vacuum Einstein's equations. The conjecture is that the exterior metric of g=1 galactic string conforms with the Newtonian intuitions and thus explains the constant velocity spectrum of distant stars if one assumes that galaxies are organized to linear structures along long strings like pearls in a necklace.

** 2. Critical and over-critical cosmologies involve accelerated cosmic expansion**

In TGD framework critical and over-critical 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 ρ+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 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. p-Adic length fractality predicts that Λ scales as 1/L^{2}(k) as a function of the p-adic scale characterizing the space-time 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**

- In zero energy ontology cosmic strings must be created from vacuum as zero energy states consisting of pairs of strings with opposite time orientation and inertial energy.
- The counterpart of Hawking radiation provides a mechanism by which cosmic strings can generate ordinary matter. The splitting of cosmic strings followed by a "burning" of the string ends provides a second manner to generate visible matter. Matter-antimatter symmetry would result if antimatter is inside cosmic strings and matter in the exterior region.
- Zero energy ontology has deep implications for the cosmic and ultimately also for biological evolution (magnetic flux tubes paly a fundamental role in TGD inspired biology and cosmic strings are limiting cases of them). The arrows of geometric time are opposite for the strings and also for positive energy matter and negative energy antimatter. This implies a competition between two dissipative time developments proceeding in different directions of geometric time and looking self-organization and even self-assembly from the point of view of each other. This resolves paradoxes created by gravitational self-organization contra second law of thermodynamics. So called super-canonical matter at cosmic strings implies large p-adic entropy resolves the well-known entropy paradox.
- p-Adic fractality and simple quantitative observations lead to the hypothesis that cosmic strings are responsible for the evolution of astrophysical structures in a very wide length scale range. Large voids with size of order 10^8 light years can be seen as structures cosmic strings wound around the boundaries of the void. Galaxies correspond to same structure with smaller size and linked around the supra-galactic strings. This conforms with the finding that galaxies tend to be grouped along linear structures. Simple quantitative estimates show that even stars and planets could be seen as structures formed around cosmic strings of appropriate size. Thus Universe could be seen as fractal cosmic necklace consisting of cosmic strings linked like pearls around longer cosmic strings linked like...

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