Jaume Amorós

Bouncing Loop Quantum Cosmology from F(T) gravity

The big bang singularity could be understood as a breakdown of Einstein’s general relativity at very high energies. By 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 ð H; Þ , where H is the Hubble parameter and the energy density of the universe. Using LQC one considers a model 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 nonsingular 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 ( _ H> 0 )

Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data

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 0r= disfavored at 7.0 s, 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 Plancks constrains due to the smallness of the value of the tensor/scalar ratio r= 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 CosmologyThe 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{sup +0.07}{sub -0.05} with 0r= 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 Plancks constrains due to the smallness of the value of the tensor/scalar ratio r≤ 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.

Nonsingular Models of Universes in Teleparallel Theories

Different models of universes are considered in the context of teleparallel theories. Assuming that the universe is filled by a fluid with an equation of state P=-ρ-f(ρ), for different teleparallel theories and different equation of state we study its dynamics. Two particular cases are studied in detail: in the first one we consider a function f with two zeros (two de Sitter solutions) that mimics a huge cosmological constant at early times and a pressureless fluid at late times; in the second one, in the context of loop quantum cosmology with a small cosmological constant, we consider a pressureless fluid (P=0⇔f(ρ)=-ρ) which means there are de Sitter and anti-de Sitter solutions. In both cases one obtains a nonsingular universe that at early times is in an inflationary phase; after leaving this phase, it passes trough a matter dominated phase and finally at late times it expands in an accelerated way.

Viability of the matter bounce scenario in Loop Quantum Cosmology for general potentials

We consider the matter bounce scenario in F (T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F (T) model that we will name tele parallelversion of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemai tre-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well- know perturbed equations in F (T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallelversion of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Plancks experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Plancks data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.We consider the matter bounce scenario in Loop Quantum Cosmology (LQC) for physical potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these models, numerically solving the dynamical equations we have seen that the teleparallel version of LQC leads to theoretical results that fit well with current observational data. More precisely, in teleparallel LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with {\it Plancks} experimental data. On the other hand, in holonomy corrected LQC the theoretical value of the tensor/scalar ratio is smaller than in teleparallel LQC, which means that there is always a set of solutions that matches with {\it Plancks} data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.

Characterization of superconducting rings using an in-field Hall probe magnetic mapping system

A Hall probe magnetic imaging system that works in magnetic fields in the range -1 T to 1 T has been implemented, and it has been used to characterize the superconducting behavior of single domain melt textured YBa/sub 2/Cu/sub 3/O/sub 7/ rings. We show that in addition to the analysis of the evolution of the local magnetic field distribution when the external magnetic field is cycled, the hysteretic behavior of the magnetic moment can also be investigated after integration of the local magnetic field. The critical current density has been determined through the critical state model and it has been compared to that calculated by inversion of the Biot-Savart law. A remarkable agreement is achieved with both methods.

A new method of computation of current distribution maps in bulk high-temperature superconductors: analysis and validation

We present a test and analysis of our method of computation of the distribution of currents in bulk superconducting samples, which is sensitive to current contribution in the deep layers of the sample. The procedure is based on measurements of the magnetic field with a Hall probe, inverted by linearization and orthogonal triangularization, known as QR decomposition, of the matrix in the resulting linear system. No assumptions on the number or geometry of domains are required. The only constraint on the method is that the critical current must be homogeneous along the c-axis. Our method is applied to real 3d samples with size in the cm range and different geometries of technological interest. The propagation of errors in the general case is analysed, and we also supply a method to estimate the error in every computation, which is applied to the computed J(Jx, Jy) in the above samples.

In-field Hall probe mapping system for characterization of YBCO welds

Artificial welding of melt-textured YBCO blocks opens the door to the fabrication of large, complex-shaped pieces required for applications. In order to evaluate the superconducting quality of the welds, we have developed a Hall probe mapping system, able to record the local magnetization at 77 K under dynamic applied fields in the range of -1 to 1 T. The system was used to characterize welded samples prepared with a new Ag induced surface melting joining technique. The magnetization maps of unwelded and welded samples of various qualities are compared and discussed. The current distributions associated to the Hall maps were calculated using the Caragol software. The magnetization and current distribution maps over the joint show that good quality welds can be reached with this joining method.

On the Malcev completion of Kähler groups

The study of compact Kähler manifolds made by Hodge and others shows that a Kähler structure imposes very strong conditions on the homotopy type of a compact complex manifold X. In particular, unlike in the case of compact differentiable or closed complex manifolds, not every finitely presented group G is the fundamental group of a compact Kähler manifold. Such groups are called Kähler groups. This note has been inspired by the recent work of F. Johnson and E. Rees ([JR]) and M. Gromov ([G]), showing that free products, and in particular free groups, are not Kähler. It has been our purpose to extend this result and find other restrictions on the presentations of Kähler groups. This is done by translating properties of cup products in H∗(X) into properties of the group bracket in π1X, an idea that came out of [JR], and also by examining the Albanese map X → Alb(X) after [C]. We describe an algorithm derived from [St] to compute Γ1/Γ2G,Γ2/Γ3G⊗R from a given presentation of a group G, and use it to give three conditions for the groups to be Kähler: The Lie algebra L2G, equivalent to the holonomy algebra, cannot be free (3.3); oneor two-relator Kähler groups either have a torsion abelianized or have a Malcev completion isomorphic to that of a compact Riemann surface group (4.7); nonfibered Kähler groups must satisfy certain lower bounds for the number of their defining relations, equivalently upper bounds for the rank of Γ2/Γ3G (5.6,5.7). In §1 we recall the real Malcev completion G⊗R of a group G, its equivalent Lie algebra LG, and a 2-step nilpotent Lie algebra L2G ∼= (Γ1/Γ2G⊗R)⊕(Γ2/Γ3G⊗R), which is determined by (Γ1/Γ3G)/Torsion and is equivalent to the cup products ∧2 H1(X)→ H(X). This algebra is actually equivalent to the holonomy algebra of G (cf. [Ch], [Ko]), and is more convenient for our computations. By [M2],[DGMS], when G is a Kähler group the algebra L2G determines the Malcev completion

Simple inflationary quintessential model

In the framework of a flat Friedmann-Lemaitre-Robertson-Walker geometry, we present a nongeodesically past complete model of our Universe without the big bang singularity at finite cosmic time, describing its evolution starting from its early inflationary era up to the present accelerating phase. We found that a hydrodynamical fluid with nonlinear equation of state could result in such scenario, which after the end of this inflationary stage, suffers a sudden phase transition and enters into the stiff matter dominated era, and the Universe becomes reheated due to a huge amount of particle production. Finally, it asymptotically enters into the de Sitter phase concluding the present accelerated expansion. Using the reconstruction technique, we also show that this background provides an extremely simple inflationary quintessential potential whose inflationary part is given by the well-known 1-dimensional Higgs potential, i.e., a double well inflationary potential, and the quintessential one by an exponential potential that leads to a deflationary regime after this inflation, and it can depict the current cosmic acceleration at late times. Moreover the Higgs potential leads to a power spectrum of the cosmological perturbations which fit well with the latest Planck estimations. Further, we compared our viable potential with some known inflationary quintessential potential, which shows that our quintessential model, that is, the Higgs potential combined with the exponential one, is an improved version of them because it contains an analytic solution that allows us to perform all analytic calculations. Finally, we have shown that the introduction of a nonzero cosmological constant simplifies the potential considerably with an analytic behavior of the background which again permits us to evaluate all the quantities analytically.

Viability of the matter bounce scenario in

We consider the matter bounce scenario in F (T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F (T) model that we will name tele parallelversion of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemai tre-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well- know perturbed equations in F (T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallelversion of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Plancks experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Plancks data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.We consider the matter bounce scenario in Loop Quantum Cosmology (LQC) for physical potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these models, numerically solving the dynamical equations we have seen that the teleparallel version of LQC leads to theoretical results that fit well with current observational data. More precisely, in teleparallel LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with {\it Plancks} experimental data. On the other hand, in holonomy corrected LQC the theoretical value of the tensor/scalar ratio is smaller than in teleparallel LQC, which means that there is always a set of solutions that matches with {\it Plancks} data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.