A. A. Marino

Some aspects of the cosmological conformal equivalence between the `Jordan frame' and the `Einstein frame'

The conformal equivalence between the Jordan and the Einstein frames can be used in order to search for exact solutions in general theories of gravity in which scalar fields are coupled with geometry in a standard or in a nonstandard way. In the cosmological arena a relevant role is played by the time parameter in which dynamics is described. In this paper we discuss the problem of conformal equivalence between a given nonstandard coupled model and the corresponding standard one. We analyse in detail the cosmological case and we see that, together with this, and through a careful analysis of the cosmological parameters and , it is possible to contribute to the discussion on which is the physical system.

Microlensing search towards M31

We present the first results of the analysis of data collected during the 1998-99 observational campaign at the 1.3 meter McGraw-Hill Telescope, towards the Andromeda galaxy (M 31), aimed to detect gravitational microlensing effects as a probe for the presence of dark matter in our Galaxy and in the M 31 halo. The analysis is performed using the pixel lensing technique, which consists of the study of flux variations of unresolved sources and has been proposed and implemented by the AGAPE collaboration. We carry out a shape analysis by demanding that the detected flux variations be achromatic and compatible with a Paczynski light curve. We apply the Durbin-Watson hypothesis test to the residuals. Furthermore, we consider the background of variables sources. Finally five candidate microlensing events emerge from our selection. Comparing with the predictions of a Monte Carlo simulation, assuming a standard spherical model for the M 31 and Galactic haloes, and typical values for the MACHO mass, we find that our events are only marginally consistent with the distribution of observable parameters predicted by the simulation.

Recovering the effective cosmological constant in extended gravity theories

In the framework of extended gravity theories, we discuss the meaning of a time-dependent “cosmological constant” and give a set of conditions to recover an asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.

Approximate angular diameter distance in a locally inhomogeneous universe with nonzero cosmological constant

We derive and solve exactly the Dyer-Roeder equation in a Friedman-Robertson-Walker cosmological model with non zero cosmological constant. To take into account non homogeneous distribution of matter we use the phenomenological clumpiness parameter. We propose also a general form of an approximate solution which is simple enough to be useful in practical applications and sufficiently accurate in the interesting range of redshifts.We discuss the general and approximate angular diameter distance in the Friedman-Robertson-Walker cosmological models with nonzero cosmological constant. We modify the equation for the angular diameter distance by taking into account the fact that locally the distribution of matter is non homogeneous. We present exact solutions of this equation in a few special cases. We propose an approximate analytic solution of this equation which is simple enough and sufficiently accurate to be useful in practical applications.

Asymptotic freedom cosmology

Abstract For a general class of scalar-tensor gravity theories, we discuss how to recover asymptotic freedom regimes when cosmic time t → ±∞. Such a feature means that the effective gravitational coupling G eff → 0, while cosmological solutions can asymptotically assume de Sitter or power-law behaviours.

Constraints on the slope of the dark halo mass function by microlensing observables

We investigate the dark halo lens mass function (MF) for a wide class of spheroidal non singular isothermal models comparing observed and observable microlensing quantities for MACHO observations towards LMC and taking into account the detection eciency. We evaluate the microlensing observable quantities, i.e. observable optical depth, number of events and mean duration, for models with homogenous power-law MF changing the upper and lower mass limits and the flattening of the dark halo. By applying the simple technique of the inverse problem method we are then able to get some interesting constraints on the slope of the MF and on the dark halo mass fraction f made out by MACHOs consistently with previous results.

Defocusing gravitational microlensing

We introduce the notion of defocusing gravitational lens considering a MACHO located behind a light source with respect to an observer. The consequence of defocusing effect is a temporal variability of star luminosity which produces a gap instead of a peak as tell-tale signature in the light curve. A general theory of (de)focusing rays (geodesics) in a gravitational field is presented. Furthermore, we give estimations of the mass of the lens and the optical depth connected to such phenomenon.

The inverse problem in microlensing: from the optical depth to galaxy models parameters

Abstract We present in this paper a simple method to obtain information on galaxy models parameters using the measured value of the microlensing optical depth, the number of observed events and also taking into account problems connected with the detection efficiency. We ask that the observable optical depth and number of events for a given halo model to be the same as the observed one, in a given direction in our Galaxy. Writing the observable quantities in terms of the halo model parameters and inverting this relation with respect to one or two of them, it is possible to get information on these latter, fixing under reasonable hypotheses the other parameters. This is what we call the inverse problem in microlensing. We apply this technique to the class of power-law models with nearly flat rotation curve, determining some constraints on the range for the core radius Rc and reducing the whole parameter space (q, Rc) compatible with the measures of τobsd and Nevobsd towards LMC.

QUINTESSENCE VERSUS DUALITY

We compare some features of quintessence cosmological scenarios with the duality symmetry existing in string dilaton cosmologies. Actually, we consider the tracker potential type V = V0/φα and show that duality is only established if α = -2.

A Possible Way to Define an Effective Cosmological Constant in Scalar-Tensor Cosmologies

The cosmological constant has attained a leading role in recent researches in cosmology. We extend the cosmic no-hair theorem to non-minimally coupled theories of gravity where ordinary matter is also present in the form of a perfect fluid. To achieve this goal we give a set of conditions for obtaining the asymptotic de Sitter expansion independently of any initial data (no fine-tuning problem), that is, we introduce a time-dependent (effective) cosmological constant. Finally, we apply the results to some specific models.