Bouncing cosmologies via modified gravity in the ADM formalism: Application to loop quantum cosmology

We consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the Universe following the spirit of Weyl’s postulate, has been fixed, f theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation; i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued f functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected loop quantum cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.Peer ReviewedPostprint (author's final draft

Riemann i les funcions de variable complexa

Conferència enmarcada dintre de la Jornada RiemannFactoria FM

On the number of defining relations for nonfibered kaehler groups

We present minimal bounds for the deficiency (least difference between numbers of generators and relations among all presentations of a group) of fundamental groups of quasiprojective manifolds which do not fiber over a curve. The bound is derived from a log version of Castelnuovo-de Franchis theorem and mixed Hodge theory. The previously known case of nonfibered compact Kaehler manifolds is presented in a unified wa

Generic behaviour of asymptotically holomorphic Lefschetz pencils

We prove that the vanishing spheres of the Lefschetz pencils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplectomorphism group of the fiber. More precisely, a number of generalized Dehn twists may be used to conjugate those spheres. This implies the non-existence of homologically trivial vanishing spheres in these pencils. To develop the proof, we discuss some basic topological properties of the space of asymptotically holomorphic transverse sections

Understanding the phenomenology of interacting dark energy scenarios and their theoretical bounds

Nongravitational interaction between dark matter and dark energy has been considered in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. The interaction rate is assumed to be linear in the energy densities of dark matter and dark energy and it is also proportional to the Hubble rate of the FLRW universe. This kind of interaction model leads to an autonomous linear dynamical system, and depending on the coupling parameters, could be solved analytically by calculating the exponential of the matrix, defining the system. We show here that such interaction rate has a very deep connection with some well-known cosmological theories. We then investigate the theoretical bounds on the coupling parameters of the interaction rate in order that the energy densities of the dark sector remain positive throughout the evolution of the universe and asymptotically converge to zero at very late times. Our analyses also point out that such linear interacting model may encounter with finite time future singularities depending on the coupling parameters as well as the dark energy state parameter. © 2020 American Physical SocietyPeer ReviewedPostprint (published version

Developable surfaces with prescribed boundary

It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only infinitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of developable surfaces is discussed.Research supported by project Clothilde, ERC research grant 741930, and research grants PID2019-103849GB-I00, from the Kingdom of Spain, 2017 SGR 932 from the Catalan Government. MAC is also with Institut de Robòtica i Informàtica Industrial (CSIC-UPC), the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech) and the Barcelona Graduate School of Mathematics (BGSMath).Peer ReviewedPostprint (published version

An inextensible model for the robotic manipulation of textiles

We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces that are inextensible, admitting only isometric motions. Inextensibility is derived in a continuous setting, prior to any discretization, which gives consistency with respect to remeshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the difference between the simulated and the real position of each point in the garment is lower than 1cm in average even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, when compared to the recorded dynamics of real textiles, description of cloth motion incorporating aerodynamic effects by using only two parameters.Peer ReviewedPostprint (published version

A representation of cloth states based on a derivative of the Gauss linking integral

Robotic manipulation of cloth is a complex task because of the infinite-dimensional shape-state space of textiles, which makes their state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a finite low-dimensional representation of cloth states that allows us to efficiently distinguish a large variety of different folded states, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and allows us to represent spatial as well as planar folded configurations in a consistent and unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the representation of cloth states and significantly more sensitive to changes in grasping affordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing that with it we can identify the different states using a distance-based classifier.This work was developed under the project CLOTHILDE which has received funding from the European Research Council (ERC) under the EU-Horizon 2020 research and innovation programme (grant agreement No. 741930). M. Alberich-Carramiñana is also with the Barcelona Graduate School of Mathematics (BGSMath) and the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech), and she and J. Amorós are partially supported by the Spanish State Research Agency AEI/10.13039/501100011033 grant PID2019-103849GB-I00 and by the AGAUR project 2021 SGR 00603 Geometry of Manifolds and Applications, GEOMVAP. J. Borràs is supported by the Spanish State Research Agency MCIN/ AEI /10.13039/501100011033 grant PID2020-118649RB-I00 (CHLOE-GRAPH project).Peer ReviewedPostprint (published version

GEOMETRIA DIFERENCIAL | EXTRAORDINARI

Extraordinar