arXiv subjects
Publications and source records attributed to Jaume Amorós.
It is shown that teleparallel $F({\mathcal T})$ theories of gravity combined with Loop Quantum Cosmology support a Matter Bounce Scenario which is an alternative to the inflation scenario in the Big Bang paradigm. It is checked thatthese bouncing models provide theoretical data that fits well with the current observational data, allowing the viability of the Matter Bounce Scenario.
The CMB map provided by the Planck project constrains the value of the ratio of tensor-to-scalar perturbations, namely $r$, to be smaller than $0.11$ (95% CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value $r=0.20^{+0.07}_{-0.05}$ with $r=0$ disfavored at $7.0 σ$, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass Planck's constrains due to the smallness of the value of the tensor/scalar ratio $r\leq 0.11$, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in the teleparallel version of Loop Quantum Cosmology.
The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the primeval singularity. One of them is Loop Quantum Cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space $(H,ρ)$, where $H$ is the Hubble parameter and $ρ$ the energy density of the universe. Using LQC when one considers a model of universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti de Sitter solution. This means that one obtains a bouncing non-singular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation and matter dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: The evolution of the universe through a contracting phase and a period of super-inflation ($\dot{H}> 0$).
Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.
We study some asymptotic properties of the sequences of symplectic Lefschetz pencils constructed by Donaldson. In particular we prove that the vanishing spheres of these pencils are, for large degree, conjugated under the action of the symplectomorphism group of the fiber. This implies the non-existence of homologically trivial vanishing spheres in these pencils. Moreover we show some basic topological properties of the space of asymptotically holomorphic transverse sections. These properties allow us to define a new set of symplectic invariants of the original symplectic structure.