How Earth could have formed from gravitationally dark matter at magnetic bubble?

The following argument tries to describe the physics of the TGD based model first. I have not evaluated the local Hubble constant before and try to do it. I will concentrate on the TGD inspired model for the formation of Earth. The idea that Earth was formed as the gravitationally dark matter at the magnetic bubble transformed to ordinary matter. This mechanism would explain also the formation of stars at the Local Bubble.

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.

1. 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.
2. 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.

1. 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.

2. 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 M⁴ projection to Einsteinian space-time with 4-D M⁴ projection.
3. The dark energy density would be ρ_d=3 Λ_loc/8π G with Λ_loc∝ 1/L_loc². 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.
4. For the usual Planck's constant ℏ, one would have the usual cosmological Λ ∝ 1/L_c², where L_c would be the radius of the horizon and of the order of 10¹⁰ 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/m³ 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.
5. If Λ_loc scales as 1/L²_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=2ⁿ-1 or their Gaussian counterparts M_n,G= (1+i)^n-1, M₁₀₇ would correspond to ordinary hadron physics and M₈₉ would correspond LHC energy scale higher by factor 512 than that of ordinary hadron physics. There are several indications for M₈₉ hadron physics as dark variants of M₈₉ hadrons with scaled up Compton length. Gaussian Mersennes M_G,79 resp. M_G,73 would correspond to scales, which are by factor 2¹⁴ resp. 2¹⁷ 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.

1. TGD predicts a hierarchy of large Planck's constant h_eff =nh₀ labelling phases of ordinary matter, which behave like dark matter at the flux tubes. In particular, the gravitation Planck's constant ℏ_gr= GMm/β₀, β₀<1, which Nottale originally suggested, would make possible quantum gravitational coherence in astrophysical scales in the TGD Universe.
2. 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.
3. For gravitationally dark matter, the gravitational Compton wavelength is Λ_gr= GM/β₀ = r_S/2β₀ 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.
4. For the Sun, the Schwartschild radius is 3 km and β₀= v₀/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.

1. β₀=v₀/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, β₀= v₀/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?

2. 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=β₀c= H_loc× L_loc i.e. H_loc= β₀× c/L_loc. This gives H_loc ≃ 3× 10⁷ kms^-1 pc^-1. Cosmic Hubble constant H_c≃ 72 km s^-1 Mpc^-1 is 11 orders of magnitude smaller.
3. The naive L_loc/L_c scaling would give a value of H_loc, which is 15 orders of magnitude smaller. For β₀ =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.