Spinorial Space-time Research Articles

Gauge Theory Without Principal Fiber Bundles

Abstract In general relativity, the strong equivalence principle is underpinned by a geometrical account of fields on spacetime, by which all fields and bodies probe the same geometry. This geometric account implies that the parallel transport of all spacetime tensors and spinors is dictated by a single affine connection. No similar account of gauge theory is put forward by standard textbooks, which use principal bundles to coordinate the parallel transport of different, interacting particles. Nonetheless, here I argue that gauge theory does afford such a geometric account, obviating the need for principal bundles.

The 1/4-BPS building blocks of brane interactions

We study, from the perspective of supersymmetry and space-time Killing spinors, the local brane densities involved in 1/4-BPS intersecting brane systems. In particular, we classify the possible local brane structures that have maximal (16) supersymmetries in 1/4-BPS intersecting brane backgrounds. Applied to BPS black holes, this classification reveals the allowed local microstructure for pure microstates. We further use these structures with local 16 supersymmetries as building blocks to generalise to 1/8-BPS systems. Moreover, we give examples of 1/8-BPS black holes for which the local supersymmetries are compatible with the combination of different entropy-generating effects from brane interaction. Finally, applying our classification to BPS domain walls, we illustrate how our formalism may possibly describe the local picture of the Hanany-Witten effect.

Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

We study the deflection and gravitational lensing (GL) of both timelike and null signals in the equatorial plane of arbitrary stationary and axisymmetric spacetimes in the strong deflection limit. Our approach employs a perturbative method to show that both the deflection angle and the total travel time take quasi-series forms ∑ n=0 [Cn ln (1-bc/b) + Dn ] (1-bc/b) n , with the coefficients Cn and Dn incorporating the signal velocity and finite distance effect of the source and detector. This new deflection angle allows us to establish an accurate GL equation from which the apparent angles of the relativistic images and their time delays are found. These results are applied to the Kerr and the rotating Kalb-Ramond (KR) spacetimes to investigate the effect of the spacetime spin in both spacetimes, and the effective charge parameter and a transition parameter in the rotating KR spacetime on various observables. Moreover, using our approach, the effect of the signal velocity and the source angular position on these variables is also studied.

Gravity Probe Spin: Prospects for measuring general-relativistic precession of intrinsic spin using a ferromagnetic gyroscope

An experimental test at the intersection of quantum physics and general relativity is proposed: measurement of relativistic frame dragging and geodetic precession using intrinsic spin of electrons. The behavior of intrinsic spin in spacetime dragged and warped by a massive rotating body is an experimentally open question, hence the results of such a measurement could have important theoretical consequences. Such a measurement is possible by using mm-scale ferromagnetic gyroscopes in orbit around the Earth. Under conditions where the rotational angular momentum of a ferromagnet is sufficiently small, a ferromagnet's angular momentum is dominated by atomic electron spins and is predicted to exhibit macroscopic gyroscopic behavior. If such a ferromagnetic gyroscope is sufficiently isolated from the environment, rapid averaging of quantum uncertainty via the spin-lattice interaction enables readout of the ferromagnetic gyroscope dynamics with sufficient sensitivity to measure both the Lense-Thirring (frame dragging) and de Sitter (geodetic precession) effects due to the Earth.

Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes

Total travel time t and time delay Delta t between images of gravitational lensing (GL) in the equatorial plane of stationary axisymmetric (SAS) spacetimes for null and timelike signals with arbitrary velocity are studied. Using a perturbative method in the weak field limit, t in general SAS spacetimes is expressed as a quasi-series of the impact parameter b with coefficients involving the source-lens distance r_s and lens-detector distancesr_d, signal velocity v, and asymptotic expansion coefficients of the metric functions. The time delay Delta t to the leading order(s) were shown to be determined by the spacetime mass M, spin angular momentum a and post-Newtonian parameter gamma , and kinematic variables r_s,~r_d,~v and source angular position beta . When beta ll sqrt{aM}/r_{s,d}, Delta t is dominated by the contribution linear to spin a. Modeling the Sgr A* supermassive black hole as a Kerr–Newman black hole, we show that as long as beta lesssim 1.5times 10^{-5} [^{prime prime }], then Delta t will be able to reach the mathcal {O}(1) second level, which is well within the time resolution of current GRB, gravitational wave and neutrino observatories. Therefore measuring Delta t in GL of these signals will allow us to constrain the spin of the Sgr A*.

Static spherically symmetric space-time and nonlinear spinor field

We studied nonlinear spinor fields in the framework of a static spherically symmetric space-time. In doing so we have suggested a rather simple method to solve the corresponding Einstein equations. As an example, a nonlinear spinor field was considered. The corresponding equations were solved analytically and numerically.

Supersymmetric DBI equations in diverse dimensions from the BRS invariance of a pure spinor superstring

We examine the BRS invariance of the open pure spinor superstring in the presence of background superfields on a Dp-brane. It is shown that the BRS invariance leads not only to boundary conditions on the spacetime spinors, but also to supersymmetric DBI equations of motion for the background superfields on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI equations for a D9-brane.

Neutrinos propagating in curved spacetimes

In the Dirac-Weyl equation that describes massless neutrino propagation in the minimal Standard Model, the ($2\times 2$ equivalence of the) gamma matrices convert Weyl spinors into spacetime tensors, and vice versa. They can thus be regarded as amalgamations of three different types of mappings, one that connects particle spinors directly forming representations to internal gauge symmetries to their spacetime counterparts that are embodied by null flags, another that translates the spacetime spinors into their corresponding tensors expressed in an orthonormal tetrad, and finally a purely tensorial transformation into the coordinate tetrad. The splitting of spinors into particle and spacetime varieties is not usually practised, but we advocate its adoption for better physical clarity, in terms of distinguishing internal and spacetime transformations, and also for understanding the scattering of neutrinos by spacetime curvature. We construct the basic infrastructure required for this task, and provide a worked example for the Schwarzschild spacetime. Our investigation also uncovers a possible under-determinacy in the flavoured Dirac-Weyl equation, which could serve as a new incision point for introducing flavour oscillation mechanisms.

Value of H, space-time patterns, vacuum, matter, expansion of the Universe, alternative cosmologies

To the experimental uncertainties on the present value H 0 of the Lundmark - Lemaitre-Hubble constant, fundamental theoretical uncertainties of several kinds should also be added. In standard Cosmology, consistency problems are really serious. The cosmological constant is a source of well-known diffculties while the associated dark energy is assumed to be at the origin of the observed acceleration of the expansion of the Universe. But in alternative cosmologies, possible approaches without these problems exist. An example is the pattern based on the spinorial space-time (SST) we introduced in 1996-97 where the H t = 1 relation ( t = cosmic time = age of the Universe) is automatically generated by a pre-existing cosmic geometry before standard matter and conventional forces, including gravitation and relativity, are introduced. We analyse present theoretical, experimental and observational uncertainties, focusing also on the possible sources of the acceleration of the expansion of the Universe as well as on the structure of the physical vacuum and its potential cosmological role. Particular attention is given to alternative approaches to both Particle Physics and Cosmology including possible preonic constituents of the physical vacuum and associated pre-Big Bang patterns. A significant example is provided by the cosmic SST geometry together with the possibility that the expanding cosmological vacuum releases energy in the form of standard matter and dark matter, thus modifying the dependence of the matter energy density with respect to the age and size of our Universe. The SST naturally generates a new leading contribution to the value of H. If the matter energy density decreases more slowly than in standard patterns, it can naturally be at the origin of the observed acceleration of the expansion of the Universe. The mathematical and dynamical structure of standard Physics at very short distances can also be modified by an underlying preonic structure. If preons are the constituents of the physical vacuum, as postulated two decades ago with the superbradyon (superluminal preon) hypothesis, the strongest implication would be the possibility that vacuum actually drives the expansion of the Universe. If an unstable (metastable) vacuum permanently expands, it can release energy in the form of conventional matter and of its associated kinetic energy. The SST can be the expression of such an expanding vacuum at cosmic level. We briefly discuss these and related issues, as well as relevant open questions including the problematics of the initial singularity and the cosmic vacuum dynamics in a pre-Big Bang era. The possibility to obtain experimental information on the preonic internal structure of vacuum is also considered.

Quantum Mechanics, vacuum, particles, Gödel-Cohen incompleteness and the Universe

Are the standard laws of Physics really fundamental principles? Does the physical vacuum have a more primordial internal structure? Are quarks, leptons, gauge bosons… ultimate objects? These three basic questions are actually closely related. If the deep vacuum structure and dynamics turn out to be less trivial than usually depicted, the conventional elementary particles will most likely be excitations of such a vacuum dynamics that remains by now unknown. We then expect relativity and quantum mechanics to be low-energy limits of a more fundamental dynamical pattern that generates them at a deeper level. It may even happen that vacuum drives the expansion of the Universe from its own inner dynamics. Inside such a vacuum structure, the speed of light would not be the critical speed for vacuum constituents and propagating signals. The natural scenario would be the superbradyon (superluminal preon) pattern we postulated in 1995, with a new critical speed c s much larger than the speed of light c just as c is much larger than the speed of sound. Superbradyons are assumed to be the bradyons of a super-relativity associated to c s (a Lorentz invariance with c s as the critical speed). Similarly, the standard relativistic space-time with four real coordinates would not necessarily hold beyond low-energy and comparatively local distance scales. Instead, the spinorial space-time (SST) with two complex coordinates we introduced in 1996-97 may be the suitable one to describe the internal structure of vacuum and standard elementary particles and, simultaneously, Cosmology at very large distance scales. If the constituents of the preonic vacuum are superluminal, quantum entanglement appears as a natural property provided c s ≫ c . The value of c s can even be possibly found experimentally by studying entanglement at large distances. It is not excluded that preonic constituents of vacuum can exist in our Universe as particles (free superbradyons), in which case we expect them to be weakly coupled to standard matter. If a preonic vacuum is actually leading the basic dynamics of Particle Physics and Cosmology, and standard particles are vacuum excitations, the Godel-Cohen incompleteness will apply to vacuum dynamics whereas the conventional laws of physics will actually be approximate and have error bars. We discuss here the possible role of the superbradyonic vacuum and of the SST in generating Quantum Mechanics, as well as the implications of such a dynamical origin of the conventional laws of Physics and possible evidences in experiments and observations. Black holes, gravitational waves, possible free superbradyons or preonic waves, unconventional vacuum radiation… are considered from this point of view paying particular attention to LIGO, VIRGO and CERN experiments. This lecture is dedicated to the memory of John Bell

Spinorial Regge trajectories and Hagedorn-like temperatures. Spinorial space-time and preons as an alternative to strings

The development of the statistical bootstrap model for hadrons, quarks and nuclear matter occurred during the 1960s and the 1970s in a period of exceptional theo- retical creativity. And if the transition from hadrons to quarks and gluons as fundamental particles was then operated, a transition from standard particles to preons and from the standard space-time to a spinorial one may now be necessary, including related pre-Big Bang scenarios. We present here a brief historical analysis of the scientific problematic of the 1960s in Particle Physics and of its evolution until the end of the 1970s, including cosmological issues. Particular attention is devoted to the exceptional role of Rolf Hage- dorn and to the progress of the statistical boostrap model until the experimental search for the quark-gluon plasma started being considered. In parallel, we simultaneously expose recent results and ideas concerning Particle Physics and in Cosmology, an discuss current open questions. Assuming preons to be constituents of the physical vacuum and the stan- dard particles excitations of this vacuum (the superbradyon hypothesis we introduced in 1995), together with a spinorial space-time (SST), a new kind of Regge trajectories is expected to arise where the angular momentum spacing will be of 1/2 instead of 1. Standard particles can lie on such Regge trajectories inside associated internal symmetry multiplets, and the preonic vacuum structure can generate a new approach to Quantum Field Theory. As superbradyons are superluminal preons, some of the vacuum excitations can have critical speeds larger than the speed of light c, but the cosmological evolution se- lects by itself the particles with the smallest critical speed (the speed of light). In the new Particle Physics and Cosmology emerging from the pattern thus developed, Hagedorn- like temperatures will naturally be present. As new space, time, momentum and energy scales are expected to be generated by the preonic vacuum dynamics, the Planck scale does not necessarily make sense in the new scenario. It also turns out that two potential evidences for a superbradyonic vacuum with a SST geometry exist already: i) the recent results on quantum entanglement at large distances favoring superluminal propagation of signals and correlations ; ii) the anisotropy of the cosmic microwave background radia- tion between two hemispheres observed by the Planck Collaboration, in agreement with the predictions of cosmic SST automatically generating a privileged space direction for each comoving observer. Simultaneously to the discussion of the large number of open questions, we comment on the required experimental and observational programs. T his paper is dedicated to the memory o f Rol f Hagedorn

Spinorial space-time and the origin of Quantum Mechanics. The dynamical role of the physical vacuum

Is Quantum Mechanics really and ultimate principle of Physics described by a set of intrinsic exact laws? Are standard particles the ultimate constituents of matter? The two questions appear to be closely related, as a preonic structure of the physical vacuum would have an influence on the properties of quantum particles. Although the first preon models were just « quark-like » and assumed preons to be direct constituents of the conventional « elementary » particles, we suggested in 1995 that preons could instead be constituents of the physical vacuum (the superbradyon hypothesis). Standard particles would then be excitations of the preonic vacuum and have substantially different properties from those of preons themselves (critical speed…). The standard laws of Particle Physics would be approximate expressions generated from basic preon dynamics. In parallel, the mathematical properties of space-time structures such as the spinoral space-time (SST) we introduced in 1996-97 can have strong implications for Quantum Mechanics and even be its real origin. We complete here our recent discussion of the subject by pointing out that: i) Quantum Mechanics corresponds to a natural set of properties of vacuum excitations in the presence of a SST geometry ; ii) the recently observed entanglement at long distances would be a logical property if preons are superluminal (superbradyons), so that superluminal signals and correlations can propagate in vacuum ; iii) in a specific description, the function of space-time associated to the extended internal structure of a spin-1/2 particle at very small distances may be incompatible with a continuous motion at space and time scales where the internal structure of vacuum can be felt. In the dynamics associated to iii), and using the SST approach to space-time, a contradiction can appear between macroscopic and microscopic space-times due to an overlap in the time variable directly related to the fact that a spinorial function takes nonzero values simultaneously in a whole time interval. Then, continuous motion can be precluded at very small spacetime scales. If discrete motion is required at such scales, the situation will possibly be close to that generating the Feynman path integral. More generally, Quantum Mechanics can naturally emerge from the spinorial space-time and from other unconventional spacetime structures in a fundamental preon dynamics governing the properties of vacuum. In such scenarios, the application of Godel - Cohen mathematics to quantum-mechanical calculations can possibly yield substantially different results from those recently obtained using the standard quantum approach without any preonic underlying structure. This is also a crucial open question for Quantum Mechanics and Particle Physics. This paper is dedicated to the memory of Bernard d’Espagnat

Big Bang, inflation, standard Physics… and the potentialities of new Physics and alternative cosmologies. Present statuts of observational and experimental Cosmology. Open questions and potentialities of alternative cosmologies

A year ago, we wrote (1) that the field of Cosmology was undergoing a posi- tive and constructive crisis. The possible development of more direct links between the Mathematical Physics aspects of cosmological patterns and the interpretation of experi- mental and observational results was particularly emphasized. Controversies on inflation are not really new, but in any case inflation is not required in pre-Big Bang models and the validity of the standard Big Bang + inflation +Λ CDM pattern has not by now been demonstrated by data. Planck has even explicitly reported the existence of anomalies. Remembering the far-reaching work of Yoichiro Nambu published in 1959-61, it seems legitimate to underline the need for a cross-disciplinary approach in the presence of deep, unsolved theoretical problems concerning new domains of matter properties and of the physical world. The physics of a possible preonic vacuum and the associated cosmology constitute one of these domains. If the vacuum is made of superluminal preons (super- bradyons), and if standard particles are vacuum excitations, how to build a suitable theory to describe the internal structure of such a vacuum at both local and cosmic level? Exper- imental programs (South Pole, Atacama, AUGER, Telescope Array...) and observational ones (Planck, JEM-EUSO...) devoted to the study of cosmic microwave background radi- ation (CMB) and of ultra-high energy cosmic rays (UHECR) are crucial to elucidate such theoretical interrogations and guide new phenomenological developments. Together with a brief review of the observational and experimental situation, we also examine the main present theoretical and phenomenological problems and point out the role new physics and alternative cosmologies can potentially play. The need for data analyses less focused a priori on the standard models of Particle Physics and Cosmology is emphasized in this discussion. An example of a new approach to both fields is provided by the pre-Big Bang pattern based on a physical vacuum made of superbradyons with the spinorial space-time (SST) geometry we introduced in 1996-97. In particular, the SST automatically gener- ates a local privileged space direction (PSD) for earch comoving observer and such a signature may have been confirmed by Planck data. Both superluminal preons and the existence of the PSD would have strong cosmological implications. Planck 2016 results will be particularly relevant as a step in the study of present open questions. This paper is dedicated to the memory of Yoichiro Nambu

Origin of the pure spinor and Green-Schwarz formalisms

The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂x m (γ m λ) α = 0 where λ α is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint ∂x m ∂x m = 0, and the Green-Schwarz fermionic spacetime spinor variables θα arise as Faddeev-Popov ghosts for this constraint. In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor λ α with a d=10 projective pure spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and superstring are then obtained as different gauge-fixings of this purely bosonic classical action, and the Green-Schwarz kappa symmetry is directly related to the pure spinor BRST symmetry. Since a d=10 projective pure spinor parameterizes $$ \frac{\mathrm{SO}(10)}{\mathrm{U}(5)} $$ , this action can be interpreted as a standard ĉ = 5 topological action where one integrates over the $$ \frac{\mathrm{SO}(10)}{\mathrm{U}(5)} $$ choice of complex structure. Finally, a purely bosonic action for the d=11 supermembrane is proposed which reduces upon double-dimensional reduction to the purely bosonic action for the d=10 Type IIA superstring.

Tests and prospects of new physics at very high energy. Beyond the standard basic principles, and beyond conventional matter and space-time. On the possible origin of Quantum Mechanics.

Recent results and announcements by Planck and BICEP2 have led to impor- tant controversies in the fields of Cosmology and Particle Physics. As new ideas and alter- native approaches can since then more easily emerge, the link between the Mathematical Physics aspects of theories and the interpretation of experimental results becomes more direct. This evolution is also relevant for Particle Physics experiments at very high energy, where the interpretation of data on the highest-energy cosmic rays remains a major theo- retical and phenomenological challenge. Alternative particle physics and cosmology can raise fundamental questions such as that of the structure of vacuum and space-time. In particular, the simplified description of the physical vacuum contained in standard quan- tum field theory does not necessarily correspond to reality at a deeper level, and similarly for the relativistic space-time based on four real variables. In a more general approach, the definition itself of vacuum can be a difficult task. The spinorial space-time (SST) we suggested in 1996-97 automatically incorporates a local privileged space direction (PSD) for each comoving observer, possibly leading to a locally anisotropic vacuum structure. As the existence of the PSD may have been confirmed by Planck, and a possible dis- covery of primordial B-modes in the polarization of the cosmic microwave background radiation (CMB) may turn out to contain new evidence for the SST, we explore other possible implications of this approach to space-time. The SST structure can naturally be at the origin of Quantum Mechanics at distance scales larger than the fundamental one if standard particles are dealt with as vacuum excitations. We also discuss possible implica- tions of our lack of knowledge of the structure of vacuum, as well as related theoretical, phenomenological and cosmological uncertainties. Pre-Big Bang scenarios and new ulti- mate constituents of matter (including superbradyons) are crucial open subjects, together with vacuum structure and the interaction between vacuum and standard matter.

BICEP2, Planck, spinorial space-time, pre-Big Bang.

The field of Cosmology is currently undergoing a positive and constructive crisis. Controversies concerning inflation are not really new. But after the 2013-2014 Planck and BICEP2 announcements, and the more recent joint analysis by Planck , BICEP2 and the Keck Array (PBKA), the basic issues can involve more direct links between the Mathematical Physics aspects of cosmological patterns and the interpretation of experimental results. Open questions and new ideas on the foundations of Cosmology can emerge, while future experimental and observational programs look very promising. The BICEP2 result reporting an excess of B -mode polarization signal of the cosmic microwave background (CMB) radiation was initially presented as a signature of primordial gravitational waves from cosmic inflation. But polarized dust emission can be at the origin of such a signal, and the evidence claimed by BICEP2 is no longer secure after the PBKA analysis. Furthermore, even assuming that significant CMB B -mode polarization has indeed been generated by the early Universe, its theoretical and cosmological interpretation would be far from obvious. Inflationary gravitational waves are not the only possible source of primordial CMB B -modes. Alternative cosmologies such as pre-Big Bang patterns and the spinorial space-time (SST) we introduced in 1996-97 can naturally produce this polarization. Furthermore, the SST automatically generates for each comoving observer a local privileged space direction (PSD) whose existence may have been confirmed by Planck data. If such a PSD exists, vector perturbations have most likely been strong in the early Universe and may have produced CMB B -modes. Pre-Big Bang cosmologies can also generate gravitational waves in the early Universe without inflation. After briefly describing detectors devoted to the study of the CMB polarization, we discuss the situation emerging from BICEP2 results, Planck results and the PBKA analysis. In particular, we further analyze possible alternatives to the inflationary interpretation of a primordial B -mode polarization of cosmic microwave background radiation.

BICEP2, Planck, spinorial space-time, pre-Big Bang.

The field of Cosmology is currently undergoing a positive and constructive crisis. Controversies concerning inflation are not really new. But after the 2013-2014 Planck and BICEP2 announcements, and the more recent joint analysis by Planck, BICEP2 and the Keck Array (PBKA), the basic issues can involve more direct links between the Mathematical Physics aspects of cosmological patterns and the interpretation of experimental results. Open questions and new ideas on the foundations of Cosmology can emerge, while future experimental and observational programs look very promising. The BICEP2 result reporting an excess of B-mode polarization signal of the cosmic microwave background (CMB) radiation was initially presented as a signature of primordial gravitational waves from cosmic inflation. But polarized dust emission can be at the origin of such a signal, and the evidence claimed by BICEP2 is no longer secure after the PBKA analysis. Furthermore, even assuming that significant CMB B-mode polarization has indeed been generated by the early Universe, its theoretical and cosmological interpretation would be far from obvious. Inflationary gravitational waves are not the only possible source of primordial CMB B-modes. Alternative cosmologies such as pre-Big Bang patterns and the spinorial space-time (SST) we introduced in 1996-97 can naturally produce this polarization. Furthermore, the SST automatically generates for each comoving observer a local privileged space direction (PSD) whose existence may have been confirmed by Planck data. If such a PSD exists, vector perturbations have most likely been strong in the early Universe and may have produced CMB B-modes. Pre-Big Bang cosmologies can also generate gravitational waves in the early Universe without inflation. After briefly describing detectors devoted to the study of the CMB polarization, we discuss the situation emerging from BICEP2 results, Planck results and the PBKA analysis. In particular, we further analyze possible alternatives to the inflationary interpretation of a primordial B-mode polarization of cosmic microwave background radiation.

Tests and prospects of new physics at very high energy. Beyond the standard basic principles, and beyond conventional matter and space-time. On the possible origin of Quantum Mechanics.

Recent results and announcements by Planck and BICEP2 have led to important controversies in the fields of Cosmology and Particle Physics. As new ideas and alternative approaches can since then more easily emerge, the link between the Mathematical Physics aspects of theories and the interpretation of experimental results becomes more direct. This evolution is also relevant for Particle Physics experiments at very high energy, where the interpretation of data on the highest-energy cosmic rays remains a major theoretical and phenomenological challenge. Alternative particle physics and cosmology can raise fundamental questions such as that of the structure of vacuum and space-time. In particular, the simplified description of the physical vacuum contained in standard quantum field theory does not necessarily correspond to reality at a deeper level, and similarly for the relativistic space-time based on four real variables. In a more general approach, the definition itself of vacuum can be a difficult task. The spinorial space-time (SST) we suggested in 1996-97 automatically incorporates a local privileged space direction (PSD) for each comoving observer, possibly leading to a locally anisotropic vacuum structure. As the existence of the PSD may have been confirmed by Planck, and a possible discovery of primordial B-modes in the polarization of the cosmic microwave background radiation (CMB) may turn out to contain new evidence for the SST, we explore other possible implications of this approach to space-time. The SST structure can naturally be at the origin of Quantum Mechanics at distance scales larger than the fundamental one if standard particles are dealt with as vacuum excitations. We also discuss possible implications of our lack of knowledge of the structure of vacuum, as well as related theoretical, phenomenological and cosmological uncertainties. Pre-Big Bang scenarios and new ultimate constituents of matter (including superbradyons) are crucial open subjects, together with vacuum structure and the interaction between vacuum and standard matter.

Two-component spinors in spacetimes with torsionful affinities

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by the traditional formalisms. Any spin-affine connexion appears to possess a torsional part which is conveniently chosen as a suitable asymmetric contribution. Such a torsional affine contribution thus supplies a gauge-invariant potential that can eventually be taken to carry an observable character, and thereby effectively takes over the role of any trivially realizable symmetric contribution. The overall curvature spinors for any spin-affine connexion accordingly emerge from the irreducible decomposition of a mixed world-spin object which in turn comes out of the action on elementary spinors of a typical torsionful second-order covariant derivative operator. Explicit curvature expansions are likewise exhibited which fill in the gap related to their absence from the literature. It is then pointed out that the utilization of the torsionful spinor framework may afford locally some new physical descriptions.

Pre-Big Bang, space-time structure, asymptotic Universe

Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95), while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2) spinor and the Lundmark-Lemaitre-Hubble (LLH) expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of the standard cosmology based on general relativity. In the new cosmology thus introduced, the contribution of the space curvature to the value of H 2 is positive definite independently of the apparent sign of this curvature, and has a much larger value than the standard curvature term. Then, a cosmological constant is no longer required. The spinorial space-time also generates automatically for each comoving observer a privileged space direction that, together with parity violation, may explain the anisotropies observed in WMAP and Planck data. Contrary to frequent statements, such a signature would not be a strange phenomenon. The effect emerges directly from the use of two complex space-time coordinates instead of the conventional four real ones, and the privileged direction would correspond to the phase of the cosmic spinor. We remind here our previous work on the subject and further discuss some cosmological implications of the spinorial space-time.