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El Big Bang I L'univers Primitiu

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El Big Bang I L'univers Primitiu TREBALL FI DE GRAU Grau en Enginyeria Mecànica EL BIG BANG I L’UNIVERS PRIMITIU: EXPANSIÓ I ABUNDÀNCIES PRIMORDIALS Memòria i Annexos Autor: Sílvia Farràs Aloy Director: Jordi José Pont Convocatòria: Juny 2020 El Big Bang i l’Univers primitiu: expansió i abundàncies primordials Resum L’objectiu del present treball és l’estudi i caracterització de l’Univers primitiu, mitjançant l’anàlisi d’algunes de les evidències experimentals en què es fonamenta la teoria del Big Bang. El projecte consta de dos blocs principals. Un primer, de caire conceptual, on es detalla la base teòrica a partir d’una recerca centrada en les observacions cosmològiques fonamentals, els models cosmològics i la teoria del Big Bang. Posteriorment, en un segon bloc, s’aborda primerament l’estudi de l’expansió (llei de Hubble) i edat de l’Univers, a partir de l’anàlisi de dades observacionals d’un conjunt de galàxies i espectres electromagnètics. A continuació, mitjançant il·lustracions gràfiques de simulacions computacionals referents a l’etapa de la nucleosíntesi primordial es caracteritza la composició química de l’Univers primitiu i l’evolució que presenta al llarg d’aquest període. Finalment, les abundàncies d’alguns elements creats en aquest període s’han comparat gràficament amb les que hi ha actualment en el Sistema Solar. Els resultats obtinguts en aquest estudi son plenament compatibles amb els valors més precisos que la comunitat científica ha publicat, tant sobre l’edat de l’Univers com sobre la composició de l’Univers primitiu. Finalment, aquest treball proposa una sèrie d’experiments destinats a millorar el nostre coneixement de les fases inicials de l’Univers, basats en la modificació d’algunes variables amb les que s’ha treballat a les simulacions computacionals. i Memoria Resumen El objetivo del siguiente trabajo es el estudio y la caracterización del Universo primitivo, mediante el análisis de algunas de las evidencias experimentales en que se fundamenta la teoría del Big Bang. El proyecto consta de dos bloques principales. Un primer bloque, de aspecto conceptual, donde se detalla la base teórica a partir de una investigación centrada en las observaciones cosmológicas fundamentales, los modelos cosmológicos y la teoría del Big Bang. Posteriormente, en un segundo bloque, se aborda el estudio de la expansión (ley de Hubble) y edad del Universo, a partir del análisis de los datos observados de un conjunto de galaxias y espectros electromagnéticos. A continuación, mediante ilustraciones gráficas de simulaciones computacionales referentes a la etapa de la nucleosíntesis primordial se caracteriza la composición química del Universo primitivo y la evolución que presenta a lo largo de este periodo. Finalmente, la gran cantidad de algunos elementos creados en este periodo se han comparado gráficamente con las que hay actualmente en el Sistema Solar. Los resultados obtenidos en este estudio son totalmente compatibles con los valores más precisos que la comunidad científica ha publicado, tanto sobre la edad del Universo así como la composición del Universo primitivo. Por último, este trabajo propone una serie de experimentos destinados a mejorar nuestro conocimiento de las fases iniciales del Universo, basados en la modificación de algunas variables con las que se ha trabajado en las simulaciones computacionales. ii El Big Bang i l’Univers primitiu: expansió i abundàncies primordials Abstract The aim of this work is the study and characterisation of the early Universe, through the analysis of some of the experimental evidence on which the Big Bang theory is based. The project consists of two main parts. The first part sets the context by summarising researches on fundamental cosmological observations, cosmological models and the Big Bang theory. The second part begins by addressing the study of the expansion (Hubble‘s law) and age of the Universe, based on the analysis of observational data from a set of galaxies and electromagnetic spectra. Then, multiple graphical illustrations of computational simulations of stages of the primordial nucleosynthesis where are used to characterise the early Universe and the evolution that occurs throughout this period. Finally, the abundances of some elements created in this period has been compared graphically with those currently in the Solar System. The results obtained in the study are consistent with the most accurate values that the scientific community has published, based on the age of the universe and on the composition of the early Universe. Finally this work proposes a series of experiments aimed at further improving our knowledge of the initial phases of the Universe, based on the modification of some variables that have been worked on in these computer simulations. iii Memoria iv El Big Bang i l’Univers primitiu: expansió i abundàncies primordials Agraïments Tota aquesta investigació no hagués arribat al final sense el suport incondicional dels meus amics i companys, que sempre m’han entès i m’han ajudat en tot allò que he necessitat en el decurs d’aquesta etapa. Gràcies també a la meva família per la paciència que han tingut i agrair, especialment al meu cosí, Tomeu Orfila, per totes les seves aportacions i aclariments relatius a la redacció de la memòria. I sens dubte al meu tutor, Jordi José, que amb la seva exigència ha aconseguit rendibilitzar al màxim el meu esforç. Sense la seva guia, aquest vaixell difícilment hagués trobat port. Gràcies de tot cor a tots vosaltres. v Memoria vi El Big Bang i l’Univers primitiu: expansió i abundàncies primordials Glossari G constant gravitacional newtoniana c velocitat de la llum ћ constant reduïda de Planck lp longitud de Planck Mp massa de Planck tp temps de Planck t0 temps de Hubble te temps anterior al temps de Hubble Ep energia de Planck k constant de Boltzmann L lluminositat estel·lar mitjana r radi J intensitat total de llum estel·lar t temps r punt arbitrari en l’espai-temps λ longitud d’ona λrec longitud d’ona observada λem longitud d’ona en repòs z desplaçament de la longitud d’ona Ɛ훾,0 densitat d’energia actual del CMB 푛훾,0 densitat numèrica de fotons CMB T(θ,ɸ) temperatura del CMB en un punt arbitrari 푎 factor d’escala còsmica 퐸푚푒푎푛(푡) energia mitjana per fotó p protó n neutró D, 2H deuteri Yp relació entre la densitat de massa d’heli i la densitat total de massa bariònica Qn energia en repòs d’un neutró e- electró e+ positró 푣푒 neutrí 푣푒̅ antineutrí 훾 fotó H hidrogen 3H triti 3He isòtop de l’heli (3 nucleons) 4He isòtop de l’heli (4 nucleons) 6Li isòtop del liti (6 nucleons) 7Li isòtop del liti (7 nucleons) vii Memoria 7 Be isòtop del beril·li (7 nucleons) 8 Be isòtop del beril·li (8 nucleons) 푎̇ grau d’expansió 푎 휌 densitat R0 radi de curvatura ĸ constant de curvatura ɛ densitat d’energia H0 taxa d’expansió actual U constant d’integració rs radi d’una esfera ⴄ relació barió-fotó (r,θ,ϕ) coordenades per definir la distància d’un observador fins a una galàxia Ω paràmetre de densitat ΩR paràmetre de densitat de la radiació ΩM paràmetre de densitat de la matèria ΩCMB,0 paràmetre de densitat del CMB Ʌ constant cosmològica 퓔w densitat d’energia no relativista 퓔m densitat d’energia relativista 퓔r densitat d’energia de la radiació 퓔n densitat d’energia dels neutrins 퓔CMB densitat actual del CMB ν velocitat relativa de la galàxia d distància d’un objecte respecte a la nostra galàxia a diàmetre angular de la galàxia s diàmetre real de la galàxia q paràmetre de desacceleració amɅ relació entre la densitat d’energia Ʌ i la densitat d’energia en la matèria arɅ relació entre la densitat d’energia de radiació i la d’energia en la matèria x posicions de les galàxies estudiades respecte a la nostra y velocitats (ν) corresponents a les galàxies estudiades y’ menció de y a l’hora de fer la relació lineal N nombre de mesures A pendent de la recta de regressió lineal B terme independent σA error del pendent σB error del terme independent tα/2;N-2 paràmetre estadístic 2 푆푥 variància d’x 푋̅ valor mig de les x Sey paràmetre utilitzat en l’estudi d’errors r coeficient de correlació lineal 퓔y propagació de l’error de la constant de Hubble 퓔xi error de cada valor individual t0 edat de l’Univers H0 constant de Hubble δt0 error de l’edat de l’Unviers δH0 error de la constant de Hubble viii El Big Bang i l’Univers primitiu: expansió i abundàncies primordials Índex RESUM ______________________________________________________________ I RESUMEN ____________________________________________________________ II ABSTRACT ___________________________________________________________ III AGRAÏMENTS _________________________________________________________ V GLOSSARI ___________________________________________________________ VII 1. PREFACI _________________________________________________________ 1 1.1. Origen del treball ..................................................................................................... 1 1.2. Motivació.................................................................................................................. 2 1.3. Requeriments previs ................................................................................................ 2 2. INTRODUCCIÓ ____________________________________________________ 5 2.1. Objectius del treball ................................................................................................. 5 2.2. Abast del treball ....................................................................................................... 5 3. COSMOLOGIA: OBSERVACIONS FONAMENTALS ________________________ 7 3.1. Paradoxa d’Olbers ...................................................................................................
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