arXiv subjects
Publications and source records attributed to S. Capozziello.
The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and inversions is identified. The result can be generalized to chains of connected tetrahedrons.
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the Hamiltonian of the system. It is shown that energy and chirality eigenstates are strictly related through the Heisenberg relations, while chirality operators conserve parity eigenstates.
We propose a predictive building-up of tetrahedral molecules, based on a previously derived chirality index, which characterizes a tetrahedral molecule, with n chiral centers, as achiral, diastereoisomer, or enantiomer as a function of the observed inversions (at most one for each center) under rotation and superimposition to its mirror immage. The set of rules which is identified allows the classification of the new molecule, obtained by the addition of another chiral center, by the determination of the selection rule with respect to the added center.
The algebraic structure of central molecular chirality can be achieved starting from the geometrical representation of bonds of tetrahedral molecules, as complex numbers in polar form, and the empirical Fischer projections used in organic chemistry. A general orthogonal O(4) algebra is derived from which we obtain a chirality index related to the classification of a molecule as achiral, diastereoisomer or enantiomer. Consequently, the chiral features of tetrahedral chains can be predicted by means of a molecular Aufbau. Moreover, a consistent Schroedinger equation is developed, whose solutions are the bonds of tetrahedral molecules in complex number representation. Starting from this result, the O(4) algebra can be considered as a quantum chiral algebra. It is shown that the operators of such an algebra preserve the parity of the whole system.
Higher order curvature gravity has recently received a lot of attention due to the fact that it gives rise to cosmological models which seem capable of solving dark energy and quintessence issues without using "ad hoc" scalar fields. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms for loop expansions of quantum fields in curved spacetimes. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce reliable models able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are recovered in this context. Furthermore, in the weak field limit, we obtain gravitational potentials which differ from the Newtonian one because of repulsive corrections increasing with distance. We evaluate the rotation curve of our Galaxy and compare it with the observed data in order to test the viability of these theories and to estimate the scale-length of the correction. It is remarkable that the Milky Way rotation curve is well fitted without the need of any dark matter halo and similar results hold also for other galaxies.
An impressive amount of different astrophysical data converges towards the picture of a spatially flat universe undergoing a today phase of accelerated expansion. The nature of the dark energy dominating the energy content of the universe is still unknown and a lot of different scenarios are viable candidates to explain cosmic acceleration. Most of the methods employed to test these cosmological models are essentially based on distance measurements to a particular class of objects. A different method, based on the lookback time to galaxy clusters and the age of the universe, is used here. In particular, we constrain the characterizing parameters of three classes of dark energy cosmological models to see whether they are in agreement with this kind of data, based on time measurements rather than distance observations.
We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered: power law, f(R) = βR^n, and logarithmic, f(R) = α\ln{R}. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance LambdaCDM model.
Higher order curvature gravity has recently received a lot of attention due to the fact that it gives rise to cosmological models which seem capable of solving dark energy and quintessence issues without using "ad hoc" scalar fields. In this letter, a gravitational potential is obtained which differs from the Newtonian one because of a repulsive correction increasing with distance. We evaluate the rotation curve of our Galaxy and compare it with the observed data in order both to test the viability of these theories and to estimate the scalelength of the correction. It is remarkable that the Milky Way rotation curve is well fitted without the need of any dark matter halo and a similar result tentatively holds also for other galaxies.
We show that a general, exact cosmological solution, where dynamics of scalar field is assigned by an exponential potential, fulfils all the issues of dark energy approach, both from a theoretical point of view and in comparison with available observational data. Moreover, tracking conditions are discussed, with a new treatment of the well known condition $Γ>1$. We prove that the currently used expression for $Γ$ is wrong.
A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth transition among the three main phases of the universe evolution (radiation era, matter domination, asymptotical de Sitter state) is naturally achieved. We use the estimated age of the universe, the Hubble diagram of Type Ia Supernovae and the angular size - redshift relation for compact and ultracompact radio structures to test whether the model is in agreement with astrophysical observation and to constrain its main parameters. Although phenomenologically motivated, the model may be straightforwardly interpreted as a two fluids scenario in which the quintessence is generated by a suitably chosen scalar field potential. On the other hand, the same model may also be read in the context of unified dark energy models or in the framework of modified Friedmann equation theories.
We show that the non-perturbative vacuum structure associated with neutrino mixing leads to a non-zero contribution to the value of the cosmological constant. Such a contribution comes from the specific nature of the mixing phenomenon. Its origin is completely different from the one of the ordinary contribution of a massive spinor field. We estimate this neutrino mixing contribution by using the natural cut--off appearing in the quantum field theory formalism for neutrino mixing and oscillation.
We present a dark energy model with a double exponential potential for a minimally coupled scalar field, which allows general exact integration of the cosmological equations. The solution can perfectly emulate a $Λ$-term model at low-medium redshift, exhibits tracking behavior, and does not show eternal acceleration.
Quintessence issues can be achieved by taking into account higher order curvature invariants into the effective action of gravitational field. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms in loop expansion of quantum fields in curved space-times. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce encouraging results able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are discussed in this context.
We investigate the effects of the gravitomagnetic corrections to the usual gravitational lens quantities for a specific lensing mass distribution modelled after spiral galaxies. An exponential disk is embedded into two different spherical halo models where disk and haloes parameters are fixed according to the observed mass to light ratios, galaxy magnitudes and rotation curves. The general expressions for the lensing deflection angle are given also taking into account the orientation of the galaxy disk plane with respect to the lens plane. It is found that the gravitomagnetic term changes the deflection angle by a typical amount of the order of ten microarcseconds.
The possibility is explored that neutrino condensates, possible candidates for the explanation of very massive objects in galactic centers, could act as background for the Mikheyev-Smirnov-Wolfeinstein mechanism responsible of neutrino oscillations. Assuming a simple neutrino star model with constant density, the lower limit of the mass squared difference of neutrino oscillations is inferred. Consequences on neutrino asymmetry are discussed.
The issues of quintessence and cosmic acceleration can be discussed in the framework of theories which do not include necessarily scalar fields. It is possible to define pressure and energy density for new components considering effective theories derived from fundamental physics like the extended theories of gravity or simply generalizing the state equation of matter. Exact accelerated expanding solutions can be achieved in several schemes: either in models containing higher order curvature and torsion terms or in models where the state equation of matter is corrected by a second order Van der Waals terms. In this review, we present such new approaches and compare them with observations.
We discuss the Kretschmann, Chern-Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman-Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr-Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.
Pixel lensing is a technique used to search for baryonic components of dark matter (MACHOs) and allows to detect microlensing events even when the target galaxies are not resolved into individual stars. Potentially, it has the advantage to provide higher statistics than other methods but, unfortunately, traditional approaches to pixel lensing are very demanding in terms of computing time. We present the new, user friendly, tool MEDEA (Microlensing Experiment Data-Analysis Software for Events with Amplification). The package can be used either in a fully automatic or in a semi-automatic mode and can perform an on-line identification of events by means of a two levels trigger and a quasi-on-line data analysis. The package will find application in the exploration of large databases as well as in the exploitation of specifically tailored future surveys.