geometr a del_universo
TRANSCRIPT
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Grandes Preguntas
¿Tuvo un origen el universo?¿Qué contiene?
¿De dónde salieron las galaxias y estrellas?
¿Por qué cae una manzana?
¿Se seguirá expandiendo?
¿Cuál es la geometría del universo?
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Estrategia y Táctica
SUPERFICIES CURVASESPACIOS CURVOS
LA RADIACIÓNCÓSMICA DEMICROONDAS
RELATIVIDAD Y GEOMETRÍA
VIENDO ELSONIDO DELUNIVERSO
...Y EL ESPACIO ES...
REFLEXIONESESPECULACIONES
CONCLUSIONES
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d
s1 s2
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d” = 0
La Geometría Euclidiana
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a
bc
a + b + c = 180º
La Geometría Euclidiana
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P
rP = 2
La Geometría Euclidiana
π
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Karl Friederich Gauss“El Príncipe”
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d’’ < 0
LA 2-ESFERA
a + b + c > 180º
πP/r < 2
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Nikolai Lobachevski
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a + b + c < 180º
d” > 0
P/r > 2
La Geometría de Lobachevski
π
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Bernard Riemann
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Geometrìas Homogéneas
Nombre Curvatura Geodésicas d”Ángulosinternos P/r
Euclides
Esférica
Lobachev.
k = 0
k =1
k = -1
Rectas
Arcos máx.
hipérbolas
d” =0
d” < 0
d” > 0
180º
> 180º
< 180º
2
< 2
> 2
π
π
π
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s
dsd
¿ ?
α
β
γ
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Geometría Gravitación
Desviación de Euclides Masas
Curvatura(s) Densidad de materia y energía
µνµνπT
cG
G2
8=
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Galaxias 105 años-luz
Grupos de galaxias 106 a-l
Cúmulos 107 a-l
Supercúmulos 10 8 a-l
Paredes 109 a-l
Universo Observable 30. 109 a-l
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PRINCIPIO COSMOLÓGICO
Uniformidad de la materia y energía
Equivalencia de puntos y direcciones
• Distribución de galaxias
• Observación de la RCF
Relativid
adE
c. de Ein stein
GEOMETRÍA UNIFORME
¿ k ?
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k = 0
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k = 1
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EL PESO DEL PREJUICIO
k = 1
Criterios estéticos
Ilusión de nuevos comienzos k = 1
k = -1 Criterios estéticos
k = 0 Simplicidad,Naturalidad
Inestabilidad de
OpciónNi Si Ni No
k = 0
k = -1
Incipiente evidenciaobservacional < 1Ω
Ω
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GEORGE GAMOW
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Arno Penzias y Robert Wilson (1965)
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t ≅ 1 seg T ≅ 1010 ºK <3000.000 años > 4000 ºK
t >3000.000 años T< 4000 ºK
hoy T = 2,7 ºK
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θ10º
1º
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n = 412 fotones/cm3
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∑∞
=
=0
)sen()(n
n Lxn
axyπ
L
∑=ml
lmml Yay
,, ),(),( φθφθ
y
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ESPECTRO DE POTENCIA DE LAS FLUCTUACIONES
∑=∆ml
lmlm YaT
,
),(),( φθφθ
∑=m
lml aC 2
lπθ ≈
lCMODELOS
TEÓRICOSPARÁMETROS
DEL UNIVERSO:k
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0=l
TEMPERATURA DE LA RCF
TÉRMINO MONOPOLAR
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TEMPERATURA DE LA RCFTÉRMINO DIPOLAR
mKT
l
353,3
1
=∆=
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TEMPERATURA DE LA RCF
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George Smoot
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TEMPERATURA DE LA RCF
20≈l
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20=l
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VIENDO EL SONIDO DEL UNIVERSO(Fluctuaciones en ) º1≤θ
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EL TONO FUNDAMENTAL
º1≈θ
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Armónicos
º1<θ
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Cobertura: 2% cielo Resolución: 0,2º35 veces COBE
Boomerang
KT µ70≈∆
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...Y EL “k” GANADOR ES...
MODELOS TEÓRICOS
PICO EN LAS FLUCTUACIONES
20
20
1
200
RH
kl
+=
200≅l ¡ k = 0 !!
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k = 0¿Por qué?
R.- INFLACIÓN
t
1 1
t tExpansión normal Expansión inflacionaria
ΩΩ
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CONSECUENCIAS
DINÁMICA
MATERIA-ENERGÍAGEOMETRÍA
120
20
=−Ω+ΩRHk
vm
k = 0
3,0=Ωm
7,0=Ωv
!Expansiónacelerada !!
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ALGUNAS CONCLUSIONES LEVEMENTE FINALES
k = 03271098,1cmgr
crit−×=ρ
1090 fotones
1080 Protones y neutrones
Materia OscuraEnergía del vacío
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LA MEGATORTA DEL UNIVERSO
Elementos pesados0,1%
Energía del vacío65%
Materia oscura fría30%
Bariones oscuros5%
Bariones luminosos0,5%
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H0 = 65 Km/seg Mpc
k = 0
3271098,1cmgr
crit−×=ρ
t0 = 14.109 años
1090 fotones
1080 Protones y neutrones
Inflación
Espectro (gaussiano de perturbaciones)
Formación de estructuras por inestabilidad gravitacional
Expansión asintóticamente exponencial
ALGUNAS CONCLUSIONES LEVEMENTE FINALES
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INTERROGACIONES, REFLEXIONES Y ESPECULACIONES
Modelo preciso de Inflación MAP (2000) - Planck (2007)
¿? Naturaleza de materia oscuraMACHOS
WIMPS
¿?
¿?Naturaleza de la energía del vacío
• vac tan pequeña
• Teo tan grande
• vac ´mat ≈
¿? Naturaleza del Big Bang TC G: CUERDAS M-BRANAS LOOP-G
ΩΩ
Ω Ω
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