# Dark Energy 2: DE and Large Scale Structure

Anuncio Dark Energy 2:
DE and Large Scale Structure
GUASA 2015
Octavio Valenzuela
IA-UNAM
Cosmic Large Scale
Structure
Ecuaciones que describen la evoluci&oacute;n del
Universo
Ec. de
Friedmann
Ec. De
aceleraci&oacute;n
de la
expansi&oacute;n
Par&aacute;metro de Hubble
Tasa de expansi&oacute;n del Universo
d =a(t)x, a(t): factor de escala
Historia de la Energ&iacute;a Oscura
Dic. 1997: Contradicciones en nuestro entendimiento
del Universo!
Edad del Universo &lt; a la de c&uacute;mulos globulares
- Poca estructura a peque&ntilde;a escala
-
Universo plano, compuesto de materia (normal + oscura fr&iacute;a),
distribuci&oacute;n de perturbaciones iniciales independiente de la escala.
El modelo ten&iacute;a que cambiar o extenderse!
una de las hip&oacute;tesis al menos-“plano,” “fr&iacute;a,” “invariante de escala,” o quiz&aacute;s “de materia.”
Ecuaciones de campo de Einstein aplicadas al Universo como
un todo: cambia con el tiempo, hay evoluci&oacute;n:
Din&aacute;mica
Debemos
estudiar la historia
de expansi&oacute;n
para acotar la
geometr&iacute;a si
conocemos
el contenido:
Materia?
⇔
Geometr&iacute;a
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=
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
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
&iquest;Cu&aacute;l puede ser la raz&oacute;n de la aceleraci&oacute;n?
Algo cuya contribuci&oacute;n a la densidad de energ&iacute;a no
se diluya: Llamemoslo Energ&iacute;a Oscura
&iquest;Qu&eacute; tan importante es el nuevo factor?
tama&ntilde;o
aceleraci&oacute;n
desaceleraci&oacute;n
&gt; Big Bang &lt;
tiempo
Informaci&oacute;n independiente de Curvatura?
Ec. de Friedmann
que tanto se aleja de
modelo plano:
Conociendo Ω, restringimos la geometr&iacute;a:
La materia (ordinaria + oscura) contribuyen con Ω ≈ 0.3,
curvature negativa. Suma de &aacute;ngulos en tri&aacute;ngulos &lt; 180o.
en el plasma primordial)
400,000 a&ntilde;o despu&eacute;s del Big Bang
400,000 a&ntilde;os luz. Horizonte ac&uacute;stico
depende cosmolog&iacute;a, bariones, fotones
ΩTot = [θpeak(deg)]-1/2.
Observaci&oacute;n: 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 .
&iquest;What is the DE Nature?
•
Cosmological Constant?
•
Other?
•
How can we test it?
•
Stay tuned
Modelo de deSitter: Inflaci&oacute;n c&oacute;smica
ρ=Λ= cte, plano
● Ec de Friedman: 3H2= Λ, H=cte
●
Horizont dH =
Aceleraci&oacute;n restringe la relaci&oacute;n entre presi&oacute;n y densidad
del Universo es decir
w=
/
w &lt; -1/3 para que haya aceleraci&oacute;n
&iquest;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 &amp; Zel’dovich (1970); Peebles &amp; Yu (1970); Doroshkevitch, Sunyaev &amp; Zel’dovich (1978)
Cooray, Hu, Huterer &amp; Joffre (2001); Eisenstein (2003); Seo
&amp; Eisenstein (2003); Blake &amp; Glazebrook (2003); Hu &amp; 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 ) &gt; 0 at small r , then galaxies are clustered, whereas if ξ (r ) &lt; 0,
they tend to avoid each other.
Sparke &amp; 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&lt;=10h−1 Mpc, the 2-point
correlation function takes roughly the form
ξ (r ) ≈ (r/r0)−γ , γ &gt; 0
• r0 is the correlation length
• When r &lt; 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 &amp; 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&gt;~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| &lt; 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 !&quot; 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?
•
•
What is Dark energy? We&acute;ve got some tools,
more yet to come. Thursday and Friday.
Conclusions
•
Crisis in Cosmology at late 90&acute;s triggered a
detailed study of cosmic expansion history
•
Unexpected: SNIa —&gt; 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&acute;t know the physics behind
El crecimiento de la estructura c&oacute;smica depende de la
naturaleza de la energ&iacute;a oscura
efecto de la expansi&oacute;n del universo
&iquest;Qu&eacute; Hacer?
&quot;
&quot;
&quot;
Medir con gran precisi&oacute;n:
La historia de expansi&oacute;n del Universo, se acelera
siempre igual o cambia esta aceleraci&oacute;n? (BAO)
El crecimiento de la estructura: como se agregan a la
estructura las galaxias (Redshift space distortion)
Conclusiones
•
La naturaleza de la Energ&iacute;a Oscura es un reto
•
Las mediciones recientes sugieren que es consistente con una
constante pero grandes inconsistencias sugieren m&aacute;s elementos
•
La opci&oacute;n de una nueva teor&iacute;a de gravedad suena atractiva pero es
mucho m&aacute;s compleja de lo que se esperaba, no existe una opci&oacute;n
completa, aunque es un reto muy grande
•
Un nuevo campo podr&iacute;a representar a esta energ&iacute;a oscura, pero
puede afectar fuertemente el crecimiento de estructura.
•
El la siguiente d&eacute;cada los nuevos catastros de galaxias definir&aacute;n
fuertes restricciones a las explicaciones
•
Universo Ec de Friedmann, de Sitter
•
Historia en 1997
•