1. Cosmology with Longhorn High-z Galaxy Surveys: HETDEX & CIP
PI: Gary Melnick (SAO)
HETDEX
l= mm, z= (Lya)
l=2.5-5mm, z=3-6.5 (Ha)
Dan Jaffe
Karl Gebhardt
Volker Bromm
Eiichiro Komatsu
Gary Hill
Phillip McQueen
Karl Gebhardt

2. The Big Picture: Four Questions in Cosmology
The nature of dark energy
What is it?
Modification to gravity? Another form of energy?
The physics of inflation
Did it happen at all?
If so, how did it happen? What powered inflation?
The origin of baryons
Physics of Baryogenesis?
The nature of dark matter
What are they? How many of them?

3. How much we don’t know about the universe
~10-34 sec Inflation Early Dark Energy
Log(Time)
<30,000 yrs Radiation Era Radiation
<8 billion yrs Matter Era Dark Matter
<now Dark Energy Era Late Dark Energy

4. The Proposal: High-z Galaxy Survey
The nature of (late) dark energy
Equation of state of dark energy
The physics of inflation
Spectrum of primordial fluctuations
The origin of baryons
Mass of neutrinos
The nature of dark matter
Mass of dark matter particles

5. Dark Energy Dark energy dominated the universe twice.
Very early time (~10-35 seconds)
Very late time (~6 billion years – today)
Fundamental ingredients in the Standard Model of Cosmology
Dark energy causes the universe to accelerate
This property defines dark energy, and this is why dark energy is not called “dark matter” – matter never accelerates the expansion of the universe.
Early acceleration – Inflation
Late acceleration – acceleration today (second inflation)

6. How to Accelerate the Universe
The second derivative of scale factor with respect to time must be positive.
Raychaudhuri Equation
P<-r/3 and/or L!

7. Example: de Sitter Universe
For more general cases, where P is different from –r, H(t) does depend on time, and the scale factor evolves quasi-exponentially:

8. Hubble’s Function: H(z)
The cosmological effects of dark energy are basically determined by the expansion rate as a function of redshift:
This function determines
Power Spectrum of Primordial Fluctuations
Growth Rate of Density Fluctuations
Distance-redshift Relations

9. Inflation: Generation of Primordial Fluctuations
QM + GR = A Surprise!
Particle Creation in Curved Space Time
Even in vacuum, an observer moving with acceleration detects a lot of particles!!
Not even GR: spacetime with uniform acceleration (no gravity still) is called “Rindler’s space”, and an observer in Rindler’s space detects particles.
A famous example is the Hawking Radiation
Curved spacetime around a black hole creates scalar particles with a black body spectrum. The black hole will eventually “evaporate” when particles carried away all the mass energy of the black hole.
Punch Line: Particles are also created in an accelerating universe.
Leonard Parker, “Particle Creation in Expanding Universes”, Physical Review Letters, 21, 562 (1968)

10. Particle Creation = Primordial Fluctuations
The particle creation causes spacetime to fluctuate.
Inflation generates primordial fluctuations in spacetime
Scalar modes create primordial density fluctuations.
Tensor modes create primordial gravitational waves.
Vector modes are not excited.
No primordial vorticity.
The amplitude of primordial fluctuations is proportional to Hubble’s function during inflation.
Therefore, precision measurements of the spectrum of primordial fluctuations enable us to determine the evolution of H(t) during inflation. This is the prime goal of Cosmic Inflation Probe.

11. CIP: Early Dark Energy
Scalar fields (whatever they are) are attractive dark energy candidates, as they can have negative pressure.

12. Observe Inflation
Inflation generates primordial fluctuations in spacetime.
(a) Fluctuations inherited in radiation
Cosmic Microwave Background
Temperature Anisotropy
Polarization Anisotropy
(b) Fluctuations inherited in matter
Dark Matter Distribution (Gravitational Lensing)
Galaxy Distribution (Redshift Surveys)
Gas Distribution (Lyman-alpha clouds)
(c) Fluctuations in spacetime itself
Primordial Gravitational Waves

13. V(phi) to P(k)
V(f)
V(f) f
V(f) f f
k3P(k) k

14. From Primordial Fluctuations to Observed Fluctuations
Primordial fluctuations in spacetime have nearly a “scale-invariant” spectrum; however, primordial density fluctuations do not.
Also, the evolution of density fluctuations is affected by the presence of radiation during the radiation era. The power spectrum of density fluctuations is therefore highly “scale-variant”.

15. P(k) of Density Fluctuations
Different wave-numbers probe different parts of H(t).
Thus, it probes the shape of V(f)
We need to cover many decades in wave-number to determine the shape of V(f)
Require a variety of probes.
HETDEX
CIP

16. Inhomogeneous
Homogeneous
INFLATION
x 100,000

17. The Current State-of-the-Art
V(f) f f f f

18. Toward “the” Inflation Model
What is necessary?
More accurate measurements of P(k)
Not just statistical error! Minimum systematic error
Sample more k-modes
One solution = A galaxy survey at high-z
Why high-z? Less non-linear power!
As the universe ages, gravitational effects distort initial power spectrum on increasingly larger scales
• At z=6, non-linear contribution at k=1 Mpc-1 is about 15%.

19. HETDEX: Late Dark Energy

20. Baryonic Features: The Standard Ruler
Eisenstein et al., ApJ 633, 560 (2005)

21. “Baryonic Oscillations” in P(k)
Baryon density fluctuations propagate through the universe before the decoupling epoch (z~1089)
The sound speed ~ the sound speed of relativistic fluid.
The baryonic sound wave could travel to a certain distance by the decoupling epoch, the sound horizon, at which baryonic density fluctuations are enhanced.
Sound horizon = Mpc determined from WMAP
Point: P(k) is the Fourier transform of the real space two-point correlation function (which was plotted in the previous slide)
the enhanced peak would be transformed into a sinusoidal oscillation in Fourier space: baryonic oscillations.

22. How to Use the Standard Ruler
We measure the correlation of galaxies on the sky.
Divide the sound horizon distance (which is known) by the angular separation of the baryonic feature. This gives the angular diameter distance, which is an integral of 1/H(z).
We also measure the correlation of galaxies along the line of sight in redshift space.
Divide the redshift separation of the baryonic feature by the sound horizon distance. This gives H(z) directly.
Therefore, the baryonic oscillations give both the angular diameter distance and H(z).

23. The Current State-of-the-Art
P/r
Seljak et al., PRD 71, (2005) [Baryonic oscillations not used]

24. Toward “the” DE Model One solution = A galaxy survey at high-z
Why high-z? Once again. Less non-linear power!

25. High Sensitivity Calls for Better Theory

26. Modeling Non-linearity: Analytical Approach

27. 512/h Mpc Box with 2563 particles
70 simulations are averaged (each takes ~ 8 hours)
Simulations done by Donghui Jeong
Z=6
Z=5
Z=4
Z=3
Z=2
Z=1

28. 256/h Mpc Box with 2563 particles
10 simulations are averaged
Z=6
Z=5
Z=4
Z=3
Z=2
Z=1

29. Redshift Space Distortion
Since we are measuring redshifts, the measured clustering length of galaxies in z-direction will be affected by peculiar velocity of galaxies.
This is the so-called “redshift space distortion”.
Angular direction is not affected at all by this effect.
In the linear regime, the clustering length in z-direction appears shorter than actually is.
This is not the “finger-of-god”! The finger-of-god is the non-linear effect.
z direction
angular direction
No peculiar motion
Peculiar motion

30. Work in Progress…
Z=5
Z=6
Z=4
Z=3
Z=2
Z=1

31. Work to be done (1): Non-linear Bias
The largest systematic error is the effect of galaxy bias on the shape of the power spectrum.
It is easy to correct if the bias is linear; however, it won’t be linear when the underlying matter clustering is non-linear.
How do we deal with it?

32. Non-linear Bias: Analytical Approach

33. Powerful Test of Systematics
Work to be done (2): Three-point Function

34. Parameter Forecast Takada, Komatsu & Futamase, astro-ph/0612374 HETDEX
CIP
CIP, in combination with the CMB data from Planck, will determine the tile and running to a few x 10-3 level!
The running predicted by a very simple inflationary model (a massive scalar field with self-interaction) predicts the running of ( ) x 10-3, which is not very far away from CIP’s sensitivity.
More years of operation, or a larger FOV may allow us to measure the running from the simplest inflationary models.
The limit on neutrino masses will be times better than the current limit.

35. Cosmic Inflation Probe Will Nail the Inflation Model
V(f) f f f f

36. HETDEX Will Nail the DE
P/r
Cosmological Const.
Gebhardt (2006)

37. Summary
High-z galaxy surveys are capable of addressing the most important questions in modern cosmology
What is dark energy?
What powered inflation?
UT surveys cover the largest range in redshift space (1.8<z<3.8 & 3<z<6.5). These two experiments are highly complementary in redshifts, and address two different (but potentially related) questions.
The nature of early & late dark energy.
Timeline?
HETDEX ~2009
CIP ~ Ask NASA HQ!