Non-gaussianity from the second-order cosmological perturbation

Several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-gaussianity in the primordial curvature perturbation \zeta, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter \zeta (and hence f_{NL}) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Non-adiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (`light non-inflaton fields'). During single-component inflation f_{NL} is constant, but multi-component inflation might generate |f_{NL}| \sim 1 or bigger. Preheating can affect f_{NL} only in atypical scenarios where it involves light non-inflaton fields. The curvaton scenario typically gives f_{NL} \ll -1 or f_{NL} = +5/4. The inhomogeneous reheating scenario can give a wide range of values for f_{NL}. Unless there is a detection, observation can eventually provide a limit |f_{NL}| \lsim 1, at which level it will be crucial to calculate the precise observational limit using second order theory.Comment: Latex file in Revtex style. 13 pages, 1 figure. v2: minor changes. Discussion in Subsection VI-A enlarged. References added. Conclusions unchanged. v3: minor typographic changes. Correlated and uncorrelated \chi^2 non-gaussianity concepts and consequences introduced. Section VI-A enlarged. Small change in Table I. References updated and added. Conclusions unchanged. Version to appear in Physical Review

Non-Gaussianity and Loop Corrections in a Quadratic Two-Field Slow-Roll Model of Inflation. Part I

In this paper it is shown that it is possible to attain a high level of non-gaussianity in a particular quadratic two-field slow-roll model of inflation by taking care of loop corrections both in the spectrum and the bispectrum. A big fNL is obtained even if ζis generated during inflation. Five issues are in consideration when constraining the available parameter space: 1. we must be sure that we are in a perturbative regime; 2. We must apply the correct condition about the (possible) loop dominance in Bζor Pζ; 3. we must satisfy the spectrum normalisation condition; 4. We must satisfy the spectral tilt constraint; 5. we must have enough inflation to solve the horizon problem.    En el artículo se muestra que es posible lograr un alto nivel de no gaussianidad en un modelo particular de inflación de dos campos y del tipo slow-roll tomando en cuenta las correcciones de lazo tanto en el espectro como en el biespectro. Un valor grande para fNL se obtiene incluso si ζ es genera durante la inflación. Cinco aspectos se tienen en cuenta al momento de restringir la ventana de parámetros disponible: 1. Debemos asegurarnos de estar en un régimen  erturbativo; 2. debemos aplicar la condición correcta acerca del (posible) dominio de las correcciones de lazo en Bζ o Pζ ; 3. debemos satisfacer la condición de normalización del espectro; 4. debemos satisfacer la restricción sobre el índice espectral; 5. Debemos tener suficiente inflación a fin de resolver el problema de horizonte.   &nbsp

Soluciones exactas de agujeros negros en la teoría generalizada de Proca

Con el fin de restringir la teoría generalizada de Proca y de determinar su compatibilidad con las futuras observaciones en el ámbito astrofísico, se estudiaron soluciones de agujeros negros en el marco de esta teoría. Para ello, en primer lugar, se determinaron las ecuaciones de campo gravitacional y de campo vectorial correspondientes a la acción generalizada de Proca para, posteriormente, obtener sus versiones adaptadas a agujeros negros estáticos y esféricamente simétricos. Posteriormente se encontraron soluciones de las ecuaciones de campo para diferentes tipos de acoplamientos dentro de esta teoría las cuales, debido a las condiciones establecidas para las funciones métricas, difieren de las soluciones de Reissner-Nordström y de Schwarzschild tan sólo en las funciones que describen al campo vectorial dependiendo del acomplamiento estudiado. A juzgar únicamente por este resultado, la teoría de la Relatividad General luce más atractiva que la teoría generalizada de Proca

No gaussianidad primordial en la perturbación en la curvatura en el escenario del curvatón

In the very successful and alternative model to the inflaton scenario, “the curvaton model”, two scalar fields are present during inflation: one, the inflaton, is in charge of generating and controlling the inflationary period, and another, the curvaton, is in charge of generating the primordial curvature perturbation ζ which in turn gives origen to the formation of large-scale structures in the Universe. The observed ζ is highly Gaussian, but the current satellite experiments, like NASA’s WMAP, search for a possible small deviation from the exact gaussianity. In this paper we will study the bispectrum Bζ (k1, k2, k3) of ζ in the curvaton scenario, whose normalisation fNL gives information about the level of non-gaussianity in ζ. This study will be done by making use of the δN formalism. We will explicitely state the advantage of this formalism and give an expression for fNL in the curvaton scenario.  En el muy exitoso y alternativo modelo para el escenario del inflatón, “el modelo del curvatón”, dos campos escalares están presentes durante inflación: uno, el inflatón, es el encargado de  generar y controlar el período inflacionario, y el otro, el curvatón, es el encargado de generar la perturbación primordial en la curvatura ζ, que a su vez da origen a la formación de la estructura a gran escala del Universo. La ζ observada es altamente gaussiana, pero los experimentos satelitales actuales, como el WMAP de la NASA, buscan una posible pequeña desviación de la gaussianidad exacta. En este artículo estudiaremos el biespectro Bζ (k1, k2, k3) de ζ en el escenario del curvatón, cuya normalización fNL da información acerca del nivel de no gaussianidad en ζ. Este estudio será realizado haciendo uso del formalismo δN . Se enunciará explícitamente la ventaja de este formalismo y se dará una expresión para fNL en el escenario del curvatón.       &nbsp

Non-gaussianity at tree and one-loop levels from vector field perturbations

We study the spectrum P_\zeta and bispectrum B_\zeta of the primordial curvature perturbation \zeta when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree level terms (both (either) in P_\zeta and (or) in B_\zeta) and viceversa. The level of non-gaussianity in the bispectrum, f_{NL}, is calculated and related to the level of statistical anisotropy in the power spectrum, g_\zeta. For very small amounts of statistical anisotropy in the power spectrum, the level of non-gaussianity may be very high, in some cases exceeding the current observational limit.Comment: LaTeX file, 11 pages, Main body: 8 pages, References: 3 pages. v2: Minor corrections. References added. Conclusions unchanged. v3: Minor corrections. Some references added and others updated. Version accepted for publication in Physical Review

Significado físico del correlador de n puntos en perturbaciones cosmológicas

Progresses made on measuring the temperature in the cosmic microwave background radiation (CMB) promise observational bounds, in particular in the spectrum amplitude Pζ of the primordial curvature perturbation ζ, its associated spectral index nζ , and level of nonaussianity fNL, that would allow us a better discrimination among cosmological inflationary models proposed to explain the origin of the large-scale structure in the Universe. The tool employed to inquire about the statistical properties of the anisotropies in the temperature of the CMB and the theoretical models built to describe such anisotropies, are the n point correlators in cosmological perturbations such as ζ. This work aims to interpret the meaning of the n point correlators in cosmological perturbations, making clear its physical content as a spatial average. As a consequence we obtain an expression for Pζ , and we analyze the implications of such an interpretation in the calculation of fNL.  Los avances realizados en materia de mediciones en la temperaturade la radiación cósmica de fondo (RCF) prometen cotas de medición, enparticular en la amplitud del espectro Pζ de la perturbación primordial enla curvatura ζ, su respectivo índice espectral nζ , y nivel de no gaussianidad fNL, que permitirían una mayor discriminación entre modelos cosmológicos inflacionarios propuestos para la explicación del origen de la estructura a gran escala de nuestro Universo. La herramienta utilizada para indagar acerca de las propiedades estadísticas de las anisotropías en la temperatura de la RCF y los modelos teóricos construidos para describir tales anisotropías, son los correladores de n puntos en perturbaciones cosmológicas tales como ζ. Este trabajo pretende interpretar el significado del correlador de n puntos en perturbaciones cosmológicas, poniendo de manifiesto su contenido físico como un promedio espacial. Como consecuencia se obtiene una expresión para Pζ , y se analizan las implicaciones de esta interpretación en el cálculo de fNL.       &nbsp

Efecto de la curvatura espacial del universo en el espectro angular de las anisotropías en la temperatura de la radiación cósmica de fondo

The inflationary paradigm solves the three classic problems of the standard cosmology: the flatness problem, the horizon problem, and the unwanted relics problem. In particular the flatness problem is solved by explaining how the relative contribution of the spatial curvature of the Universe to the total energy density decreases exponentially during infla-tion. In addition, the inflationary scenario offers us an efficient mechanism to generate small perturbations in the spatial curvature that would explain the anisotropies in the temperature of the cosmic microwave background radiation (CMB) observed nowadays. The traditional inflationary models that neglect the relative contribution reproduce the recent WMAP observations on the angular spectrum Clof the anisotropies in the tempe­rature of the CMB, but fail in the lowest multipoles where the observations show an unexpected suppression. Such a strange behaviour leads us to pro­pose an analysis of the angular spectrum Cl at large scales (low multipoles) by taking into account the relative contribution, and offer a better adjustment to the observed data, revealing in this way the characteristic topology of our observable Universe.    El paradigma inflacionario resuelve los tres problemas clásicos de la cosmología estándar: el problema de planitud, el problema de hori­zonte y el problema de las reliquias no deseadas. En particular, el problema de planitud se resuelve al explicar cómo la contribución relativa de la cur­vatura espacial del Universo  a la densidad total de energía decrece exponencialmente durante la inflación. Además, el escenario inflacionario nos ofrece un mecanismo eficiente para generar pequeñas perturbaciones en la curvatura espacial que explicarían las anisotropías en la temperatura de la radiación cósmica de fondo (RCF) observadas hoy en día. Los tradi­cionales modelos inflacionarios que desprecian la contribución relativa reproducen las recientes observaciones del satélite WMAP sobre el espectro angular Cl de las anisotropías en la temperatura de la RCF, pero fallan en los multipolos más pequeños, en donde las observaciones presentan una inesperada caída. Este extraño comportamiento nos conduce a proponer un análisis del espectro angular Cl a grandes escalas (pequeños multipolos) teniendo en cuenta la contribución relativa,y ofrecer un mejor ajuste a los datos experimentales, evidenciando así la topología característica del Universo observado

The inflationary prediction for primordial non-gaussianity

We extend the \delta N formalism so that it gives all of the stochastic properties of the primordial curvature perturbation \zeta if the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation \fnl of the bispectrum of \zeta, which is the main signal of non-gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained.Comment: Revtex Latex file. 4 pages, no figures. v4: minor changes, typos corrected, references added and updated. Version published in Physical Review Letter

On the Issue of the \zeta Series Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum

We calculate the trispectrum T_\zeta of the primordial curvature perturbation \zeta, generated during a {\it slow-roll} inflationary epoch by considering a two-field quadratic model of inflation with {\it canonical} kinetic terms. We consider loop contributions as well as tree level terms, and show that it is possible to attain very high, {\it including observable}, values for the level of non-gaussianity \tau_{NL} if T_\zeta is dominated by the one-loop contribution. Special attention is paid to the claim in JCAP {\bf 0902}, 017 (2009) [arXiv:0812.0807 [astro-ph]] that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-gaussianity f_{NL} and \tau_{NL} in the bispectrum B_\zeta and trispectrum T_\zeta of \zeta, respectively, are also studied for the case in which \zeta is not generated during inflation.Comment: LaTex File, 27 pages, 8 figures. v2: Previous Section 2 has been removed. Two new sections (3 and 4) discussing the classicality condition given by Byrnes, Choi, and Hall, in JCAP 0902, 017 (2009), and the probability that an observer sees a non-gaussian distribution have been added. v3: Version accepted for publication in Physical Review

No gaussianidad y correcciones de lazo en un modelo inflacionario de rodadura lenta con potencial escalar cuadrático de dos componentes. Parte II

We calculate the trispectrum Tζ(k1, k2, k3, k4) of the curvature perturbation ζ, generated during an inflationary slow-roll epoch and considering a two-component quadratic scalar potential. At calculating we consider tree-level and one-loop contributions, showing that it is possible to obtain an observable value for the non-gaussianity level τNL if Tζ is dominated by the one-loop contribution. The work is developed taking into account that there exist some physical restrictions that reduce the available parameter window. Such conditions are: the existence of a coupling constant that guarantees making the calculation in a perturbative regime, the relative weight of the tree-level and one-loop contributions, the spectrum normalisation, the observed spectral index, and the minimum amount of inflation required to solve the horizon problem.Se calcula el triespectro Tζ(k1,k2,k3,k4) de la perturbación en la curvatura ζ, generado durante una época inflacionaria de rodadura lenta y considerando un potencial escalar cuadrático de dos componentes. En el cálculo se consideran contribuciones a nivel árbol y a un lazo, y se muestra que es posible obtener un valor observable para el nivel de no gaussianidad τNL si Tζ es dominado por la contribución a un lazo. El trabajo se desarrolla teniendo en cuenta que existen algunas restricciones físicas que reducen la ventana de parámetros disponible. Estas condiciones son: la existencia de una constante de acoplamiento que garantiza la realización del cálculo en un régimen perturbativo, el peso relativo de las contribuciones a nivel árbol y a un lazo, la normalización del espectro, el índice espectral observado y el monto de inflación mínimo necesario para resolver el problema de horizonte