Quaternionic (super)twistors extensions and general superspaces

In a attempt to treat a supergravity as a tensor representation, the 4-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors[14], with N = p + k: These quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and 4N odd- quaternionic coordinates where each coordinate is a quaternion composed by four C-felds (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case the number of felds of the supergravity is determined by the number of components of the tensor representation of the 4-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp (N) = Sp (N;HC) \ U (N;HC) is elucidated from this theoretical context.Comment: To be published in the IJGMMP 2016, corrected version, 16 pages without figure

Quaternionic structures, supertwistors and fundamental superspaces

Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The specific construction contains naturally the supertwistor one of the previous work by Litov and Pervushin [1] and it is shown that in the case of extended supersymmetry such an approach leads to the separation of a class of superspaces and and its groups of motion. We briefly discuss this particular extension to the domain of quaternionic superspaces as nonlinear realization of some kind of the affine and the superconformal groups with the final end to include also the gravitational field[6] (this last possibility to include gravitation, can be realized on the basis of the reference[12] where the coset ((Sp(8))/(SL(4R)))~((SU(2,2))/(SL(2C)))was used in the non supersymmetric case). It is shown that this quaternionic construction avoid some unconsistencies appearing at the level of the generators of the superalgebras (for specific values of p and q; p+q=N) in the twistor one.Comment: Improved version. Accepted in the International Journal of Geometrical Methods in Modern Physics (IJGMMP)12 pages, no figures. In memoriam of Professor Boris Moyseevich Zupnik, pioneer of the development of supersymmetry, group theory and modern mathematical methods in theoretical physic

Description of Supernova Data in Conformal Cosmology without Cosmological Constant

We consider cosmological consequences of a conformal invariant formulation of Einstein's General Relativity where instead of the scale factor of the spatial metrics in the action functional a massless scalar (dilaton) field occurs which scales all masses including the Planck mass. Instead of the expansion of the universe we get the Hoyle-Narlikar type of mass evolution, where the temperature history of the universe is replaced by the mass history. We show that this conformal invariant cosmological model gives a satisfactory description of the new supernova Ia data for the effective magnitude - redshift relation without a cosmological constant and make a prediction for the high-redshift behavior which deviates from that of standard cosmology for $z>1.7$.Comment: 13 pages, 1 figure, includes discussion of SN1997ff, text revise

Conformal Cosmological Model Parameters with Distant SNe Ia Data: "gold" and "silver"

Assuming that supernovae type Ia (SNe Ia) are standard candles one could use them to test cosmological theories. The Hubble Space Telescope team analyzed 186 SNe Ia\cite{Riess_04} to test the Standard Cosmological model (SC) associated with expanded lengths in the Universe and evaluate its parameters. We use the same sample to determine parameters of Conformal Cosmological model (CC) with relative reference units of intervals, so that conformal quantities of General Relativity are interpreted as observables. We concluded, that really the test is extremely useful and allows to evaluate parameters of the model. From a formal statistical point of view the best fit of the CC model is almost the same quality approximation as the best fit of SC model with $\Omega_\Lambda=0.72, \Omega_m=0.28$. As it was noted earlier, for CC models, a rigid matter component could substitute the $\Lambda$-term (or quintessence) existing in the SC model. We note that a free massless scalar field can generate such a rigid matter. We describe results of our analysis for more recent "gold" data (for 192 SNe Ia).Comment: 13 pages, 4 figures, accepted in International Journal of Modern Physics

Conformal and Affine Hamiltonian Dynamics of General Relativity

The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum energy of physical fields provides a good description of the type Ia supernova luminosity distance--redshift relation. Introducing the uncertainty principle at the Planck's epoch within our model, we obtain the hierarchy of the Universe energy scales, which is supported by the observational data. We found that the invariance of the Maurer-Cartan forms with respect to the general coordinate transformation yields a single-component strong gravitational waves. The Hamiltonian dynamics of the model describes the effect of an intensive vacuum creation of gravitons and the minimal coupling scalar (Higgs) bosons in the Early Universe.Comment: 37 pages, version submitted to Gen. Rel. Gra