Solving 7 problems of particle physics and cosmology at one blow?
The SUM of all fears and hopes
“You can't always get what you want … but if you try … you might find … you get what you need”
So let's keep trying.
Report on progress in Spectral Unification Model building
Solving 7 problems of particle physics and cosmology at one blow and consolidating a bridge to span 14 orders of magnitudes in energy from 125 GeV to O(10) YeV
Tom Thumb and the Brave Model Tailors
ABSTRACT: We present minimalist matched extensions of both the Standard Model (SM) of elementary-particle forces and General Relativity (GR) in the form of an effective quantum field theory valid up to an order of magnitude of 10 YeV coupled to gravity with an extended scalar mimetic sector. This so called Spectral Unification Model (SUM) relies on two hypotheses: i) the space-time-matter-radiation structure of the physical universe is the solution of a generalized Heisenberg commutation relation (abbreviated in C2M for Chamseddine-Connes-Mukhanov) expressed as an index-like formula in noncommutative geometry and its dynamics is computed from ii) the spectral action principle which is basically a stronger hypothesis than the usual diffeomorphism invariance of the action of general relativity. The C2M commutation relation in dimension four is essentially a quantization condition that determines in a unique way the noncommutative space defining our space-time as a tensor product of continuous and discrete spaces. It implies that the volume of the continuous part is quantized and provides a noncommutative space predicting with the help of its spectral action the existence of a unified model of all particle interactions based on a Pati-Salam (PS) symmetry and as a special case the SM while the volume quantization gives a modified version of Einstein gravity with a mimetic sector. Thus the SUM provides a consistent picture of particle physics from the electroweak scale to the PS gauge couplings unification (1) scale and of cosmology from inflation (2) until today accelerating expansion (3) with baryogenesis (4) occurring through leptogenesis during reheating. The new matter content consists essentially in three ultra-heavy right-handed neutrinos and a SM-singlet scalar whose vacuum expectation value around 1011 GeV breaks the PS symmetry and gives a Majorana mass to the right-handed neutrinos. At low energies, the model reduces to the SM, augmented by seesaw generated neutrino masses and mixing (5). The Einstein's equations are modified such that the cosmological constant (6) is now an integration constant and is not present in the action. The volume quantization condition expressed in space-times with Lorentzian signature generates a scalar field modifying only the longitudinal part of the graviton which plays the role of mimetic dark matter (7). In conclusion, seven fundamental problems of particle physics and cosmology can be solved at one blow in the SUM which is very economical in new hypotheses beyond the SM spectrum and spacetime dimensions and is compatible with experiments and observations from zeptometer scale to the enneameter one.
DISCUSSION: At the time being, it is difficult to envision a direct probe for the SUM but any upcoming experimental evidence for supersymmetric particles at the TeV scale, any kind of wimp or a proton disintegration signal would probably falsify it. We emphasize that the SUM is computed from a mathematically quite rigid noncommutative geometric framework based on few axioms which number has decreased since its inception as the experimental validation of the standard model has been completed. On the other hand, once the SUM spectrum posited, all its phenomenological consequences discussed up to now have been derived thanks to well established quantum field theories, renormalisation methods and Einstein general relativity. Last but not least all the conditions required to fulfil low energy experiments and cosmological observations are so restrictive that the SUM is quite unique. The reason why it has escaped examination up to now by high energy physics community must probably be attributed to its lack in new particle phenomenology at accessible energies. After all until the construction of the LHC and its 2012 discovery there were clever people who did not believe in the existence of the Higgs boson despite the confirmation of the Glashow-Weinberg-Salam model at LEP. The thorough study of minimal non-supersymmetric SO(10) GUTs which shares some important features with SUM (up to the seesaw scale) was also left aside for many years due to problems with tachyonic instabilities proven to be absent in the full quantum theory (perhaps even more probably due to its non-SUSY nature). The situation for the SUM may change in a foreseeable future particularly if conventional dark matter and TeV scale particles search stay unsuccessful. On a more cheerful tone the fact that we can envision on a pretty firm basis, in lieu of the string landscape, one specific bridge from our electroweak precision data set to the fuzzy PS gauge couplings unification extrapolation (spanning fourteen orders of magnitudes in energy from the 125 GeV Higgs mass to the ≈1016 GeV natural scale of spectral action) is a significant progress providing incentives to address for instance the important hierarchy problem not dealt with here. It is indeed worth reminding that the spectral action includes naturally a dilaton field which guarantees the scale invariance of the standard model interactions, and provides a mechanism to generate mass hierarchies. Moreover considerations of scale invariance require including new terms in the spectral action that makes it possible to avoid cosmological and black hole singularities in GR.
The place of the Spectral Unification Model in the Grand Loop of Physics.
This picture is a possible update of the 1980s Glashow's cosmic Uroboros in light of the current (2017) available data, emphasizing the Higgs boson scalar discovery (as well as the lack of Dark Matter or SUSY particle detection) and its potential significance for other scales in a spectral noncommutative geometric perspective epitomized by the Chamseddine-Connes-Mukhanov (C²M) commutation relation shown below Tom Thumb wearing seven-league boots (as a replacement to the classic snake devouring its tail). In this framework the recently discovered Higgs boson mass value fixes a new small scale picture for the quantum matter-radiation dynamics arena consisting in two layers of 4D spacetime separated by a distance of 10⁻²⁰ cm and connected thanks to the Higgs field. For such a noncommutative space structure to be a consistent solution of the C²M equation requires a third layer at 10⁻²⁹ cm associated with a hypothetical sigma scalar that triggers the seesaw mechanism. This new scalar would explain on the one side the weak mass of left-handed neutrinos and on the other side a baryogenesis through leptogenesis scenario implying three superheavy right-handed neutrinos also naturally derived from spectral noncommutative first principles. Strong, weak and electromagnetic interactions are seen as manifestation of gravity on the former extended spacetime and all merge at some unification scale in a Pati-Salam model. Last but not least, the C²M commutation relation implies also volume quantization which can lead to mimetic dark matter and dark energy phenomenology at very large scales.