We use the quantum operators O c G , which are diffeomorphisms of gravity creating the intentionality under the action integrals to prove and determine the gluing intention for adherence of the matter-energy (taking the corresponding mass-energy tensor T ab ) to create complex bodies in the scale of conforming the fragmented Universe such as we know. The reverse is the planting of the energy model of gravity in accordance with the implications in space-time due to the diffeomorphisms of gravity, which were designed to explain the existence of the intention as kernel of the integral operators of the actions with this intention as direction of the energy-matter. The time, in particular, can be shown through instantons of a gauge field (this as electromagnetic field, and in this case appears the torsion) of gravity, which appears in natural way as the same integral operators obtained. Finally, using the complex Riemannian structure of our model of the space-time, and the K-invariant G-structure of the orbits used to obtain curvature, are obtained as consequences of the diffeomorphisms, the field equations to the energy-matter tensor density in each case of the gravitational field.
- agglutination and gluing of sticking cells
- curvature on quantum gravity
- gravitational field intention
- gravitational diffeomorphisms
- integration invariants
- local diffeomorphisms
- regular representation
The Universe outside their quantum model is a fragmented cosmos, where the matter is separated in different gradients of interaction of particles of fundamental level, which goes conforming scales of the matter until to shape the complex structures of all sidereal objects and the life that we know. However, in this process and for the alone presence of matter in the space is created a permanent will with persistent action and the long scope which is the gravitational field.
The permanence of this field is the control aspects of regulation in the sidereal objects such as the movements, shape of the objects, shape of the local space, auto-gravitation, and conformation of the chemical structures. Also their self-recomposing, as well as the different natural process to the life as the kinematic equilibrium of the living beings, biorhythm, biochemical auto-regulations, etcetera, which requires sedimentation and other process that brings the gravitational field, as example, the connection in equilibrium levels depending of the position between all bodies in the space. In addition, the time is a consequence possible of the gravitational field which has an effect, the curvature, where the time being the distance between cause and effect; the instantons  1 of the curvature energy is the distance between gravitational field and curvature in layers of the matter-energy that goes composing the sidereal objects and the Universe. Likewise, this determines an integrated action with the intention of connect the space-time with gravity as the encoding of the Universe, at least in the Einstein-Cartan field conception considering also the Dirac equation to the energy level.
Likewise, we have:
Why the gravity intention is the cohesion? Because, in the beginning of the Universe, the only ingredient was energy. After the Big Bang, the energy was being fragmented in matter and other energy manifestations in the Universe, such as we know in our days. The gravity is the ingredient of that primal energy (the energy before the Big Bang), but this is the version of that primal energy when matter in the space and time appeared (as well as local time or global time in the Universe).
Why the gravity intention is the shape? Because the Universe needs the gravity, to be used in the interpretations of elements of the Universe as are time, space, and energy. For example, space could be curvature, time could be second curvature (or torsion), and energy could be curvature energy in any of their modalities (first and second curvature energies).
2. Integrated action of gravity with the space-time
The Universe before their fragmentation (as has been interpreted in different cosmological theories in the beginning of the Universe) was conformed for energy due to the Big Bang. After when this was freeze gradually is conformed for a quantum process in an Early Universe composed in their totality by neutrinos as basic particles components. These neutrinos were differentiated for a natural process in new neutrinos giving some aspects of our Universe, as possibly the dark matter production. Other neutrino classes as the right-handed neutrinos were establishing with the baryon-genesis process; and other particles as the tachyons and the fermions/anti-fermions in a polarization process creating the charge
To establish the concept of agglutination and join of matter, first it is necessary to analyze the matter on their equivalence, the energy. Before, the Universe was only energy that was available, including the space and time. There was no space and time as we know. These were born after the Big Bang, when the quantum proliferation of particles begun, which conformed the matter particles, these atoms and after molecules. But, what determines this way to create matter. This requires an implicit conscience to create matter from microscopic level, and as this primal matter was part of an energy flow that defines space-time, the rest was stayed as matter energy but without the qualities of compactification of the mass. This gives the beginning to the gravitational energy, which is as natural as the manifestation of a field, the gravitational field.
But, what happens with the space and time? How the gravity enters in the shape of the space and the time? Is gravity consequence of the intention of field in the Early Universe to control the inflation and of this way, to get a defined expansion with a causality-defined arrow?
The torsion of the space is related with the electromagnetic phenomena of the space-time, and gravity more torsion can to define helicities, spins, and polarization rules between particles in the fundamental context of the matter, movement, and space.
Such seems that the intentionality of the field in all the ages of the Universe has been maintaining the cohesion of the space-time such that the primordial component of field, which could be their connection will not be broken and the evolution obeys a sequence of microscopic model (Dirac model) of the Universe, where particles as neutrinos are re-combined. The Lagrangian model must involve the individual actions of gravity and torsion and their joint action,
then the action involving the integral term of gravity and torsion is :
The neutrinos and anti-neutrinos, as was mentioned before, are relevant and primordial in the production of matter to obtain gravity. The role of torsion is to explain the mechanisms of matter/anti-matter in gravity.
To establish a Dirac model that gives explanation from the neutrinos and fermions (which establish the energy required to the coupling of torsion and gravity), the joint action between gravity and torsion comes through given torsion connections in the form:
However, there exist some ambiguities in the Einstein-Cartan theory with the Immirzi parameter. For example, actions can be modified by total derivatives, without effects to on-shell physics given to create movement (that is to say, equations of motion), but such terms confirm the structural coefficients to the quantum context. For other side, in pure gravity without torsion, one can add the following identically zero term due to Bianchi identities of symmetry properties of the Riemann tensor:
which confirm that the gravity establishes a global behavior in the Universe, not being true in the presence of torsion to the quantum level. For example, the action
where the tensor is the dual of the curvature tensor , which is nontrivial in torsionful geometries, but conformal with certain homogeneity degree, doing the gravity persist even in the post-Newtonian limit when the torsion let of act, because begins exist the vacuum of the Universe.
But in the torsion case, the movement equations imply:
where is clear an inconsistent due to the equality between a vector
The fermion-piece that will be added to the Holst action is:
together with Dirac kinetic term, the fermion action reads:
which establish an equivalent to the Einstein-Cartan theory independent of Immirzi parameter
In Eq. (11),
which in simplified shape is written as
Then our model of cohesion by gravity is possible, since the scattering in the space-time is decreased under the last action (see Figure 1(a) ).
3. Diffeomorphisms in gravity
Likewise, to energy level, let E be the energy, S be the space, and T be the time, and the corresponding topological spaces be and  such that the following commutativity of the diagram is satisfied:
where in the context of the energy-(space-)time, an application
considering that f : T → E is a smooth mapping between manifolds (the composition
and analogy to the space S had a smooth mapping between manifolds S and E such as g : S → E, where the image is a submanifold of the space
Then a diffeomorphism between the space
that establishes the variation of the energy-(space-)time states in the covering space E . Their differential is the curvature. Their integral is the variation principle
But how the energy states vary in this broth of space-(energy-)time given by the Universe of such lucky that the matter can be formed with the step of time. Here, the time happens as distance between cause and effect or distance between initial state and final state of a waving in the space.
Let X, be a field acting in the space-time as energy that involves space and time . An oriented string
with the correspondence rule4
which is translated in the differential
where we have used the property of
where is the energy states space defined explicitly7:
Expression (24) proves the Conjecture 1.1, given in Section 1, since this demonstrates that the field is a matter-production source (the particle process does appear 2-spin particles expressed inside the energy integral) that is to say, the gravity is the performance of the space-time, and
Likewise, the gravity intention ℑ
Finally, we can affirm considering the Dirac field equation and coordinates systems given for
Here is where appears the expression of difference of the energy-matter tensor to the equation of field (23), to the curvature tensor
In , it was concluded that the torsion field stays univocally determined through
Then this treatment to obtain a detailed description through microscopic context in field theory of the gravity (as matter-energy that is produced in the nucleon-synthesis, where is originated the matter and with it the fragmented Universe) is known with precision.
But, these material products (such as planets, stars, galaxies, nebulas, etc.) are followed and joined by wave-links of gravity which conform their orbits and relative positions in the Universe.
We could say that the dark matter is the result of energy-matter with hadrons in action.
4. Observational confirmations and conclusions
As was mentioned in the beginning of this chapter, the inflation is normed by the matter production and for the existence of inflatons (condensation of gravitinos, which come of the interactions in the leptogenesis ( Figure 2 )). This determines the first inflation in the double inflation determined in the conformal SUGRA model which corresponds to our string model
- An instanton, or also called pseudo-particle in particle physics, is in theoretical and mathematical physics, a classical solution to motion equations with a finite, non-null action as well as quantum mechanics or in quantum field theory. Likewise, this solution is a solution to the equations of motion in classical field theory on a Euclidean space-time.
- Remember that in QFT, field and wave can be the same using the two-duality principles: field and particles are the same and also wave and particle. Then by equality transitivity, field and wave are the same. Likewise, in string theory a string is a field.
- φ is an energy state of a field X.
- φ, X. O c φ = d ℑ φ = L s φ φ • d φ .
- The appearing of a vector υ(x), is when we derive again the expression (23). Then we obtain a vector as appears in the integrant of the integral expression given in Eq. (22).
- The integral in the right member is realized over the space Ω . ⊆ R 3 × I s .
- Also we can to define this space considering the images to n‐ particles in m‐ systems (always with n ≤ m) in T ∗ Cn, m, as:
- Conscience of the presence of matter. This conscience is the only presence of matter that does to change the spin of energy of the space between material bodies. Remember, the energy change and provokes movement.