The recent view of the TGD counterpart of the inflationary cosmology

The question of Marko Manninen related to the inflation theory inspired the following considerations related to the TGD counterpart of the inflationary period assumed to precede radiation dominated phase and to produce ordinary matter in the decay of inflaton fields.

Very briefly.

1. In TGD, the role of inflaton fields decaying to ordinary matter is taken by what I call cosmic strings, which are 3-D extremely thin string-like objects, have a huge energy density (string tension) and decay to monopole flux tubes and liberate ordinary matter and dark matter in the process. That cosmic strings and monopole flux tubes form a “gas” in M⁴× CP₂ solves the flatness problem: M⁴ is indeed flat!

In TGD, quantum coherence in cosmic scales replaces the idea that the observed universe corresponds to an exponentially expanding coherence region and saves from the multiverse. This solves the problem due to the constancy of the CMB background temperature.

Cosmic strings and monopole flux tubes

In TGD, space-times are 4-D surfaces in H=M⁴× CP₂.

1. Cosmic strings are 3-D string like. objects which have 2-D M⁴ projection and do not have a counterpart in GRT. They are of the form. X²× Y² ⊂ M⁴xCP₂ where X² is a string world sheet. They can be arbitrarily long and have length which is measured even in billions of light years. They are not possible in string models or in GUTs.
2. Cosmic strings are unstable against the thickening of M⁴ projection. This thickening creates Einsteinian space-time. The thickening reduces their string tension and this liberates energy as ordinary matter and the TGD counterpart of dark matter. This process is the TGD counterpart of inflaton field decay.

This process repeats itself as a similar process for monopole flux tubes. The thickening need not involve exponential expansion of these space-time surfaces. This decay leads from the cosmic string dominated phase to a radiation dominated phase and generation of Einsteinian space-time and cosmology.

Primordial cosmology and the almost constant temperature of the CMB

Primordial cosmology preceding the radiation dominated phase corresponds in the TGD framework to a “gas” like phase formed by a network of cosmic strings which can be arbitrarily long and are always closed. Reconnection is the basic topological reaction for them. This phase has no counterpart in Einstein’s theory.

A natural assumption is that there is a quantum coherence in the scale of the cosmic string along the string. One expects a hierarchy of quantum coherence scales corresponding to string length scales which in the TGD framework would correspond to p-adic length scales and/or to hierarchy of dark scales assignable to the h_eff hierarchy of phases behaving like dark matter. The phase transitions increasing the value of h_eff are possible and scale their length. Both transitions would be fundamental for them.

One can pose several questions.

1. TGD predicts also a hierarchy of Planck constants h_eff=nh₀, where h₀ is the minimal value of effective Planck constant, which corresponds to a dimension of an algebraic extension of rationals. This hierarchy of phases of ordinary matter behaving like dark matter solves the missing baryon problem whereas the energy of cosmic strings explains the galactic dark matter.
2. A more detailed view of this hypothesis suggests that n decomposes to a product n=n₁n₂ of integers characterizing algebraic extensions assignable to M⁴ and CP₂ degrees of freedom. The holomorphy= holography ansatz gives support for this conjecture. Number theoretic vision forces the increase of algebraic complexity meaning the increase of h_eff during cosmic evolution. h_eff=h₀ would be the simplest option in the primordial phase.
3. Quantum coherence in the length scale of cosmic string is possible in the scale of strings already in the primordial cosmology and even for the minimal value of h_eff equal to h₀. This suggests that the observed almost constant value of the CMB temperature in the scale of the cosmic string. But what about longer scales?
4. But is quantum coherence possible in arbitrarily long length scales with h_eff=h₀ or is dark matter with h_eff>h₀ needed? These phases should emerge unavoidably during cosmic evolution: Is it enough to assume that macroscopic quantum coherence in arbitrarily long scales emerges during cosmic evolution?

Do quantum fluctuations replace the thermal fluctuations of inflation theory

If long length scale quantum coherence is possible in the length scale of cosmic strings, one ends up with the following questions.

1. Does gravitational quantum coherence due to long cosmic strings explain the almost constant value of the CMB temperature? One has ρ ∝ T⁴, which gives δ T/T ∝ 4δ ρ/ρ.

This allows to imagine two options.

1. If arbitrarily long cosmic strings are possible in the primordial phase, quantum coherence could be present in all scales already in the primordial phase with h_eff=h₀.
2. If the lengths of cosmic strings are bounded in the primordial phase so that they are proportional too h_eff , long cosmic strings must be created later by reconnection in phase transitions increasing the value of h_eff. These phase transitions could also increase the length of cosmic strings, rather than only its thickness.

The dimension of G is [L²]/[h]. In TGD the only dimensional parameter is CP₂ length scale R and this suggests the formula G= R²/ℏ, which generalizes to the formula G= R²/ℏ_eff. One must have ℏ ≈ (10⁷-10⁸)ℏ₀ to explain CP₂ radius fixed by electron mass from p-adic mass calculations.

Again one can consider two options.

1. R is a fundamental constant and the value of G_eff= R²/h_eff varies and is different in the dark phases and decreases with h_eff. This looks strange but since we cannot yet observe dark matter, one cannot exclude this option. For this option one would have for the dark matter ρ= 3/(4π G_eff a²) =3ℏ_eff/(4π R² a²).
2. G= R²/ℏ₀ is a fundamental constant and the effective radius squared R²_eff= R²(ℏ_eff/ℏ₀) of CP₂ varies. It could geometrically correspond to the size of the M⁴ projection of the cosmic string, or more precisely the thickening of Y²⊂ CP₂. CP₂ scale would correspond to the Planck scale. For this option one would have ρ= (3ℏ₀/4π R²_effa²) =3ℏ_eff/(4π R² a²).

For both options the density of dark matter would increase with ℏ_eff. Consider now what quantum criticality predicts.

1. Quantum criticality means that the quantum state is a superposition of states with different values of h_eff. This means fluctuations and long range correlations since quantum coherence scales are typically proportional to h_eff and even h_eff² as in atomic physics. This implies that the thermal fluctuations correspond to the fluctuations of ℏ_eff

δ T/T = (1/4) δ ρ_cr/ρ_cr= (1/4) δ ℏ_eff/ℏ_eff.

Density fluctuations are in the range δ T/T ∈ [10^-4,10^-5]. The nominal value of δ T/T is 10^-4/3 (see this). This corresponds to δ ρ_cr/ρ_cr=4δ T/T δh_eff/h_eff= 1.3× 10^-4.

If one assumes that h_eff=h is the average value of h_eff and the decomposition h_eff=n₁n₂h₀ and uses the estimate n= R²/G ∈ [10⁷-10⁸], one obtains δ h_eff/h_eff= δ n₁/n₁+ δ n₂/n₂. For δ n₁=1 and δ n₂=1 one has n₁=n₂≈ n^1/2 ∈ [10^3.5,10⁴], one has very naive estimate δn/n∈ 2× [10^-3.5,10^-4]]. The order of magnitude is correct.

The justification for the decomposition comes from the holography=holomorphy hypothesis which implies that the two polynomials defining the space-time surface as a complex surface in generalized sense gives rise to two extensions of rationals with dimensions n₁ and n₂. These extensions can be assigned to M⁴ degrees of freedom (string world sheets X²) and to CP₂ degrees of freedom (partonic 2-surfaces Y²).

For the cold spot of CMB the density fluctuation is 4 times larger than on the average. This could be explained as being due to n₁→ 8n and n₂=n₁→ n₁/8 in n→ n₁n₂≈ n₁² giving for δ n₁=δ n₂=1 the outcome δ n/n= 1/(8n₁)+ 8/n₁ ≈ 8/n₁ so that the fluctuation is 4 times larger. For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.