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1 cosmología al alcances del calculo

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Primera parte de un curso de cosmología de cinco presentaciones, a nivel del cálculo diferencial e integral, una introducción a nuestra comprensión del universo.

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1 cosmología al alcances del calculo

  1. 1. Héctor Rago hectorrago@gmail.com C.I.D.A. 2013 PARTE I INTRODUCCIÓN A LA EXPANSIÓN
  2. 2. EL UNIVERSO AL ALCANCE DEL CÁLCULO Estrategia El universo: Intuición Matemáticas, tecnología Propagación de luz en un espacio en expansión Corrimiento al rojo Uniformidad del espacio Descripción de la expansión: factor de escala, Ley de Hubble Parámetros La gravedad controla la expansión: las ecuaciones de Friedman Universos de papel: radiación, materia, vacío. El big bang. Edad del universo Horizontes, distancias, cono de luz y límites de un universo El universo real. Observaciones y parámetros “reales” . La Radiación Cósmica La cosmología estándar. Aceleración y energía del vacío. edad de nuestro universo
  3. 3. BIBLIOGRAFÍA Cosmology, the Science of the universe, Edward Harrison, Cambridge University Press, 1995. Introducción a la cosmología, (HR), http://webdelprofesor.ula.ve/ciencias/rago/ (cursos) Misconceptions about the big bang, (Tamara Davis and Charles Lineweaver), Sci. American, marzo 2005, en http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf La Geometría del universo y la radiación cósmica de fondo, (HR), Acta Científica Venezolana, 51: 116–124, 2000, en http://www.webdelprofesor.ula.va/ciencias/rago/ (divulgación) Cosmos and Cosmology, en Astrobiology:Origins from Big-bang to Civilization, Kluwer Academic Publisher, pp33-40, 2000. en http://webdelprofesor.ula.ve/ciencias/rago/ (divulgación) A new model standard model of the universe. (O. Gron) http://arxiv.org/pdf/0801.0552.pdf Graficador: http://fooplot.com/ Calculadora en línea: http://www.eeweb.com/toolbox/calculator EL UNIVERSO AL ALCANCE DEL CÁLCULO
  4. 4. Velocidad de la luz Constante gravitacional Parámetro de Hubble Tiempo de Hubble Radio o longitud de Hubble Densidad Total o crítica Omega de la materia Omega de la radiación Omega del vacío CONSTANTES Y PARÁMETROS H0 −1 =13,8×109 años
  5. 5. “Observation and theory get on best when they are mixed together helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation… It is also a good rule not to put overmuch confidence in the observational results that are put forward until they are confirmed by theory” Sir Arthur Eddington “Si las ecuaciones se niegan a decirlo, yo me niego a afirmarlo” James Pebbles
  6. 6. ESCALAS Y UNIFORMIDAD
  7. 7. LA EXPANSIÓN DEL ESPACIO Enfoque cualitativ0 Las galaxias NO se expanden La distancia entre A y B No es No es una explosión, no hay diferencias de p LAB (t1) = a(t1)[x3 − x2 ] LAB (t2 ) = a(t2 )[x3 − x2 ] LAB (t3 ) = a(t3 )[x3 − x2 ]
  8. 8. EL ESPACIO EUCLIDEO Si z Coord. Cartesianasds2 = dx2 +dy2 +dz2
  9. 9. EL ESPACIO COSMOLOGICO Si z dimensiones? Coordenada comóvil Factor de escala
  10. 10. LEY (TEORICA) DE HUBBLE Hoy: Def: Parámetro de Hubble
  11. 11. EL PARÁMETRO DE DESACELERACIÓN q L(t) = a(t)r1 ˙˙L(t) = ˙˙a(t)r1 ˙˙L(t) = ˙˙a(t) a L ˙˙L(t) = ˙˙a(t)H 2 aH 2 L q(t) = − ˙˙a(t) aH 2 t a t a t a t a
  12. 12. EL TIEMPO DE HUBBLE a Si q = 0 → t0 = tH q > 0 → t0 < tH q < 0 → t0 > tH
  13. 13. . . . . . . . . . . . . . . . . . . Vr > c ?? LA LEY DE HUBBLE Y VELOCIDADES DE GALAXIAS
  14. 14. LA LEY DE HUBBLE Y VELOCIDADES DE GALAXIAS Si: Velocidades mayores que las de la luz V L c Movimiento peculiar en el espacio, relatividad especial V LLH c
  15. 15. ESFERA DE HUBBLE – RADIO DE HUBBLE Galaxias entran Velocidad relativa entre LH y una galaxia en LH Velocidad de la esfera de Hubble Vr > c Vr < c
  16. 16. ESFERA DE HUBBLE – RADIO DE HUBBLE Ver lista de problemas > 0 resultado : ˙NH = 3NH Hq < 0 = 0 Ejercicio: Calcule la tasa a la que cambia el número de galaxias encerradas en la esfera de Hubble Denotemos por NH al número de galaxias en una esfera de radio LH NH =ξVH = AξLH 3 Pero ξ ~ a−3 y LH 3 = c3 a3 ˙a3 NH = D ˙a3 dNH dt = d dt D ˙a3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟= −3 D ˙a3 ˙˙a ˙a dNH dt = −3NH ˙˙a ˙a =+3NH Hq
  17. 17. VELOCIDAD PECULIAR Velocidad de recesión Velocidad Peculiar Si r1 depende del tiempo Su velocidad relativa a nosotros En la esfera de Hubble, es: . . Vpec = a(t) dr1 dt Si es un fotón hacia nosotros
  18. 18. ¿PODEMOS VER UNA GALAXIA MAS ALLÁ DE LH ? MORALEJA: La esfera de Hubble NO es el límite del universo!!

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