Aula 1/5 Princípios - IF mquartin/seminarios/cosmologia-ECG.2013-CBPF.pdf · Aula 1/5 Princípios…

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    Aula 1/5Aula 1/5PrincpiosPrincpios

    Curso de Cosmologia VII ECG, CBPF Ago/2013Curso de Cosmologia VII ECG, CBPF Ago/2013

    Miguel QuartinMiguel QuartinInstituto de Fsica, UFRJInstituto de Fsica, UFRJ

    Astrofsica, Relativ. e Cosmologia (ARCOS)Astrofsica, Relativ. e Cosmologia (ARCOS)

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    1. Sobre o Curso1. Sobre o Curso Material didtico:Material didtico:

    ResumoResumo Meus SlidesMeus Slides Hogg,Hogg, Distance measures in cosmology (astroph/9905116) Distance measures in cosmology (astroph/9905116) Roberto Trotta, Roberto Trotta, Bayes in the Sky, arXiv:0803.4089Bayes in the Sky, arXiv:0803.4089

    Bibliografia suplementar nvel bsico:Bibliografia suplementar nvel bsico: Barbara Ryden, Barbara Ryden, Intro. to CosmologyIntro. to Cosmology

    Bibliografia suplementar nBibliografia suplementar nvel avanado:vel avanado: Amendola & Tsujikawa, Amendola & Tsujikawa, Dark EnergyDark Energy Mukhanov, Mukhanov, Physical Foundations of CosmologyPhysical Foundations of Cosmology

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    Sobre o Curso (2)Sobre o Curso (2) Tpicos abordados:Tpicos abordados:

    [Aula 1] Fundamentos da Cosmologia[Aula 1] Fundamentos da Cosmologia [Aula 2] Dinmica, modelos simples e [Aula 2] Dinmica, modelos simples e CDMCDM [Aula 3] Cosmologia Observacional[Aula 3] Cosmologia Observacional [Aula 4] [Aula 4] Estatstica BayesianaEstatstica Bayesiana [Aula 5] Anlise de dados e mtodos numricos[Aula 5] Anlise de dados e mtodos numricos

    Tpicos no-abordados:Tpicos no-abordados: Cosmologia Relativstica, Cosmologia Relativstica, Formao de estruturasFormao de estruturas, , InflaoInflao,, Nucleossntese Nucleossntese primordial, CMB, Matria Escura, Lentes Gravitacionais primordial, CMB, Matria Escura, Lentes Gravitacionais etc.etc.

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    Unidades de PlanckUnidades de Planck

    Usando as unidades de Planck, tem-se numericamente Usando as unidades de Planck, tem-se numericamente queque

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    Unidades de Planck (2)Unidades de Planck (2)

    Usando as unidades de Planck, tem-se numericamente Usando as unidades de Planck, tem-se numericamente queque

    Podemos simplificar nossas equaes omitindo essas Podemos simplificar nossas equaes omitindo essas constantesconstantes As constantes podem ser re-obtidas por anlise As constantes podem ser re-obtidas por anlise

    dimensionaldimensional Exs:Exs:

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    Grandezas teisGrandezas teis

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    2. Fundamental Observations2. Fundamental Observations

    Olber's ParadoxOlber's Paradox

    Homogeneity and isotropyHomogeneity and isotropy

    Hubble's (Lematre's) LawHubble's (Lematre's) Law

    Cosmologist Particle BookCosmologist Particle Book

    The CMBThe CMB

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    Olber's ParadoxOlber's Paradox

    Why is the night Why is the night sky dark?sky dark? Infinite and static Infinite and static

    universe bright universe bright sky!sky!

    Solution 1: Solution 1: universe has universe has finite sizefinite size

    Solution 2: Solution 2: universe has a universe has a finite agefinite age

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    Olber's Paradox (2)Olber's Paradox (2)

    Parenthesis: Luminosity vs. Brightness vs. Intensity vs. FluxParenthesis: Luminosity vs. Brightness vs. Intensity vs. Flux

    Luminosity (L)Luminosity (L) = total energy / time ; emitted or received = total energy / time ; emitted or received It is a It is a propertyproperty of the source; does of the source; does notnot depend on distance depend on distance

    Intensity (I)Intensity (I) = = BrightnessBrightness = energy/(time = energy/(time xx det. area det. area xx solid ang.) solid ang.) It is a It is a propertyproperty of the source; does of the source; does notnot depend on distance depend on distance

    Specific Intensity (ISpecific Intensity (Ivv) = I / (unit frequency)) = I / (unit frequency)

    Flux (f)Flux (f) = Luminosity / (4 = Luminosity / (4 distance distance22)) depends on distancedepends on distance

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    Olber's Paradox (3)Olber's Paradox (3) Let's compute the sky brightnessLet's compute the sky brightness

    Let Let nn be the average # density be the average # density of starsof stars

    Let Let LL be their average be their average luminosity ( = energy/time)luminosity ( = energy/time)

    The intensity differential dJ is:The intensity differential dJ is:

    Where did we Where did we go wrong?go wrong?

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    Olber's Paradox (4)Olber's Paradox (4)

    Stars have finite (angular) size they obstruct stars Stars have finite (angular) size they obstruct stars behind thembehind them JJ no longer no longer ; ; instead J average surface brightness of a star instead J average surface brightness of a star

    L and/or n may depend on distanceL and/or n may depend on distance We would needWe would need

    Universe could have finite size and/or ageUniverse could have finite size and/or age Cutoff in the integralCutoff in the integral

    Flux might not go down as 1/rFlux might not go down as 1/r22 Due to non-euclidean geometryDue to non-euclidean geometry Due to redshift / expansionDue to redshift / expansion

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    Homogeneity & IsotropyHomogeneity & Isotropy The universe is* homogeneous and isotropic on large scalesThe universe is* homogeneous and isotropic on large scales

    Minimum scale ~ 100 MpcMinimum scale ~ 100 Mpc * our observations are * our observations are consistentconsistent with this hypotheses with this hypotheses

    Isotropy & homogeneity independentIsotropy & homogeneity independent Isotropy around every point homogeneityIsotropy around every point homogeneity

    Copernican Principle:Copernican Principle: we don't live in a special we don't live in a special location in the universelocation in the universe

    Cosmological Principle:Cosmological Principle: on sufficiently large on sufficiently large scales, the properties of scales, the properties of the Universe are the the Universe are the same for all observerssame for all observers

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    Homogeneity & Isotropy (2)Homogeneity & Isotropy (2)

    Anisotropic & Anisotropic & HomogeneousHomogeneous

    Isotropic & Isotropic & InhomogeneousInhomogeneous

    Isotropy & homogeneity independent Isotropy around every point homogeneity

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    Homogeneity & Isotropy (3)Homogeneity & Isotropy (3)

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    The Hubble's LawThe Hubble's Law

    The Doppler allows us to measure radial velocities with The Doppler allows us to measure radial velocities with high precision;high precision;

    Desvio parao azul

    Desvio parao vermelho

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    The Hubble's Law (2)The Hubble's Law (2) Lematre (and later Hubble)* found out that galaxies are, Lematre (and later Hubble)* found out that galaxies are,

    in average, receding from us;in average, receding from us; The redshift is linear with distanceThe redshift is linear with distance The velocity is approx. also linear with distanceThe velocity is approx. also linear with distance

    * Stigler's law of eponymy: "No scientific discovery is * Stigler's law of eponymy: "No scientific discovery is named after its original named after its original discoverer."discoverer."

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    109 anos-luz 2 x 109 anos-luz

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    Variao de

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    The Hubble's Law (3)The Hubble's Law (3)

    Hubble's Law does not violate the copernican principle!Hubble's Law does not violate the copernican principle! Isotropic and homogeneous expansion produces Hubble's Isotropic and homogeneous expansion produces Hubble's

    law for all observerslaw for all observers

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    The Hubble's Law (4)The Hubble's Law (4) We can describe such an expansion by a time-dependent We can describe such an expansion by a time-dependent

    scale factor a(t)scale factor a(t) Inhomogeneity a(t, r)Inhomogeneity a(t, r) Anisotropy (shear) a(Anisotropy (shear) a( t, t, , , ) or {a(t), b(t), c(t)}) or {a(t), b(t), c(t)}

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    The Hubble's Law (5)The Hubble's Law (5)

    If galaxies are receding from us, were we once together?If galaxies are receding from us, were we once together? Simplest first assumption: H(t) = const = HSimplest first assumption: H(t) = const = H00 This implies ALL galaxies were together at the SAME timeThis implies ALL galaxies were together at the SAME time

    This is the base of the Big-Bang modelThis is the base of the Big-Bang model The above calculation ignores gravityThe above calculation ignores gravity

    Gravity pulls galaxies in and slows expansion with timeGravity pulls galaxies in and slows expansion with time

    H(t) > HH(t) > H0 0 in the past tin the past t 00 < 13.8 Gyr < 13.8 Gyr

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    Cosmologist Particle BookCosmologist Particle Book 4 types of particle are important is cosmology:4 types of particle are important is cosmology:

    Photons, baryons (protons+neutrons+electrons), neutrinos Photons, baryons (protons+neutrons+electrons), neutrinos and dark matterand dark matter e- mass

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    Cosmologist Particle Book (2)Cosmologist Particle Book (2)

    In thermal equilibrium the energy density of photons is In thermal equilibrium the energy density of photons is given by the given by the blackbodyblackbody spectrum spectrum

    The total energy and The total energy and number density are:number density are:

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    The The isotropic isotropic CMBCMB

    We receive photons in the microwave spectrum from all We receive photons in the microwave spectrum from all directions isotropica