Can f(R) gravity contribute to (dark) radiation?

We discuss the possibility that suitable modifications of gravity could account for some amount of the radiation we observe today, in addition to the possibility of explaining the present speed up of the universe. We start introducing and reviewing cosmological reconstruction methods for metric $f(R)$ theories of gravity that can be considered as one of the straightforward modifications of Einstein's gravity as soon as $f(R)\neq R$. We then take into account two possible $f(R)$ models which could give rise to (dark) radiation. Constraints on the models are found by using the Planck Collaboration 2015 data within a cosmographic approach and by obtaining the matter power spectrum of those models. The conclusion is that $f(R)$ gravity can only contribute minimally to the (dark) radiation to avoid departures from the observed matter power spectrum at the smallest scales (of the order of $0.01$Mpc$^{-1}$), i.e., precisely those scales that exited the horizon at the radiation dominated epoch. This result could strongly contribute to select reliable $f(R)$ models.Comment: 29 pages, 10 figures, RevTex4. Discussion improved. Version accepted in JCA

The spectrum of gravitational waves in an f(R) model with a bounce

We present an inflationary model preceded by a bounce in a metric $f(R)$ theory. In this model, modified gravity affects only the early stages of the universe. We analyse the predicted spectrum of the gravitational waves in this scenario using the method of the Bogoliubov coefficients. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e., corresponding to modes that are currently entering the horizon.Comment: 4 pages, 2 figures. Contribution to the Spanish Relativity Meeting in Portugal 2012 (ERE2012), Guimaraes, Portuga

3-Form Cosmology: Phantom Behaviour, Singularities and Interactions

The latest cosmological observations by the Planck collaboration (and combined with others) are compatible with a phantom-like behaviour (w <-1) for the dark energy equation of state that drives the current acceleration of the Universe. With this mindset, we look into models where dark energy is described by a 3-form field minimally coupled to gravity. When compared to a scalar field, these models have the advantage of more naturally accommodating a cosmological-constant and phantom-like behaviours. We show how the latter happens for a fairly general class of positive-valued potentials, and through a dynamical system approach, we find that in such cases the 3-form field leads the Universe into a Little Sibling of the Big Rip singular event into the future. In this work, we explore the possibility of avoiding such singularity via an interaction in the dark sector between cold dark matter and the 3-form field. For the kind of interactions considered, we deduce a condition for replacing the LSBR by a late time de Sitter phase. For specific examples of interactions that meet this condition, we look for distinctive imprints in the statefinder hierarchy , through the composite null diagnostic (CND).The Authors are grateful to Juan M. Aguirregabiria and Cesar Silva for enlightening discussions on dynamical system analysis. The Authors also acknowledge Nelson Nunes for helping us to understand several issues related to 3-forms. The work of MBL is supported by the Portuguese Agency "Fundacao para a Ciencia e Tecnologia" through an Investigador FCT Research contract, with reference IF/01442/2013/CP1196/CT0001. She and JMorais wish to acknowledge the partial support from the Basque government Grant No. IT592-13 (Spain) and FONDOS FEDER under grant FIS2014-57956-P (Spanish government). J. Morais is also thankful to UPV/EHU for a PhD fellowship and UBI for hospitality during the completion of part of this work. The authors acknowledge the COST Action CA15117 (CANTATA)

COMPLETE ORTHOGONAL SYSTEMS OF 3D SPHEROIDAL MONOGENICS

In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil Théodoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szegö kernel function over 3D prolate spheroids

A phenomenological exploration within Theoretical Cosmology: from the Early to the Late Universe.

262 p.En esta tesis se han explorado posibles extensiones del Modelo Estándar de la Cosmología. Hemos obtenido las predicciones teóricas de los modelos considerados y sus principales características. Los resultados presentados están basados en tres proyectos principales en los que he participado conjuntamente con mi supervisora, Mariam Boudmadi López, y otros colaboradores. Estos proyectos enfocan tres áreas diferentes de investigación en la Cosmología actual: teorías métricas de gravedad modificada tipo f(R) y modelos de energía oscura (EO) dinámica descrita por campos de 3-forma.Asimismo, en esta tesis hemos considerado la Cosmología Cuántica en el contexto del Universo primordial. Además, tal como sugiere el titulo, en esta tesis el foco principal se ha centrado en un tratamiento puramente teórico de los diferentes modelos considerados. Esta tesis está dividida en cinco partes principales. En la Parte I se introducen los principales conceptos de la Cosmología actual,juntamente con los métodos y observables cosmológicos usados para caracterizar los diferentes modelosanalizados. La Parte II se centra en la evolución del Universo tardío y está dividida en dos capítulos. Enel primero se presentan los resultados de un modelo en que la EO y la radiación oscura son descritas pormodificaciones de la gravedad del tipo f(R). En el segundo se estudián modelos de EO descrita por uncampo de 3-formas que interacciona con la materia oscura. En la Parte III, se estudian los efectos de épocas pre-inflacionarias en el espectro de potencias primordial en modelos inspirados por el formalismo de la Tercera Cuantización. Finalmente, en la Parte IV se presentan las conclusiones y comentariosfinales de la tesis y en la Parte V se incluyen los apéndices con una revisión de la teoría de las perturbaciones cosmológicas lineales y con cálculos y resultados auxiliares.FSC; Ecolabe

A phenomenological exploration within Theoretical Cosmology: from the Early to the Late Universe.

262 p.En esta tesis se han explorado posibles extensiones del Modelo Estándar de la Cosmología. Hemos obtenido las predicciones teóricas de los modelos considerados y sus principales características. Los resultados presentados están basados en tres proyectos principales en los que he participado conjuntamente con mi supervisora, Mariam Boudmadi López, y otros colaboradores. Estos proyectos enfocan tres áreas diferentes de investigación en la Cosmología actual: teorías métricas de gravedad modificada tipo f(R) y modelos de energía oscura (EO) dinámica descrita por campos de 3-forma.Asimismo, en esta tesis hemos considerado la Cosmología Cuántica en el contexto del Universo primordial. Además, tal como sugiere el titulo, en esta tesis el foco principal se ha centrado en un tratamiento puramente teórico de los diferentes modelos considerados. Esta tesis está dividida en cinco partes principales. En la Parte I se introducen los principales conceptos de la Cosmología actual,juntamente con los métodos y observables cosmológicos usados para caracterizar los diferentes modelosanalizados. La Parte II se centra en la evolución del Universo tardío y está dividida en dos capítulos. Enel primero se presentan los resultados de un modelo en que la EO y la radiación oscura son descritas pormodificaciones de la gravedad del tipo f(R). En el segundo se estudián modelos de EO descrita por uncampo de 3-formas que interacciona con la materia oscura. En la Parte III, se estudian los efectos de épocas pre-inflacionarias en el espectro de potencias primordial en modelos inspirados por el formalismo de la Tercera Cuantización. Finalmente, en la Parte IV se presentan las conclusiones y comentariosfinales de la tesis y en la Parte V se incluyen los apéndices con una revisión de la teoría de las perturbaciones cosmológicas lineales y con cálculos y resultados auxiliares.FSC; Ecolabe

Medical Applications of Materials Manufactured by the AM Process

The use of 3D printing for manufacturing parts has made it possible to produce components with complex geometries according to drawings made on the computer. 3D printing offers many advantages in the manufacture of polymers and composites, including high precision, low cost, and custom geometry. Several techniques are used in 3D printing, the ones discussed in this monograph are the main ones for polymers. These are: fused deposition modeling (FDM), Injection 3D printing (3DP), Stereolithography (SLA), and finally selective laser sintering (SLS). The 3D printing technique has several applications, however, the focus in this project is to analyze the various medical applications and the main advantages and disadvantages associated with it. Some of the main applications of this type of technology that will be described throughout the project are: - Bioprinting of tissues and organs - Customized Implants and Protheses - Anatomical Models for Surgical Application - Pharmaceutical Application The main objective will be to analyze, for these procedures, what are the advantages associated with the use of 3D technology and what are the goals for the future in this field. In addition, it will be important to mention the advantages and disadvantages of this combination (3D printing and medicine) in a more general overview, identifying numerous advantages but also potential risks that need to be taken into account. In order to deepen the analysis further, two practical cases will be studied, ensuring their contextualization for the project and also a verification of the improvements and processes facilitated by the application of 3D technology in these fields