Acoustic Waves in the Universe as a Powerful
Cosmological Probe Acoustic Waves in the Universe as a Powerful
Cosmological Probe
Eiichiro Komatsu
Department of Astronomy, UT Acoustic Seminar, March 2, 2007
Eiichiro Komatsu
Department of Astronomy, UT
Acoustic Seminar, March 2, 2007
Our Universe Is Old Our Universe Is Old
The latest determination of the age of our Uni verse 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 reac h. The Rule: “Farthest Place” = “Earliest Epoch”
For the errorbar to make sense, obviously it must be ear lier than 160 million years after the Big Bang.
So, what is the earliest epoch that we can see directly?
The latest determination of the age of our Uni verse 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 reac h. The Rule: “Farthest Place” = “Earliest Epoch”
For the errorbar to make sense, obviously it must be ear lier than 160 million years after the Big Bang.
So, what is the earliest epoch that we can see directly?
The Most Distant Galaxy?
The Most Distant Galaxy?
Going Farther…
Going Farther…
QuickTime™ and a YUV420 codec decompressor are needed to see this picture.
How far have we reached?
How far have we reached?
Our Universe is 1 3.73 billion years o ld.
The most distant g alaxy currently kno wn is seen at 800 million years after t he Big Bang.
1/17 of the age of t he Universe today
Our Universe is 1 3.73 billion years o ld.
The most distant g alaxy currently kno wn is seen at 800 million years after t he Big Bang.
1/17 of the age of t
he Universe today
How far can we reach?
How far can we reach?
Galaxies cannot be used to determine the age o f the Universe accurately.
Distant galaxies are very faint and difficult to find.
Fundamental “flaw” in this method: galaxies can not be as old as the Universe itself --- after all, it takes some time (~hundreds of millions of year s) to form galaxies.
So, is 800 million years after the Big Bang th e farthest place we can ever reach?
Galaxies cannot be used to determine the age o f the Universe accurately.
Distant galaxies are very faint and difficult to find.
Fundamental “flaw” in this method: galaxies can not be as old as the Universe itself --- after all, it takes some time (~hundreds of millions of year s) to form galaxies.
So, is 800 million years after the Big Bang th e farthest place we can ever reach?
NO!
Night Sky in Optical (~0.5nm)
Night Sky in Optical (~0.5nm)
Night Sky in Microwave (~1mm)
Night Sky in Microwave (~1mm)
Full Sky Microwave Map Full Sky Microwave Map
Penzias & Wilson, 1965
Uniform, “Fossil” Light from the Big Bang
- Isotropic (2.7 K everywhere) - Unpolarized
Galactic Center Galactic Anti-
center
A. Penzias & R. Wilson, 1965
A. Penzias & R. Wilson, 1965
CMB
T = 2.73 K Helium Supe
rfluidity
T = 2.17 K
QuickTime™ and a Sorenson Video decompressor are needed to see this picture.
COBE/DMR, 1992 COBE/DMR, 1992
Isotropic?
CMB is anisotropic! (at th
e 1/100,000 level)
COBE to WMAP COBE to WMAP
COBE
WMAP
COBE 1989
WMAP 2001
[COBE’s] measurements als o marked the inception of co smology as a precise science . It was not long before it was followed up, for instanc e by the WMAP satellite, whi ch yielded even clearer imag es of the background radiati on.
Press Release from th e Nobel Foundation
CMB: The Most Distant Light CMB: The Most Distant Light
CMB was emitted when the Universe was only 380,000 years ol d. 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
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 lis tening 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 sou p of photons, electrons, protons, Helium nuclei, and dark matter particles.
Ripples in CMB propagate in the cosmic soup: the pattern of the ripples, the cosmic sound wave, can be used to determine composition of the U niverse!
The Basic Idea: Hit it and listen to the cosmic sound.
Analogy: Brass and ceramic can be discriminated by hitting them and lis tening 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 sou p of photons, electrons, protons, Helium nuclei, and dark matter particles.
Ripples in CMB propagate in the cosmic soup: the pattern of the ripples, the cosmic sound wave, can be used to determine composition of the U niverse!
QuickTime™ and a
Sorenson Video decompressor are needed to see this picture.
Composition of Our Universe Determined by WMAP
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?
How do we “hear”
the cosmic sound from this?
Do the Fourier Analysis:
The Angular Power Spectrum Do the Fourier Analysis:
The Angular Power Spectrum
CMB temperature anisotropy is very close to Gaussian; thus, its spherical harmonic transf orm, a
lm, is also Gaussian.
Since a
lmis Gaussian, the power spectrum:
completely specifies statistical properties of CMB.
CMB temperature anisotropy is very close to Gaussian; thus, its spherical harmonic transf orm, a
lm, is also Gaussian.
Since a
lmis Gaussian, the power spectrum:
completely specifies statistical properties of CMB.
€
C l = a lm a lm *
Cosmic Sound Wave!
Cosmic Sound Wave!
What the Sound Wave Tells Us 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 R. Sachs and A. Wolfe, 1967
•SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN
EQUATIONS TO THE FIRST ORDER IN PERTURBATIONS EQUATIONS 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:
€
ds
2= a
2[ ( −1+ h
00) dτ
2+ ( δ
ij+ h
ij) 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 Hydrodynami cal Perturbations
Sound Waves From Hydrodynami cal Perturbations
When coupling is strong, photons and baryons move together and behave a s 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.)
When coupling is strong, photons and baryons move together and behave a s 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 Boltzmann to Hydrodynamics
Multipole expansion
Energy density, Velocity, Stress
Multipole expansion
Energy density, Velocity, Stress
Energy density Velocity
Stress
Photons 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 Baryons
Cold Dark Matter
Approximate Equation System in the Strong Coupling Regime
Approximate Equation System in the Strong Coupling Regime
SOUND WAVE!
A Big, Big Challenge A Big, Big Challenge
Let’s face it: “WMAP has done a great job in det ermining composition of our Universe very accur ately, but…”
We don’t really understand the nature of dark energy or dark matter. They occupy 96% of the total energy i n 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 ener gy and dark matter?
Let’s face it: “WMAP has done a great job in det ermining composition of our Universe very accur ately, but…”
We don’t really understand the nature of dark energy or dark matter. They occupy 96% of the total energy i n 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 ener
gy and dark matter?
A Holy Grail: Go Even Farther Back…
A Holy Grail: Go Even Farther Back…
We cannot use CMB to probe the epoch earlier t han 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.
We cannot use CMB to probe the epoch earlier t han 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!
Go Farther!
CMB
Neutrino
Gravity Wave
Summary & Conclusions Summary & Conclusions
CMB offers the earliest and most precise picture of the Universe that 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.
CMB offers the earliest and most precise picture of the Universe that 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.
