General solution for scalar perturbations in bouncing cosmologies

Bouncing cosmologies, suggested by String/M-theory, may provide an alternative to standard inflation to account for the origin of inhomogeneities in our universe. The fundamental question regards the correct way to evolve the scalar perturbations through the bounce. In this work, we determine the evolution of perturbations and the final spectrum for an arbitrary (spatially flat) bouncing cosmology, with the only assumption that the bounce is governed by a single physical scale. In particular, we find that the spectrum of the pre-bounce growing mode of the Bardeen potential (which is scale-invariant in some limit, and thus compatible with observations) survives unaltered in the post-bounce only if the comoving pressure perturbation is directly proportional to the Bardeen potential rather than its Laplacian, as for any known form of ordinary matter. If some new physics acting at the bounce justifies such relation, then bouncing cosmologies are entitled to become a real viable alternative for the generation of the observed inhomogeneities. Our treatment also includes some class of models with extra-dimensions, whereas we show that bounces induced by positive spatial curvature are structurally different from all bounces in spatially flat universes, requiring a distinct analysis.Comment: 24 pages, 2 figure

Secondary caustics in close multiple lenses

We investigate the caustic structure of a lens composed by a discrete number of point-masses, having mutual distances smaller than the Einstein radius of the total mass of the system. Along with the main critical curve, it is known that the lens map is characterized by secondary critical curves producing small caustics far from the lens system. By exploiting perturbative methods, we derive the number, the position, the shape, the cusps and the area of these caustics for an arbitrary number of close multiple lenses. Very interesting geometries are created in some particular cases. Finally we review the binary lens case where our formulae assume a simple form.Comment: 9 pages with 5 figures. Accepted by A&

Signs of the cusps in binary lenses

The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a caustic in a cusp. In this paper, we generalize the former definition of the sign of the cusps. Then we apply it to the binary lens. We demonstrate that the cusps on the axis joining the two lenses are positive while the others are negative. To achieve our objective, we combine catastrophe theory, usually employed in the derivation of the properties of caustics, with perturbative methods, in order to simplify calculations and get readable results. Extensions to multiple lenses are also considered.Comment: 18 pages, 2 figures. Accepted by Journal of Mathematical Physics. After it is published, it will be found at http://ojps.aip.org/jmp

The experiment of Community involvement in a project planning within the historical context of Rome city

The PhD student proposes a method of community involvement in the planning and in the regeneration of historical centers, in support of the city’s accessibility and people’s well-being. The outcomes of the research are the analysis and the studies conducted over three years with people with sensory, physical and cognitive impairments on the sustainable mobility of historical spaces of Rome, thanks to an agreement between the Phd Student Start up Research Project financed by Sapienza, Università di Roma and the Municipality of Rome. Citizens are involved in the analysis process: they communicate their opinions, impressions, perceptions and needs related to the city experience through a dedicated help-desk, in return, they receive an advice service and a design project for their apartment that suits their necessities. Thanks also to several tours and surveys conducted with people with special needs, the phd student studies the human senses, the perception of the space, the physical barriers, natural and urban elements, with the aim to elaborate an accessibility-map of the City Center Cultural Heritage and Archaeological Sites. Citizens can contribute by sharing information about the status of the public spaces, or by giving advice on adaptive-ergonomic urban furnishings. The research aims to elaborate an application for mobile systems that identifies an interactive cartography of the city available for all the citizens, especially people with reduced mobility. The map, developed on multiple layers, also contains the layer made up of people’s emotions and their perceptions

Caustics in special multiple lenses

Despite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the others with respect to their Einstein radii, and a system where mutual distances between lenses are small compared to the Einstein radius of the total mass. Finally we review the case of a planetary system adding some new information (area of caustics, duality and higher order terms).Comment: 11 pages, 7 figures, submitted to A &

Scalar perturbations in regular two-component bouncing cosmologies

We consider a two-component regular cosmology bouncing from contraction to expansion, where, in order to include both scalar fields and perfect fluids as particular cases, the dominant component is allowed to have an intrinsic isocurvature mode. We show that the spectrum of the growing mode of the Bardeen potential in the pre-bounce is never transferred to the dominant mode of the post-bounce. The latter acquires at most a dominant isocurvature component, depending on the relative properties of the two fluids. Our results imply that several claims in the literature need substantial revision.Comment: 10 pages, 1 figur

A solution to the anisotropy problem in bouncing cosmologies

Bouncing cosmologies are often proposed as alternatives to standard inflation for the explanation of the homogeneity and flatness of the universe. In such scenarios, the present cosmological expansion is preceded by a contraction phase. However, during the contraction, in general the anisotropy of the universe grows and eventually leads to a chaotic mixmaster behavior. This would either be hard to reconcile with observations or even lead to a singularity instead of the bounce. In order to preserve a smooth and isotropic bounce, the source for the contraction must have a super-stiff equation of state with $P/\rho=w>1$. In this letter we propose a new mechanism to solve the anisotropy problem for any low-energy value of $w$ by arguing that high energy physics leads to a modification of the equation of state, with the introduction of non-linear terms. In such a scenario, the anisotropy is strongly suppressed during the high energy phase, allowing for a graceful isotropic bounce, even when the low-energy value of $w$ is smaller than unity.Comment: 9 pages, accepted for publication in JCA

Caustics of 1/rn1/r^n binary gravitational lenses: from galactic haloes to exotic matter

We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as $1/r^n$. With $n<1$ this corresponds to power-law dust distributions like the singular isothermal sphere. The $n>1$ regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We find that there are still three topologies for caustics as in the standard Schwarzschild binary lens, with the main novelty coming from the secondary caustics of the close topology, which become huge at higher $n$. After drawing caustics by numerical methods, we derive a large amount of analytical formulae in all limits that are useful to provide deeper insight in the mathematics of the problem. Our study is useful to better understand the phenomenology of galaxy lensing in clusters as well as the distinct signatures of exotic matter in complex systems.Comment: 28 pages, 19 figures, focus expanded to galactic haloe

Gravitational Lensing of stars in the central arcsecond of our Galaxy

In the neighborhood of Sgr A*, several stars (S2, S12, S14, S1, S8, S13) enjoy an accurate determination of their orbital parameters. General Relativity predicts that the central black hole acts as a gravitational lens on these stars, generating a secondary image and two infinite series of relativistic images. For each of these six stars, we calculate the light curves for the secondary and the first two relativistic images, in the Schwarzschild black hole hypothesis, throughout their orbital periods. The curves are peaked around the periapse epoch, but two subpeaks may arise in nearly edge-on orbits, when the source is behind or in front of Sgr A*. We show that for most of these stars the secondary image should be observable during its brightness peak. In particular, S14 is the best candidate, since its secondary image reaches K=23.3 with an angular separation of 0.125 mas from the apparent horizon of the central black hole. The detection of such images by future instruments could represent the first observation of gravitational lensing beyond the weak field approximation.Comment: 28 pages, 9 figures, in press on Ap

Regular two-component bouncing cosmologies and perturbations therein

We present a full investigation of scalar perturbations in a rather generic model for a regular bouncing universe, where the bounce is triggered by an effective perfect fluid with negative energy density. Long before and after the bounce the universe is dominated by a source with positive energy density, which may be a perfect fluid, a scalar field, or any other source with an intrinsic isocurvature perturbation. Within this framework, we present an analytical method to accurately estimate the spectrum of large-scale scalar perturbations until their reentry, long after the bounce. We also propose a simple way to identify non-singular gauge-invariant variables through the bounce and present the results of extensive numerical tests in several possible realizations of the scenario. In no case do we find that the spectrum of the pre-bounce growing mode of the Bardeen potential can be transferred to a post-bounce constant mode.Comment: 19 pages, 9 figure