Acoustic Waves in the Universe as a Powerful Cosmological Probe
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Transcript of Acoustic Waves in the Universe as a Powerful Cosmological Probe
Acoustic Waves in the Universe as a Powerful
Cosmological Probe
Eiichiro KomatsuDepartment of Astronomy, UT
Acoustic Seminar, March 2, 2007
Our Universe Is Old
The latest determination of the age of our Universe is: 13.730.16 billion years
How was it determined? In essence, (time) = (distance)/c was used. “Distance” to what??
It must be a distance to the farthest place we could reach. The Rule: “Farthest Place” = “Earliest Epoch”
For the errorbar to make sense, obviously it must be earlier than 160 million years after the Big Bang.
So, what is the earliest epoch that we can see directly?
The Most Distant Galaxy?
Going Farther…
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How far have we reached?
Our Universe is 13.73 billion years old.
The most distant galaxy currently known is seen at 800 million years after the Big Bang. 1/17 of the age of t
he Universe today
How far can we reach? Galaxies cannot be used to determine the age
of the Universe accurately. Distant galaxies are very faint and difficult to find.
Fundamental “flaw” in this method: galaxies cannot be as old as the Universe itself --- after all, it takes some time (~hundreds of millions of years) to form galaxies.
So, is 800 million years after the Big Bang the farthest place we can ever reach?NO!
Night Sky in Optical (~0.5nm)
Night Sky in Microwave (~1mm)
Full Sky Microwave Map
Penzias & Wilson, 1965Uniform, “Fossil” Light from the Big Bang
-Isotropic (2.7 K everywhere)
-Unpolarized
Galactic CenterGalactic Anti-center
A. Penzias & R. Wilson, 1965
CMBT = 2.73 K
Helium SuperfluidityT = 2.17 K
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COBE/DMR, 1992
Isotropic?
CMB is anisotropic! (at the 1/100,000 level)
COBE to WMAPCOBE
WMAP
COBE1989
WMAP2001
[COBE’s] measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation.
Press Release from the Nobel Foundation
CMB: The Most Distant Light
CMB was emitted when the Universe was only 380,000 years old. WMAP has measured the distance to this epoch. From (time)=(distance)/c we obtained 13.73 0.16 billion years.
Use Ripples in CMB to Measure Composition of the Universe
The Basic Idea: Hit it and listen to the cosmic sound. Analogy: Brass and ceramic can be discriminated by hitting them and li
stening to the sound created by them. We can use sound waves to determine composition.
When CMB was emitted the Universe was a dense and hot soup of photons, electrons, protons, Helium nuclei, and dark matter particles. Ripples in CMB propagate in the cosmic soup: the pattern of the ripple
s, the cosmic sound wave, can be used to determine composition of the Universe!
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Composition of Our Universe Determined by WMAP
Dark Energy
Ordinary Matter
Dark Matter
76%
20%
4%
Mysterious “Dark Energy” occupies 75.93.4% of the total energy of the Universe.
How do we “hear” the cosmic sound from this?
Do the Fourier Analysis: The Angular Power Spectrum
CMB temperature anisotropy is very close to Gaussian; thus, its spherical harmonic transform, alm, is also Gaussian.
Since alm is Gaussian, the power spectrum:
completely specifies statistical properties of CMB.
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Cl = almalm*
Cosmic Sound Wave!
What the Sound Wave Tells Us
Distance to z~1100
Baryon-to-Photon Ratio
Matter-Radiation Equality Epoch
Dark Energy/New Physics?
R. Sachs and A. Wolfe, 1967
•SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONSEQUATIONS TO THE FIRST ORDER IN PERTURBATIONS
Introduce temperature fluctuations, =T/T:
Expand the Boltzmann equation to the first order:
where
describes the Sachs-Wolfe effect: purely GR-induced fluctuations.
For metric perturbations in the form of:
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ds2 = a2 −1+ h00( )dτ 2 + δ ij + hij( )dx idx j[ ]
the Sachs-Wolfe terms are given by
where is the directional cosine of photon propagations.
Newtonian potential Curvature perturbations
1. The 1st term = gravitational redshift
2. The 2nd term = integrated Sachs-Wolfe effect
h00/2
hij/2
(higher T)
Sound Waves From Hydrodynamical Perturbations
When coupling is strong, photons and baryons move together and behave as a single, perfect fluid.
When coupling becomes less strong, they behave as an imperfect fluid with viscosity.
So, the problem can be formulated as “hydrodynamics”. (cf S-W effect was pure GR.)
Collision term describing coupling between photons and baryons via electron scattering.
Boltzmann to Hydrodynamics
Multipole expansion
Energy density, Velocity, StressEnergy density
Velocity
Stress
Photons
f2=9/10 (no polarization), 3/4 (with polarization)
A = -h00/2, H = hii/2
C=Thomson scattering optical depth
CONTINUITY
EULER
Photon-baryon coupling
Baryons
Cold Dark Matter
Approximate Equation System in the Strong Coupling Regime
SOUND WAVE!
A Big, Big Challenge
Let’s face it: “WMAP has done a great job in determining composition of our Universe very accurately, but…” We don’t really understand the nature of dark energy
or dark matter. They occupy 96% of the total energy in our Universe!
Even the most optimistic cosmologists would not dare to say, “we understand our Universe”. Definitely not.
The next frontier: What is the nature of dark energy and dark matter?
A Holy Grail: Go Even Farther Back…
We cannot use CMB to probe the epoch earlier than 380,000 years after the Big Bang directly. Photons were scattered by electrons so frequently tha
t the Universe was literally “foggy” to photons. We would need to stop relying on photons (EM
waves). What else? Neutrinos can probe the epoch as early as a second a
fter the Big Bang. Gravity Waves: the ultimate probe of the earliest mom
ent of the Universe.
Go Farther!
CMB
Neutrino
Gravity Wave
Summary & Conclusions CMB offers the earliest and most precise picture of the Universe th
at we have today. A wealth of cosmological information, e.g.
The age of the Universe = 13.73 billion years Composition: DE (76%), DM (20%), Ordinary Mat. (4%)
CMB has limitations. It does not tell us much about the nature of the most dominant energy comp
onents in the Universe: Dark Energy (DE) and Dark Matter (DM) Expect some news on DM from the Large Hadron Collider (LHC) next year. DE is harder to do.
Go beyond CMB. Neutrinos! (Very low energy: 1.94K -> hard to detect) Gravity waves! The ultimate cosmological probe.