Updated Cosmic Strings
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
fourmomentum as the Noether charge associated with
curvature scalar looks in retrospect completely
obvious and resolves the long standing ambiguities.
This identification explains the nonconservation
of gravitational fourmomentum which is in contrast
with the conservation of inertial fourmomentum
and implies breaking of Equivalence Principle.
There are good reasons to believe that this
breaking can be avoided for elementary p"/public_html/articles/
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}= (1g)/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 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 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. pAdic
length fractality predicts that Λ 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
 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.
Matterantimatter 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
selforganization and even selfassembly from the
point of view of each other. This resolves
paradoxes created by gravitational
selforganization contra second law of
thermodynamics. So called supercanonical matter at
cosmic strings implies large padic entropy
resolves the wellknown entropy paradox.
 pAdic 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 supragalactic 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...
4. Cosmic strings, gamma ray bursts, and
supernovae
During year 2003 two important findings related to cosmic strings
were made.
 A correlation between supernovae and gamma ray bursts was
observed.
 Evidence that some unknown p"/public_html/articles/ of mass m≈2m_{e}
and decaying to gamma rays and/or electron positron pairs
annihilating immediately serve as signatures of dark matter. These
findings challenge the identification of cosmic strings and/or
their decay products as dark matter, and also the idea that gamma
ray bursts correspond to cosmic fire crackers formed by the
decaying ends of cosmic strings. 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 p"/public_html/articles/ 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.
For details see the updated chapter Cosmic Strings.
