On the renormalization procedure for quantum fields with modified dispersion relation in curved spacetimes

We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to $2s$ powers of the spatial momentum, the subtraction necessary to renormalize $$and$$ depends on $s$. We first describe our previous analysis for spatially flat Friedman-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.Comment: Talk given at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, July 200

Extreme parameter sensitivity in quasidilaton massive gravity

We reanalyze the behavior of Friedmann-Lema\^itre-Robertson-Walker cosmologies in the recently proposed quasidilaton massive-gravity model, and discover that the background dynamics present hitherto unreported features that require unexpected fine-tuning of the additional fundamental parameters of the theory for an observationally consistent background cosmology. We also identify new allowed regions in the parameters space and exclude some of the previously considered ones. The evolution of the mass of gravitational waves reveals non-trivial behavior, exhibiting a mass squared that may be negative in the past, and that presently, while positive, is larger than the square of the Hubble parameter. These properties of the gravity-wave mass have the potential to lead to observational tests of the theory. While quasidilaton massive gravity is known to have issues with stability at short distances, the current analysis is a first step toward the investigation of the more stable extended quasidilaton massive gravity theory, with some expectation that both the fine-tuning of parameters and the interesting behavior of the gravity-wave mass will persist.Comment: 10 pages, 7 figure

Massless Interacting Scalar Fields in de Sitter space

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.Comment: 8 pages. Summarized version of JHEP 09 (2016) 117 [arXiv:1606.03481]. Published in the Proceedings of the 19th International Seminar on High Energy Physics (QUARKS-2016

O(N)O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in $\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.Comment: 31 pages, 5 figures. Minor changes. Published versio

Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions

We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $\lambda\phi^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.Comment: 32 pages, 4 figure

Ecoturismo como alternativa de desarrollo sustentable en el parque ecoturístico Tiacaque, Estado de México

Contiene cuadros, esquemas, fotografias y mapasEn el siguiente trabajo se hace una propuesta del ecoturismo como una alternativa para el desarrollo sustentable del Parque Ecoturístico Tiacaque, con la finalidad de preservar los recursos e impulsar el desarrollo loca

Human capital and biological well-being : a first exploration of intragenerational and intergenerational effects in 20th-century Spain

El text s'ha presentat com a comunicació a l'European Population Conference 2010. Viena (Àustria), 1-4 de setembre de 2010.During the last five decades, Spain experienced a rapid transition towards high levels of development and well-being standards among Western societies. The specific contribution of human capital to the attainment of high development levels and its interaction with wellbeing and its biological components remains understudied. It is ignored to what extend economic growth and modernization would have rendered in terms of health without the improvement of educational status, particularly among mothers. It is also unknown to what extent differences in health status among Spanish regions and social classes are due to the human capital factor. In this paper it is aimed to explore the relationship between human capital formation and the biological wellbeing throughout the 20th century in Spain. The former will be approached by educational levels whereas cohort adult height will serve as a proxy of biological well-being. We will study both intra and intergenerational effects of human capital accumulation on the biological well-being of the Spanish population born between 1910 and 1976. A number of sociodemographic and socioeconomic characteristics will be used as control variables. The bulk of this work is based on microdata from the waves of the Spanish National Health Survey (ENSE) held between 1987 and 2006. Demographic analysis together with regression techniques form the core of the methodology.Durant les darreres cinc dècades, Espanya ha experimentat una ràpida transició cap a nivells de desenvolupament i benestar més alts. La contribució específica del capital humà a aquest procés i la seva interacció amb el benestar biològic és un aspecte encara poc investigat dins d'aquesta transició. En aquest sentit, desconeixem fins a quin punt el creixement econòmic espanyol hauria repercutit, en termes de salut, si no s'hagués donat, en paral·lel, una millora en els nivells de formació, particularment entre les mares. Es desconeix també el paper específic que ha jugat la formació del capital humà, en la configuració de les diferències de salut entre les regions espanyoles i entre les classes socials. En aquest treball s'explora, per a Espanya, la relació entre el capital humà i el benestar biològic de la població al llarg del segle XX,. El capital humà es troba a partir del nivell d'instrucció, mentre que pel benestar biològic s'utilitza l'alçada adulta de les generacions. Es plantegen dos nivells d'anàlisi: intrageneracional i intergeneracional, per a les cohorts nascudes entre 1910 i 1976, a partir de microdades de l'Enquesta Nacional de Salut (ENSE; edicions 1987-2006). Es combina l'anàlisi demogràfica amb l'anàlisi de regressió i s'introdueixen diverses variables sociodemogràfiques com a controladors de la relació abans esmentada.Durante las últimas cinco décadas, España ha experimentado una rápida transición hacia altos niveles de desarrollo y bienestar. La contribución específica del capital humano a este proceso así como su interacción con el bienestar biológico, es un aspecto aún poco investigado dentro de esa transición. En este sentido, se desconoce hasta qué punto el crecimiento económico español habría repercutido de igual forma, en términos de salud, sin una mejora en paralelo de los niveles de formación, particularmente entre las madres. Se desconoce también el papel específico de la formación del capital humano, en la configuración de las diferencias de salud entre las regiones españolas y las clases sociales. En este trabajo se explora la relación entre el capital humano y el bienestar biológico de la población a lo largo del siglo XX en España. El capital humano se deduce del nivel educativo mientras que para el bienestar biológico se utiliza la estatura adulta de las generaciones. Se plantean dos niveles de análisis: intrageneracional e intergeneracional para las cohortes nacidas entre 1910 y 1976 a partir de microdatos de la Encuesta Nacional de Salud (ENSE; ediciones 1987-2006). Se combina el análisis demográfico con el análisis de regresión y se introducen diversas variables sociodemográficas como controladores de la relación mencionada