**3. Other cosmological phenomena re-interpretations related to 2D and 3D-torsion geometrical models and the signal analysis realized**

In the studies of the Universe the creation of geometrical models or numerical simulation of the space–time phenomena is more complicated and obeys to a reinterpretation that obeys a modern field theories and cohomology theory of topological spaces, even the incorporation of microscopic theories of the Universe, because here are cause of all phenomena in the Universe.

However, as has been said the most important geometrical invariant is the curvature, being the torsion a second curvature.

For example, a re-interpretation that obeys a modern field theories and cohomology theory of topological spaces, with the incorporation of microscopic theories of the Universe can be established as follows.

We can create a 2D-numerical model of the screw effect and re-interpretation in the cosmology objects as black holes or sources as stars or behavior intersidereal magnetic alignment of galaxies, using 2-dimensional complex surfaces considering the Morera's and Cauchy-Goursat's theorems to be evaluate them and can be applied in an numerical program. For example, on singularities or poles in the space–time, considering the space–time a complex Riemannian manifold with singularities. This could represent the surface of the real part of the function *g z*ð Þ¼ *<sup>z</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> *:* The moduli space of this point is less than 2 and thus lie inside one contour. Likewise, the contour integral can be split into two smaller integrals using the Cauchy-Goursat theorem having finally the contour integral [12] ∮ C g zð Þdz ¼ ∮ C 0‐ 1 z‐z1 dz <sup>¼</sup> <sup>0</sup>‐2*π*<sup>i</sup> <sup>¼</sup>

‐2*π*i, (see the **Figure 5a**)). Likewise this value is a traditional cohomological functional element of H<sup>f</sup> <sup>Π</sup>‐ℓ<sup>0</sup> *;* <sup>Ω</sup><sup>r</sup> ð Þ¼ <sup>C</sup>*:* This element is a contour around the singularity as can be viewed in the **Figure 5a**).

Form a cosmological evolution, the torsion play a fundamental role in the forming of all interstellar objects, even the Universe itself. The macroscopic density fluctuations are echoes from big-bang until today "Large CMB" (where quantum field fluctuations had place (**Figure 5**)).

Likewise, from a point of purely cosmological view, the existence of these singular points reveals the existence of sidereal objects where big quantities of flow (using Poincarè arguments) of energy are expulsed or/and attracted along the space–time as twistors satisfying the geometrical Penrose model of a black hole. The torsion as field observable always is present. The spins s and –s, corresponds to different field interactions whose images can correspond to the twistor spaces Pþ, and P�*:*

Here we can incorporate the following cohomology space that re-interprets field theory objects with geometrical objects considering the Universe as complex Riemannian manifold (topological space) to a field source:

$$\operatorname{H}^{1}(\mathbb{P}T, \operatorname{O}(\cdot \mathbf{2} \mathbf{i} \cdot \mathbf{2})) \cong \ker(\operatorname{U}\_{h(\mathbb{k})}) = \{\mathfrak{q} \in \operatorname{C}^{2}(\mathbb{U})|\_{h(\mathbb{k})}\mathfrak{q} = \mathbf{0}, \operatorname{in} \mathbf{U} \subset \operatorname{M}\},\tag{3}$$

The field torsion results evident with some work on twistor-spinor framework [7, 9], and using the electronics interpretations studied in other additional experiments that extend the design of experiments in electronics and realized in our researches (**Figure 6**).

A study realized from a point of view of the mathematical physics and particle physics carries to the following conjecture, considering the particle fermion with boson gauge for torsion and called broson.

**Conjecture 3.1 (F. Bulnes, M. Ramírez, L. Ramirez, O. Ramírez).** The macroscopic image of the broson actions must be a flow electro-gravitational energy

whose micro-states begin from the actions of non-Abelian fields that are measured

*(a) The curvature can be measured to quantum level [8] as distortions given by the link-wave between a hypothetical particle as dilaton (gauged graviton) and the trace on relativistic Feynman diagram followed in quantum gravity [5, 8]. (b) The torsion in the case of the cylindrical trajectory, for different times and considering the causality structure of the space–time, can be determined by different deviations to the world lines in each case having as microscopic oscillations predicted by the Majorana fermions [13]. (c) [14]. Microscopic perturbation on a cylindrical surface. Also is considered the causal structure given by light cones. The red segment in the Figure 6b), corresponds to the surface model given in 9c). (d). Curve of the cylindrical waves. (e). Observe that similar waves of the spectrum power of CMB radiation temperature anisotropy in terms for 90<sup>o</sup> until 0.4<sup>o</sup> to the multi-pole moment. Remember the relation ofh singularities with the field torsion in the aspect*

*Numerical Simulations of Detections, Experiments and Magnetic Field Hall Effect Analysis…*

**Definition 3.1.** A broson is a hypothetical particle that is a fermion and that come from the Branes, being this hypothetical particle wrapped by gauge bosons in

The value of broson is the intrinsic geometry of the torsion as field observable, associated to a bundle. In field theory can be considered a framework operator belonging to certain algebras (can be quantum algebras) that comply with certain conditions to solve field equations (as Dirac equation for example ð Þ *<sup>P</sup>* <sup>þ</sup> <sup>χ</sup><sup>T</sup> oa

using **H**-states (states or densities in a Hamiltonian manifold, are not **H**-particles necessarily) as basis [16]. Likewise, the Dirac equation can take the following form:

The gauge bosons produce torsion in the microscopic space due the electromagnetic characteristic of these bosons that are photons [14] realizing backreaction with the covered space by the gravity. As a result pending for prove will be:

**Theorem (F. Bulnes) 3.1.** We consider the space–time with CPVT effects. The **H**-torsion is the deformation energy between neutrinos and antineutrinos or curva-

The way of the evolution of the Universe depends of the mechanism between the vacuum space, where live fields of particles and the energy derived from the

ture/fermion spin energy (space–time-curvature/spin couplings between

d **h** ¼ 0, ∀**h** ∈ **H**, (4)

<sup>μ</sup> ¼ 0)

by the gauge fields.

*of big production or decaying of energy.*

*DOI: http://dx.doi.org/10.5772/intechopen.96779*

**Figure 6.**

the space–time [15].

fermions/anti-fermions).

**35**

**4. Conclusions and future research**

#### **Figure 5.**

*(a). Pole or singularity of the complex function g z*ð Þ¼ *<sup>z</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> *: (b). The black hole with astronomic catalogue SS 433 is a giant black hole that wobbles. With the VLA and the VLBA, we have watched the wiggle of its jets over time. Here spectral image, we can see its corkscrew appearance obtained for the screw effect. This appearance obeys to the agitation produced by the gravitational field and electromagnetic fields due the particles around (right-handed neutrinos keV) of the black hole in the vacuum space. (c). Source 2-dimensional model considering the little perturbations in its horizon detected in neighborhood of the source (also can be considered as singularity type. For example a peak or cusp). The surface is Z = (0.2coth (*�*0.2ln (0.3x^2 + 0.2y^2)))/ (x^2 + y^2) where happens the perturbation phenomena. This surface represents a quantum field fluctuations in the beginning of the Universe from big-bang stage until any stage of the space–time evolution before of the baryongenesis.*

*Numerical Simulations of Detections, Experiments and Magnetic Field Hall Effect Analysis… DOI: http://dx.doi.org/10.5772/intechopen.96779*

#### **Figure 6.**

fluctuations are echoes from big-bang until today "Large CMB" (where quantum

Likewise, from a point of purely cosmological view, the existence of these singular points reveals the existence of sidereal objects where big quantities of flow (using Poincarè arguments) of energy are expulsed or/and attracted along the space–time as twistors satisfying the geometrical Penrose model of a black hole. The torsion as field observable always is present. The spins s and –s, corresponds to different field interactions whose images can correspond to the twistor spaces Pþ,

Here we can incorporate the following cohomology space that re-interprets field theory objects with geometrical objects considering the Universe as complex Rie-

The field torsion results evident with some work on twistor-spinor framework [7, 9], and using the electronics interpretations studied in other additional experiments that extend the design of experiments in electronics and realized in our

A study realized from a point of view of the mathematical physics and particle physics carries to the following conjecture, considering the particle fermion with

**Conjecture 3.1 (F. Bulnes, M. Ramírez, L. Ramirez, O. Ramírez).** The macro-

*433 is a giant black hole that wobbles. With the VLA and the VLBA, we have watched the wiggle of its jets over time. Here spectral image, we can see its corkscrew appearance obtained for the screw effect. This appearance obeys to the agitation produced by the gravitational field and electromagnetic fields due the particles around (right-handed neutrinos keV) of the black hole in the vacuum space. (c). Source 2-dimensional model considering the little perturbations in its horizon detected in neighborhood of the source (also can be considered as singularity type. For example a peak or cusp). The surface is Z = (0.2coth (*�*0.2ln (0.3x^2 + 0.2y^2)))/ (x^2 + y^2) where happens the perturbation phenomena. This surface represents a quantum field fluctuations in the beginning of the Universe from big-bang stage until any stage of the space–time evolution before of the*

scopic image of the broson actions must be a flow electro-gravitational energy

ð Þ <sup>U</sup> *h k*ð Þ<sup>φ</sup> <sup>¼</sup> <sup>0</sup>*;* in U <sup>⊂</sup> <sup>M</sup> , (3)

*<sup>z</sup>*�<sup>1</sup> *: (b). The black hole with astronomic catalogue SS*

<sup>¼</sup> <sup>φ</sup>∈C<sup>2</sup>

field fluctuations had place (**Figure 5**)).

*Recent Advances in Numerical Simulations*

mannian manifold (topological space) to a field source:

<sup>ð</sup>P<sup>T</sup> *; <sup>O</sup>*ð Þ ‐2*h*‐<sup>2</sup> Þ ffi ker U, *h k*ð Þ

boson gauge for torsion and called broson.

*(a). Pole or singularity of the complex function g z*ð Þ¼ *<sup>z</sup>*<sup>2</sup>

and P�*:*

H1

**Figure 5.**

*baryongenesis.*

**34**

researches (**Figure 6**).

*(a) The curvature can be measured to quantum level [8] as distortions given by the link-wave between a hypothetical particle as dilaton (gauged graviton) and the trace on relativistic Feynman diagram followed in quantum gravity [5, 8]. (b) The torsion in the case of the cylindrical trajectory, for different times and considering the causality structure of the space–time, can be determined by different deviations to the world lines in each case having as microscopic oscillations predicted by the Majorana fermions [13]. (c) [14]. Microscopic perturbation on a cylindrical surface. Also is considered the causal structure given by light cones. The red segment in the Figure 6b), corresponds to the surface model given in 9c). (d). Curve of the cylindrical waves. (e). Observe that similar waves of the spectrum power of CMB radiation temperature anisotropy in terms for 90<sup>o</sup> until 0.4<sup>o</sup> to the multi-pole moment. Remember the relation ofh singularities with the field torsion in the aspect of big production or decaying of energy.*

whose micro-states begin from the actions of non-Abelian fields that are measured by the gauge fields.

**Definition 3.1.** A broson is a hypothetical particle that is a fermion and that come from the Branes, being this hypothetical particle wrapped by gauge bosons in the space–time [15].

The value of broson is the intrinsic geometry of the torsion as field observable, associated to a bundle. In field theory can be considered a framework operator belonging to certain algebras (can be quantum algebras) that comply with certain conditions to solve field equations (as Dirac equation for example ð Þ *<sup>P</sup>* <sup>þ</sup> <sup>χ</sup><sup>T</sup> oa <sup>μ</sup> ¼ 0) using **H**-states (states or densities in a Hamiltonian manifold, are not **H**-particles necessarily) as basis [16]. Likewise, the Dirac equation can take the following form:

$$\mathbf{d} \cdot \mathbf{h} = 0, \ \forall \mathbf{h} \in \mathbf{H}, \tag{4}$$

The gauge bosons produce torsion in the microscopic space due the electromagnetic characteristic of these bosons that are photons [14] realizing backreaction with the covered space by the gravity. As a result pending for prove will be:

**Theorem (F. Bulnes) 3.1.** We consider the space–time with CPVT effects. The **H**-torsion is the deformation energy between neutrinos and antineutrinos or curvature/fermion spin energy (space–time-curvature/spin couplings between fermions/anti-fermions).

### **4. Conclusions and future research**

The way of the evolution of the Universe depends of the mechanism between the vacuum space, where live fields of particles and the energy derived from the

field interaction. This mechanism due the conjecture 2.1, in the section 2, explain the possible field interacting in the space as oscillations born from the microscopic space–time characteristics.

However, considering the limitations of our experiments with electronic devices only we can see and interpret with arguments of geometry, certain traces of electronic signals that evidences the torsion under a magnetic field determined in certain voltage range and a movement of cylindrical trajectory, which as we know, is the constant torsion. However, this verifies the conjecture 1.2., and some theorems established in other studies in theoretical physics and mathematical physics.

One of the future goals is obtain advanced Hall magnetic sensor designed inside the quantum electronics, which permits an evidence of torsion more clear and no so depending of the geometry restrictions as a trajectory of constant torsion, without the managing of a dilaton and more sensible of the microscopic environment and the presence of gravity. This will have that to be through the fermions differencing in the non-harmonic analysis that appear in the anti-symmetric behavior of the curvature energy measured from field interactions [8].

The applications of torsion further of Universe understanding, are diverse and much, with vanguard technological developments:

**Technical notation and singles**

*DOI: http://dx.doi.org/10.5772/intechopen.96779*

M Complex space–time.

mV Mili-volts.

τ ωð Þ 1, ω<sup>2</sup> Spectral torsion. Torsion energy.

H1

**Figure 7.**

H1

**37**

δð Þ t1, t2 2-dimensional impulse function. Here t1 ¼ t2, where <sup>δ</sup>ð Þ¼ t1, t2 <sup>δ</sup>ð Þ<sup>t</sup> <sup>δ</sup>ðÞ¼ <sup>t</sup> <sup>δ</sup><sup>2</sup>

**H** Hopf algebra which is an operators algebras of quantum

Lð Þ <sup>U</sup>″, Oð Þ ‐<sup>2</sup> Cohomological group or space of integrals of the field

*h k*ð Þ Differential operator of the field equation with helicity

equation of electromagnetic field. VLBA Very Long Baseline Array. Term in astrophysics referred

<sup>ð</sup><sup>Π</sup> � <sup>∐</sup>*;* <sup>O</sup>ð Þ <sup>V</sup> Þ ¼ <sup>C</sup> Cohomological functional. Contents all complex values

VLA Radio-astronomical observatory (called Karl G. Jansky

meters over sea level. Large CMB Cosmic Microwave Background of Large range.

spaces represents all these integrals.

τ Torsion. Here in our research is torsion energy.

Socorro, New Mexico. keV Kilo-electron-volts. Energy unity that corresponds to

1,6 � <sup>10</sup>�<sup>19</sup> joules.

*H* Magnetic field produced in the dilaton during the

*The responsible electromagnetic energy of the accretion and iso-rotation of a galaxy through its spinor representation [18, 19]. This responsible electromagnetic energy can be proved that is torsion energy.*

*Numerical Simulations of Detections, Experiments and Magnetic Field Hall Effect Analysis…*

ð Þt *:*

geometry is interpreted as Higgs states algebra.

equations whose sheaf holomorphic vector bundle of helicity �2, has algebraic representation through a lines bundles whose polynomials have zeros in the poles or singularizes evaluated by Conway integrals, for example.

h(k). This differential operator appears in the wave

to a system of ten radio telescopes which are operated remotely from their Array Operations Center located in

of cohomological contours to singularities which as poles are evaluated by Cauchy integrals, Conway integrals and extensions of these. This cohomological equality of

Very Large Array (VLA)) is located to an altitude 2124

field states. This also can be identifying as a Hamiltonian densities manifold. In mathematical physics and derived

sensing process of the Hall torsion sensor.


If we consider the multi-poles as the sources of the electromagnetic nature of the space–time (of fact their moduli stack is obtained by equivalences in field theory using some *gerbes* of derived categories as has been mentioned in field theory in some before works [17]), we can to use the loops around of these poles as contours of the cohomological functionals H1 ðΠ � ∐*;* Oð Þ V Þ ¼ C, [18, 19] to evaluate through the residue theorem their energy and these values that are amplitudes, can be used in spinor waves, of fact we can consider the partial wave expansions of the space–time suggested by the conformal actions in 4-dimensional and 2-dimensional spaces.

The Conway integrals can be considered in axisymmetric boundaries and also non-axisymmetric cases where matter is confined within axisymmetric boundaries, for example in a galaxy. If we consider the electromagnetic nature of the isorotations for magnetic intersidereal fields in galaxies, we need other formalism based in twister geometry, where elliptic integrals are analogues in the space H1 Lð Þ <sup>U</sup>″, Oð Þ ‐<sup>2</sup> *:*

The cohomological analogous are "poles" which can be interpreted as "sources" of electromagnetic radiative energy (see the **Figure 7**).

Finally, is opportune to sign that the methods and results of the research are numerical simulations (much 2D and 3D-dimensional geometrical models and some analogies with the sidereal objects), on themes parallel and related to the gravity (no gravity precisely) considering the torsion methods and experiments of our torsion theory as analogous to detect gravity waves, but in this case detect waves of torsion in an indirect way.

*Numerical Simulations of Detections, Experiments and Magnetic Field Hall Effect Analysis… DOI: http://dx.doi.org/10.5772/intechopen.96779*

**Figure 7.**

field interaction. This mechanism due the conjecture 2.1, in the section 2, explain the possible field interacting in the space as oscillations born from the microscopic

However, considering the limitations of our experiments with electronic devices only we can see and interpret with arguments of geometry, certain traces of electronic signals that evidences the torsion under a magnetic field determined in certain voltage range and a movement of cylindrical trajectory, which as we know, is the constant torsion. However, this verifies the conjecture 1.2., and some theorems established in other studies in theoretical physics and mathematical physics. One of the future goals is obtain advanced Hall magnetic sensor designed inside the quantum electronics, which permits an evidence of torsion more clear and no so depending of the geometry restrictions as a trajectory of constant torsion, without the managing of a dilaton and more sensible of the microscopic environment and the presence of gravity. This will have that to be through the fermions differencing in the non-harmonic analysis that appear in the anti-symmetric behavior of the

The applications of torsion further of Universe understanding, are diverse and

If we consider the multi-poles as the sources of the electromagnetic nature of the space–time (of fact their moduli stack is obtained by equivalences in field theory using some *gerbes* of derived categories as has been mentioned in field theory in some before works [17]), we can to use the loops around of these poles as contours of the

The cohomological analogous are "poles" which can be interpreted as "sources"

Finally, is opportune to sign that the methods and results of the research are numerical simulations (much 2D and 3D-dimensional geometrical models and some analogies with the sidereal objects), on themes parallel and related to the gravity (no gravity precisely) considering the torsion methods and experiments of our torsion theory as analogous to detect gravity waves, but in this case detect waves of torsion

residue theorem their energy and these values that are amplitudes, can be used in spinor waves, of fact we can consider the partial wave expansions of the space–time suggested by the conformal actions in 4-dimensional and 2-dimensional spaces. The Conway integrals can be considered in axisymmetric boundaries and also non-axisymmetric cases where matter is confined within axisymmetric boundaries, for example in a galaxy. If we consider the electromagnetic nature of the isorotations for magnetic intersidereal fields in galaxies, we need other formalism based in twister geometry, where elliptic integrals are analogues in the space

ðΠ � ∐*;* Oð Þ V Þ ¼ C, [18, 19] to evaluate through the

• Advanced vehicles of anti-gravitation and electromagnetic impulse,

• Nanomedicine: Spintronics and radionics devices of total cure,

• More understanding of the Universe: deep understanding

space–time characteristics.

*Recent Advances in Numerical Simulations*

curvature energy measured from field interactions [8].

• Total control of the mind, conscience and brain,

• Artificial intelligence: advanced positron brains,

of electromagnetic radiative energy (see the **Figure 7**).

much, with vanguard technological developments:

• Quantum Communication,

cohomological functionals H1

H1

**36**

Lð Þ <sup>U</sup>″, Oð Þ ‐<sup>2</sup> *:*

in an indirect way.

*The responsible electromagnetic energy of the accretion and iso-rotation of a galaxy through its spinor representation [18, 19]. This responsible electromagnetic energy can be proved that is torsion energy.*
