As fundamental to our understanding of particle physics as the Higgs field is, it is equally important to our understanding of cosmology.
It makes a big contribution to the energy in empty space, the so-called dark energy, which astronomical observations reveal to be a weirdly tiny, yet positive, number. The discovery of the Higgs boson was a triumph for the theory of quantum fields, the amalgamation of quantum mechanics and relativity which dominated 20th century physics. But quantum field theory has great trouble explaining the mass of the Higgs boson and the energy in empty space.
In both cases, the problem is essentially the same. The quantized vibrations of the known fields and particles become wild on small scales, contributing large corrections to the Higgs boson mass and to the dark energy density and generally giving them values much greater than those we observe.
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But the LHC has looked for these extra partner particles and, so far, failed to find them. It seems that nature has found a simpler way to tame quantum phenomena on short distances, in a manner which we have yet to fathom. Meanwhile, our most powerful-ever telescope, the Planck satellite, has scanned the universe on the largest visible scales. What it has revealed is equally surprising. The whole shebang can be quantified with just six numbers: the age and temperature of the cosmos today; the density of the dark energy and the dark matter both mysterious, but simple to characterize ; and the strength, and slight dependence on scale, of the tiny initial variations in the density of matter from place to place as it emerged from the big bang.
The accelerated expansion of space is due to the adaptability of the cosmic DM gas. When the volume V increases, fusion and fission processes continue to equilibrate one another by producing more DM and more DE. Since DM particles are electrically neutral, they cannot produce photons and they are not heated or cooled by contact with ordinary matter . Invisible cosmic DM gas is thus isothermal in the whole universe. Even when space is expanding, its density and temperature is regulated everywhere by mutually controlled fusion and fission processes. Thermal agitation leads to pressure effects.
They are important for the constitutions of DM atmospheres  , but nearly negligible for the accelerated expansion of space.
The conjecture that the scale factor had to be finite for the present universe was correct, but it is not constant. This is not sure anymore  and may result from a misunderstanding. Indeed, Einstein could only regret that he did not realize himself that our universe might be expanding, even when. However, this required the additional idea that cosmic expansion could start with.
Maybe, Einstein did not consider this possibility because of 5.
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He could not explain how apparently empty space might produce energy, but he did not simply believe that this is impossible. To prepare the following chapter, we present some essential consequences of the theory of STQ in a short and different way. The basic idea was that Nature could impose a third restriction in addition to those which led to the development of relativity and quantum mechanics. The function applies to free particles in any inertial reference frame. It depends on the rest-mass m o of these particles.
It is its wave function, which allows us to express knowledge. It defines the probability distribution for possible positions in space, but provides also information about motions in terms of possible values of p and E. Relativistic Quantum Mechanics RQM combines the relations 17 and accounts thus for c and h, but it is assumed that the wavelength could be infinitely small.
This is equivalent to believing that the energy E and momentum p could have arbitrarily high values. If there did exist a finite limit a for the smallest measurable distance, we would have to accept that. The value of a is thus determined by the highest possible momentum. Because of 17 , it would be obtained when and when the energy E has the highest possible value. This requires a photon and that its energy cannot be increased.
It would thus have to be equal to the total positive energy content of the whole universe. Its value would be. Although it is gigantic, it could be finite. STQ confirms that energies , even for material particles . They can be distinguished from one another by means of their wave functions when the quantum of length. The wave function has to be defined for all values of x, but it can have the same or opposite signs on the intercalated lattice with respect to the normal lattice. Although the functions are different, the probability distribution will be unaffected.
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Such a modulation of wave functions is possible for any reference frame in our four-dimensional space-time. This yields four quantum numbers. Each one of them can be a positive or negative integer number, but they are everywhere identical for particles of given type. This is compatible, by multiplexing . Small and large-scale variations can be combined. The electric charge is always determined in units e by. The Standard Model of elementary particles accounts for three generations of quarks and leptons.
They correspond to and display the same family structure, in terms of triplets. When states of type correspond to up-quarks , while states of type correspond to down-quarks. In both cases, there are 3 possible permutations, defining different color states R, G or B. The electron is an elementary particle in the state, where. Antiparticles are characterized by opposite signs for all quantum numbers.
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Moreover, there are states of type with 6 possible permutations and two states, when. This octet defines particles and antiparticles of charge. They are elementary DM particles. They are the supersymmetric partners of gluons. Supersymmetry results from the fact that the z-component of the spin vector along a given z-axis is defined by large-scale angular variations of -functions around this axis. These variations are independent of small-scale variations, defined by u-quantum numbers.
Every particle state for fermions corresponds thus to a state for bosons and vice-versa. Elementary particles can be transformed into one another by means of annihilation and creation processes. However, the sum of u-quantum numbers has to be conserved for every one of the four space-time axes, as well for bosons as for fermions. This accounts for the fact that a quark can change its color by creating or annihilating a gluon.
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For instance,. Narks can also create or annihilate gluons, since , for instance. Narks and quarks are thus particles that are subjected to strong interactions. They yield attractive forces that can lead to scattering or binding. This means that the three spatial reference axes have to be involved with the same probability. Nucleons are thus constituted of 3 quarks in R, G and B color states. Narks can constitute a greater variety of compound particles. The cosmic DM gas is composed of neutralons and compound neutral particles.
They interact most frequently by elastic scattering, which leads to pressure effects and explains astrophysical observations . DM particles allow also for fusion and fission processes.
They are important for cosmology, but STQ has also other consequences. Since the initial state of our universe should be the simplest possible one, it would correspond to a unique quantum . Is it one among those, which are possible according to STQ? The best candidate would then be a photon. Since STQ requires only that , to account for all possible elementary particles, the value of the quantum of length could be a function of cosmic time.
Its initial value would thus determine the energy of the primeval photon. According to quantum mechanics, it is not possible to specify its position with absolute precision in our 3-D space. However, the probability distribution could be uniformly distributed over the surface of the smallest possible hypersphere.
This means that its radius. The primeval photon had even to be in a quantum mechanical state where all orientations of its momentum vector were equally probable. Their magnitude was defined by and , where the wavelength was determined by periodic boundary conditions. The available 3-D space was reduced, indeed, to the surface of the hypersphere of radius. The wavelength was thus equal to the length of any great circle of the hypersphere. All possible waves were propagating there with equal amplitude in any direction and the average value of all momenta p was zero, although.
The energy E of the primeval photon was equivalent to a mass M, since.