**What happens in rapid local cosmic expansion pulses that replace the uniform expansion in TGD?**

This rapid local expansion is essentially an explosion. A supernova explosion throwing out a shell of matter, and as the interpretation of Local Bubble suggests, also the magnetic bubble, is a good starting point in the modelling.

- A flux tube containing dark matter (in the sense of TGD) expands rapidly. The thickness of the flux tubes increases rapidly and then settles to a constant value as a new minimum energy situation is found.
- The cross-sectional area S of the flux tube serves as a parameter. The magnetic energy E
_{m}∝ 1/S and the volume energy E_{V}∝ (its coefficient is analogous to the cosmological constant) associated with the monopole flux are the energies. In equilibrium, the sum E_{n}+E_{V}is minimized as a function of S (see this). The total density for the flux tube determines the effective cosmological constant Λ_{loc}, i.e. the effective string tension, which decreases as the flux tube thickens. This means energy release, which causes an explosion.

**The Big Bang analogy as a model**

It is tempting to apply Big-Bang analogy to the explosion phase.

- The density ρ
_{d}= 3 Λ/8π G of dark energy would define a map between very long and short length scales identified as L_{c}= Λ^{-1/2}and R_{d}=ρ_{d}^{-1/4}. L_{c}could correspond correspond to the horizon radius or age of the local Universe identifiable as the size of associated causal diamond (CD) in zero energy ontology (ZEO) (see this and this). At the microscopic level, L_{c}could correspond to the length of the flux tube and R_{c}to its thickness.These identifications would relate macroscopic and even astrophysical scales and elementary particle mass scales. I have considered the possible consequences of this map earlier.

- As the energy minimum is reached, the expansion of the flux tube ceases. It can be also thought that H
_{loc}and Λ_{loc}approach cosmological values. Therefore one could model the emerging expanding space sheet as a local Big-Bang with the help of the parameters Λ_{loc}, L_{loc}, and H_{loc}, which have large values at the beginning of the explosion. The explosion would be a scaled down analog for the TGD counterpart of inflation, which would have led to effectively 2-D cosmic strings with 2-D M^{4}projection to Einsteinian space-time with 4-D M^{4}projection. - The dark energy density would be ρ
_{d}=3 Λ_{loc}/8π G with Λ_{loc}∝ 1/L_{loc}^{2}. L_{loc}would be the scale of the space-time sheet determined by the length of the flux extending to a horizon which would correspond to light-like 3-surface, whose possible role as space-time boundaries was understood only quite recently (see this). L_{loc}would quite concretely be the radius of the horizon. The horizon would correspond to the edge of a spacetime sheet. - For the usual Planck's constant ℏ, one would have the usual cosmological Λ ∝ 1/L
_{c}^{2}, where L_{c}would be the radius of the horizon and of the order of 10^{10}ly. The scale R_{c}∝ (8π G/3 Λ)^{1/4}would be much smaller than Λ_{c}and from the estimate ρ_{c}≈ m_{p}/m^{3}and proton Compton length 3.48× 10^{-15}m would roughly correspond to a wavelength of .75× 10^{-4}meters. The peak wavelength of the microwave background is 1 mm. This suggests a biology-cosmology connection. - If Λ
_{loc}scales as 1/L^{2}_{loc}, and L_{loc}≈ AU corresponds to the scale of the Earth-Sun system, L_{loc}in the Sun-Earth system would be smaller by the factor AU/L_{c}≃ 1.6× 10^{-15}than at the level of cosmology.The scaling of R

_{c}≈ 10^{-4}m by this factor would give R_{loc}≈ 10^{-19}m. This is by factor 1/100 smaller than the Compton scale of intermediate bosons. What could this mean?TGD predicts (see this) and this) scaled up variants of strong interaction physics assignable at p-adic primes identifiable as Mersenne primes M

_{n}=2^{n}-1 or their Gaussian counterparts M_{n,G}= (1+i)^{n-1}, M_{107}would correspond to ordinary hadron physics and M_{89}would correspond LHC energy scale higher by factor 512 than that of ordinary hadron physics. There are several indications for M_{89}hadron physics as dark variants of M_{89}hadrons with scaled up Compton length. Gaussian Mersennes M_{G,79}*resp.*M_{G,73}would correspond to scales, which are by factor 2^{14}*resp.*2^{17}that of ordinary hadron physics. The Compton radius of proton for the M_{G,73}hadron physics be of the order of R_{loc}≈ 10^{-19}m.

**Matter at the magnetic bubbles is dark**

The fact that monopole flux tubes associated with the magnetic bubble carry dark matter in the TGD sense is not yet taken into account.

- TGD predicts a hierarchy of large Planck's constant h
_{eff}=nh_{0}labelling phases of ordinary matter, which behave like dark matter at the flux tubes. In particular, the gravitation Planck's constant ℏ_{gr}= GMm/β_{0}, β_{0}<1, which Nottale originally suggested, would make possible quantum gravitational coherence in astrophysical scales in the TGD Universe. - The gravitationally dark monopole flux tubes would be naturally associated with the magnetic bubble corresponding to the Earth (analogous to the one created in a supernova) and also connect the magnetic bubble with the Sun and mediate gravitational interaction with it. Matter at the magnetic bubble would have been dark before condensing to form Earth for which matter mostly corresponds to the usual value of Planck's constant.
- For gravitationally dark matter, the gravitational Compton wavelength is Λ
_{gr}= GM/β_{0}= r_{S}/2β_{0}and does not depend on the mass of the particle m at all. This is in accordance with the Equivalence Principle. That particles of all masses have the same Compton wavelength makes gravitational quantum coherence possible and is essential in the TGD inspired quantum biology. - For the Sun, the Schwartschild radius is 3 km and β
_{0}= v_{0}/c is of order 2^{-11}on basis of Nottale's estimates, which came from the model for planetary orbits as Bohr orbits. The Compton wavelength Λ_{gr}would be about 6000 km, about the radius of the Earth! Is this a mere accident? The thickness of the dark gravitational flux tube R_{loc}would therefore be of the order of the Earth's radius R_{E}, and the length L_{loc}would be of the order of AU.The parameters of the local Big-Bang would therefore be R

_{loc}= R_{E}and L_{loc}=AU at the beginning of the explosion that led to the creation of the Earth as dark gravitationally dark matter transformed to ordinary. The slowing down of the explosion would be due to the transformation of the gravitationally dark matter to ordinary matter.

**What about the value of local Hubble constant?**

The previous arguments have not said anything about the value of the local Hubble's constant H_{loc} in the beginning of the explosion. Here the formula for ℏ_{gr} serves as a guideline.

- β
_{0}=v_{0}/c is the velocity parameter appearing in the gravitational Planck constant ℏ_{gr}. It could correspond to a typical expansion rate at a distance L_{loc}≈ AU.In the case of the Sun, β

_{0}= v_{0}/c≃ 2^{-11}applies. Could it be the rate of expansion for the Earth-related dark magnetic bubble during the*initial stages*of the explosion, which would later slow down as dark matter is transformed to ordinary? - The counterpart of Hubble's formula would give a prediction for the local recession velocity at Earth-Sun distance L
_{loc}= AU= 4.4× 10^{-6}pc as v_{loc}=β_{0}c= H_{loc}× L_{loc}i.e. H_{loc}= β_{0}× c/L_{loc}. This gives H_{loc}≃ 3× 10^{7}kms^{-1}pc^{-1}. Cosmic Hubble constant H_{c}≃ 72 km s^{-1}Mpc^{-1}is 11 orders of magnitude smaller. - The naive L
_{loc}/L_{c}scaling would give a value of H_{loc}, which is 15 orders of magnitude smaller. For β_{0}=1, i.e. its maximum value which seems to be valid ate the surface of the Earth in quantum biology, the value would be give 14-15 orders smaller, so that the L_{loc}/L_{c}scaling would seem to make sense in this case.

**Acknowledgements**: I want to thank Avril Emil for interesting questions related to the notion of local Big-Bang.

See the article Magnetic Bubbles in TGD Universe or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

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