Dark Energy 2: DE and Large Scale Structure

Dark Energy 2:
DE and Large Scale Structure
GUASA 2015
Octavio Valenzuela
IA-UNAM
Cosmic Large Scale
Structure
Ecuaciones que describen la evolución del
Universo
Ec. de
Friedmann
Ec. De
aceleración
de la
expansión
Parámetro de Hubble
Tasa de expansión del Universo
d =a(t)x, a(t): factor de escala
x: coordenada comovil
Historia de la Energía Oscura
Dic. 1997: Contradicciones en nuestro entendimiento
del Universo!
Edad del Universo < a la de cúmulos globulares
- Poca estructura a pequeña escala
- Densidad promedio
-
Paradigma teórico motivado por simplicidad:
Universo plano, compuesto de materia (normal + oscura fría),
distribución de perturbaciones iniciales independiente de la escala.
El modelo tenía que cambiar o extenderse!
una de las hipótesis al menos-“plano,” “fría,” “invariante de escala,” o quizás “de materia.”
Ecuaciones de campo de Einstein aplicadas al Universo como
un todo: cambia con el tiempo, hay evolución:
Dinámica
Debemos
estudiar la historia
de expansión
para acotar la
geometría si
conocemos
el contenido:
Materia?
⇔
Geometría
Expressing Distances in an Expanding Universe
The geometry and expansion rate of the Universe effects angular sizes and distances
measured. Integrate over components of RW metric.
DH = c/Ho ! Hubble Distance (distance light travels in Hubble time, tH = 1/Ho)
DC=
! Radial Co-moving Distance
DM = DC (flat) ! Transverse Co-moving Distance, differs for curved space (see Hogg
2000)
DA = L(proper length)/θ(angular size) = DM/(1+z) ! Angular Distance
DL = sqrt (L/4π*flux) = DM(1+z) = DA(1+z)2 ! Luminosity Distance
If Λ = 0 and flat geometry, then
DL = 2c/Ho [z/(G+1)] {1+[z/(G+1)]} where G = (1 + z)1/2
See Ned Wright’s Javascript Cosmology Calculator for DL for different
cosmologies:
http://www.astro.ucla.edu/~wright/CosmoCalc.html
E(z)=\sqrt{\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_\Lambda}
Angular diameter distance vs z
(plotting DA/DH where DA=L/θ)
Luminosity distance vs z
(plotting DL/DH)
DH=c/Ho= 3000h-1Mpc
At high z, angular diameter distance is
such that 1 arcsec is about 5 kpc.
flat, Λ=0 – solid
open, Λ=0 – dotted
flat, non-zero Λ - dashed
(from Hogg 2000 astro-ph 9905116)
Now we need a standard candle or ruler
Type Ia Supernovae
Brightness
Brightness tells us
distance away DL
(lookback time t)
Redshift tells us the
expansion factor a
Time after explosion
If we know
the light curve slope
we can estimate the
maximum brightness
sqrt(L/(4Pi Brightness))
14
Four months in the life of a SN Ia
On the Rise:
Age:
-6 days
Maximum
Powered by radioactivity
Vejecta=10-20,000 km/s
+26 days
+47 days
+102 days
Elements produced=
Fe,Co,Ni,Si,Ca
Color Images of SNe Ia
Fainter
High Redshift SN and Expansion History: Acceleration
Just recently
1.0
Found: Hubble,
Followed: Hubble
Dark Matter Dominated
Found: Ground,
Followed: Hubble
Dark Energy Dominated
Relative Brightness (Δm)
Constant acceleration
0.5
Acceleration/
Deceleration
0.0
Freely expanding
-0.5
Constant deceleration
Brighter
-1.0
0.0
present
0.5
1.0
Redshift z
1.5
2.0
past
The Accelerating Universe
By 1998 two teams measured ~100 SNe Ia
Surprise! The Universe is accelerating, propelled by dark energy.
High-z
SCP
¿Cuál puede ser la razón de la aceleración?
Algo cuya contribución a la densidad de energía no
se diluya: Llamemoslo Energía Oscura
¿Qué tan importante es el nuevo factor?
tamaño
aceleración
desaceleración
> Big Bang <
tiempo
Información independiente de Curvatura?
Ec. de Friedmann
Parametro de densidad Ω
que tanto se aleja de
modelo plano:
Conociendo Ω, restringimos la geometría:
La materia (ordinaria + oscura) contribuyen con Ω ≈ 0.3,
curvature negativa. Suma de ángulos en triángulos < 180o.
Radiación de fondo proporciona una
regla estándar (Velocidad del sonido
en el plasma primordial)
400,000 año después del Big Bang
400,000 años luz. Horizonte acústico
depende cosmología, bariones, fotones
ΩTot = [θpeak(deg)]-1/2.
Observación: θpeak = 1o.
flat
El universo es plano:
positively
curved
negatively
curved
ΩTot = 1 .
[Miller et al.; de Bernardis et al; WMAP]
Concordance:
ΩΜ = 0.3,
ΩΛ = 0.7 .
¿What is the DE Nature?
•
Cosmological Constant?
•
Other?
•
How can we test it?
•
Stay tuned
Modelo de deSitter: Inflación cósmica
ρ=Λ= cte, plano
● Ec de Friedman: 3H2= Λ, H=cte
● edad=2/(3H)
●
Horizont dH =
3c*edad = 2/H, constante!!
Aceleración restringe la relación entre presión y densidad
del Universo es decir
la ecuación de estado
w=
/
w < -1/3 para que haya aceleración
¿Is w, constant? We must accurately measure the expansion history?
PPProbing DE via cosmology
• We “see” dark energy through its effects on the expansion of the
universe: • Three (3) main approaches – Standard candles • measure dL (integral of H-1) – Standard rulers • measure dA (integral of H-1) and H(z) – Growth of fluctuations. • Crucial for testing extra ! components vs modified gravity. Standard Ruler
• Suppose we had an object whose length we know as a function of
cosmic epoch. • By measuring the angle (⍬) subtended by this ruler (✗) as a function of
redshift we map out the angular diameter distance dA • By measuring the redshift interval (△z) associated with this distance we
map out the Hubble parameter H(z) Ideal Properties of Standard Ruler
To get competitive constraints on Dark Energy, we need to see
changes in H(z) at ~1 % level, this would give us statistical errors in
DE equation of State to ~10%
We need to be able to calibrate the ruler accurately over most of
the age of the Universe.
We need to be able to measure the ruler over much of the volume
of the Universe
We need to be able to make independent accurate measurements
of the ruler
Where do we find such a ruler?
Individual Cosmological objects will probably never be uniform
enough.
Use Statistics of large scale structure of matter and
radiation. (aka. if we stick with early times and large scale, perturbative
treatment of the Universe will still be valid, and the calculations will be under control.)
Preferred length scales arise from Physics of early Universe and
imprinted on the distribution of matter and radiation
Sunyaev & Zel’dovich (1970); Peebles & Yu (1970); Doroshkevitch, Sunyaev & Zel’dovich (1978)
Cooray, Hu, Huterer & Joffre (2001); Eisenstein (2003); Seo
& Eisenstein (2003); Blake & Glazebrook (2003); Hu & Haiman (2003)
Slide from Shirley Ho
Non-Linear
Linear
Cartoon Picture
• At early times the universe was hot, dense and ionized. Photons and matter were
tightly coupled by Thomson scattering. – Short m.f.p. allows fluid approximation. • Initial fluctuations in density and gravitational potential drive acoustic waves in the
fluid: compressions and rarefactions. • These show up as temperature fluctuations in the CMB [harmonic wave] The 2-point correlation function
• The two-point correlation function ξ (r ): One way to describe the
tendency of galaxies to cluster together
• If we make a random choice of two small volumes V1 and V2, and the
average spatial density of galaxies is n per cubic megaparsec,
then the chance of finding a galaxy in V1 is just nV1.
• If galaxies tend to clump together, then the probability that we then
also have a galaxy in V2 will be greater when the separation r12
between the two regions is small.
• We write the joint probability of finding a galaxy in both volumes as
if ξ (r ) > 0 at small r , then galaxies are clustered, whereas if ξ (r ) < 0,
they tend to avoid each other.
Sparke & Gallagher 2007
• We generally compute ξ (r ) by estimating the distances of galaxies from
their redshifts, making a correction for the distortion introduced by peculiar
velocities.
• Observationally it has been found that on scales r<=10h−1 Mpc, the 2-point
correlation function takes roughly the form
ξ (r ) ≈ (r/r0)−γ , γ > 0
• r0 is the correlation length
• When r < r0, the probability of finding one galaxy within radius r of another
is significantly larger than for a strictly random distribution.
•
Since ξ (r ) represents the deviation from an average density, it must at
some point become negative as r increases.
Sparke & Gallagher 2007
The two-point correlation function
ξ (r ) for galaxies in the 2dF survey.
•
Ellis et al. 2002, MNRAS
The correlation length r0 ≈ 5h−1 Mpc
– 6h−1 Mpc for the ellipticals,
which are more strongly clustered,
– smaller for the star-forming galaxies
•
The slope γ ≈ 1.7
•
For r 0>~50h−1 Mpc, which is roughly the
size of the largest wall or void features, ξ
(r ) oscillates around zero: the galaxy
distribution is fairly uniform on larger
scales.
The correlation function is not very useful for describing the one-dimensional filaments or two-dimensional walls.
If our volume V1 lies in one of these, the probability of finding a galaxy in V2 is high only when it also lies within the
structure.
Since ξ (r ) is an average over all possible placements of V2, it will not rise far above zero once the separation r
Exceeds the thickness of the wall or filament (use of three-point and four-point correlation functions?)
We do not yet have a good statistical method to describe the strength and prevalence of walls and filaments.
Power spectrum
• The Fourier transform of ξ (r) is the power spectrum P(k)
so that small k corresponds to a large spatial scale.
• Since ξ (r ) is dimensionless, P(k) has the dimensions of a volume.
• The function sin(kr)/kr is positive for |kr| < π, and it oscillates with
decreasing amplitude as kr becomes large
•
so, very roughly, P(k) will have its maximum when k−1 is close to the
radius where ξ (r ) drops to zero.
What are we waiting for?
• Find a tracer of the mass density field and compute
its 2-point function.
• Locate the features in the above corresponding to the
sound horizon, s.
• Measure the !" and !z subtended by the sound
horizon, s, at a variety of redshifts, z.
• Compare to the value at z~103 to get dA and H(z) Is this our Universe? Do you believe it?
Conclusions
•
Baryonic Acoustic Oscillations provide an
accurate standard ruler
•
How good is that?
•
More information? Redshift Space distortion?
•
What is Dark energy? We´ve got some tools,
more yet to come. Thursday and Friday.
Conclusions
•
Crisis in Cosmology at late 90´s triggered a
detailed study of cosmic expansion history
•
Unexpected: SNIa —> Universe is not slowing
down instead is accelerating, but only since
recently
•
The agent may contribute with a constant in Energy
density and dominates the Energy inventory.
•
We don´t know the physics behind
El crecimiento de la estructura cósmica depende de la
naturaleza de la energía oscura
efecto de la expansión del universo
¿Qué Hacer?
"
"
"
Medir con gran precisión:
La historia de expansión del Universo, se acelera
siempre igual o cambia esta aceleración? (BAO)
El crecimiento de la estructura: como se agregan a la
estructura las galaxias (Redshift space distortion)
Conclusiones
•
La naturaleza de la Energía Oscura es un reto
•
Las mediciones recientes sugieren que es consistente con una
constante pero grandes inconsistencias sugieren más elementos
•
La opción de una nueva teoría de gravedad suena atractiva pero es
mucho más compleja de lo que se esperaba, no existe una opción
completa, aunque es un reto muy grande
•
Un nuevo campo podría representar a esta energía oscura, pero
puede afectar fuertemente el crecimiento de estructura.
•
El la siguiente década los nuevos catastros de galaxias definirán
fuertes restricciones a las explicaciones
•
Universo Ec de Friedmann, de Sitter
•
Historia en 1997
•
SNIa calibradores, aceleración,
•
Energía Oscura: Como se estudia? Expansión, crecimiento de
estructura
•
Naturaleza: Campo/partícula, Gravedad, Cte: Vacío
•
Futuros Sondeos