Cosmology with High-z Gal axy Survey
Eiichiro Komatsu
University of Texas at Austin Fermilab, May 8, 2006
HETDEX
•Gary Hill
•Phillip McQueen
•Karl Gebhardt
=0.34-0.57m,
z=1.8-3.8 (Ly ) =2.5-5m, z=3-6.5 (H)
PI: Gary Melnick (SAO)
•Dan Jaffe
•Karl Gebhardt
•Volker Bromm
•Eiichiro Komatsu
The Big Picture:
Four Questions in Cosmology
The nature of dark energy
What is it?
Modification to gravity? (e.g., brane world)
Another form of energy? (e.g., vacuum 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?
How much we don’t know about the universe
~10-34 sec Inflation Early Dark Energy
<30,000 yrs Radiation Era Radiation
<8 billion yrs Matter Era Dark Matter
<now Dark Energy Era Late Dark Energy
Log(Time)
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
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 caused 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)
How to Accelerate the Universe
The second derivative of scale factor wit h respect to time must be positive.
Raychaudhuri Equation
P<-/3 and/or !
Example: de Sitter Universe
For more general cases, where P is different
from –, H(t) does depend on time, and the
scale factor evolves quasi-exponentially:
Hubble’s Function: H(z)
Dark energy affects cosmology mainly t hrough the expansion rate as a function of redshift:
• This function determines
• Power Spectrum of Primordial Fluctuations
• (Approximately) Growth Rate of Density Fluct uations
• Distance-redshift Relations
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 “Rindl er’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 s pectrum. The black hole will eventually “evaporate” when particles carried away al l the mass energy of the black hole.
Punch Line: Particles are also created in an accelerating un iverse.
Leonard Parker, “Particle Creation in Expanding Universes”, Physical R eview Letters, 21, 562 (1968)
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 proport ional to Hubble’s function during inflation.
Therefore, precision measurements of the spectrum of primo rdial fluctuations enable us to determine the evolution of H(t) during inflation. This is the prime goal of Cosmic Inflation Probe.
CIP: Early Dark Energy
Scalar fields (whatever they are) are
attractive early dark energy candidates, as
they can have negative pressure.
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
V(phi) to
V()
P(k)
V()
V()
k k3P(k)
From Primordial
Fluctuations to Observed Fluctuations
Primordial fluctuations in spacetime have nearl y a “scale-invariant” spectrum; however, primor dial 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”.
P(k) of Density Fluctuations
Different wave-numbe rs probe different part s of H(t).
Thus, it probes the sha pe of V()
We need to cover ma ny decades in wave-n umber to determine th e shape of V()
Require a variety of pr obes.
HETDEX
CIP
INFLATION
Inhomogeneous Homogeneous
x 100,000
V(
)
The Current
State-of-the-Art
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%.
Achieving 1% accuracy drives the observing strategy
Science Drivers:
To best constrain inflation and overlap with CMB, need adequate statistics on scales from 1 Mpc to 100 Mpc
H is an ideal line due to its strength
Grating
CIP is stationed at L2 to achieve proper passive cooling.
HETDEX: Late Dark Energy
Baryonic Features: The Standard Ruler
Eisenstein et al., ApJ 633, 560 (2005)
“Baryonic Oscillations” in P(k)
Baryon density fluctuations propagate through the uni verse before the decoupling epoch (z~1089)
The sound speed ~ the sound speed of relativistic fluid.
The baryonic sound wave could travel to a certain dist ance by the decoupling epoch, the sound horizon, at which baryonic density fluctuations are enhanced.
Sound horizon = 147 +- 2 Mpc determined from WMAP
Point: P(k) is the Fourier transform of the real space t wo-point correlation function (which was plotted in the previous slide)
the enhanced peak would be transformed into a sinusoidal o scillation in Fourier space: baryonic oscillations.
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 th e line of sight in redshift space.
Divide the redshift separation of the baryonic feature by th e sound horizon distance. This gives H(z) directly.
Therefore, the baryonic oscillations give both th
e angular diameter distance and H(z).
The Current State-of-the-Art
Seljak et al., PRD 71, 103515 (2005) [Baryonic oscillations not us ed]
P/
Toward “the” DE Model
One solution = A galaxy survey at high-z
Why high-z? Once again. Less non-linear power!
HET
Mt. Fowlkes west Texas
Hobby-Ebery Telescope (9.
2m)
Goals for HETDEX
• HETDEX measures redshifts for about 1 mill ion LAEs from 2<z<4
•Wavelength coverage: 340-550 nm at R~800
• Baryonic oscillations determine H(z) and Da (z) to 1% and 1.4% in 3 redshift bins
• Constraints on constant w to about one per cent
• Tightest constraints on evolving w at z=0.4 (
to a few percent)
Ly- emitters as tracers
Properties of LAEs have been investigated through NB imaging
Most work has focused on z ~ 3 – 4, little is known at z ~ 2
Limiting flux densities ~few e-17 erg/cm2/s
They are numerous
A few per sq. arcmin per z=1 at z~3
But significant cosmic variance between surveys
5000 – 10000 per sq. deg. Per z=1 at z~3
Largest volume MUSYC survey still shows significant variance in 0.25 sq. deg ree areas
Bias of 2 – 3 inferred
Basic properties of LAEs would make them a good tracer if they could be detected with a large area integral field spectrograph units (IFUs)
Has the advantage of avoiding targeting inefficiency
VIRUS
Visible IFU Replicable Unit Spectrograph
Prototype of the industrial replication concept
Massive replication of inexpensive unit spectrograph cuts costs and development time
Each unit spectrograph
Covers 0.22 sq. arcmin and 340-550 nm wavelength range, R=850
246 fibers each 1 sq. arcsec on the sky
145 VIRUS would cover
30 sq. arcminutes per observation
Detect 14 million independent resolution elements per exposure
This grasp will be sufficient to obtain survey in ~110 nights
Using Ly- emitting galaxies as tracers, will measure the galaxy po wer spectrum to 1%
Prototype is in construction
Delivery in April
Layout of 145 IFUs w/ 1/9 fill
(20’ dia field) New HET wide field corrector FoV
0.22 sq. arcmin
Layout with 1/9 fill factor is optimized for HETDEX
IFU separation is smaller than non-linear scale size
LAEs are very numerous so no need to fill-in – want to maximize area (HETD EX is sampling variance limited)
Well-defined window function
Dithering of pointing centers removes aliasing
Experimental Requirements
A LAE DE survey reaching <1% precision requires:
large volume to average over sample variance
200-500 sq. degrees and z ~ 2
this is 6-15 Gpc3 at z~2-4
surface density ~3000 per sq. degree per z=1; ~1 M galaxies
LAEs have 18,000 /sq. deg./z=1 at line flux ~1e-17 erg/cm2/s
only require a fill factor of ~1/9 to have sufficient statistics
so we can trade fill factor for total area
lowest possible minimum redshift (bluest wavelength coverage)
z = 1.8 at 3400 A is a practical limit
ties in well with high redshift limit of SNAP and other experiments
These science requirements determined the basic specifi
cations of VIRUS
Status of HETDEX
• The prototype VIRUS unit is being built and will be on the McDonald 2.7m in Aug 2006, wit h 50 night observing campaign
• Pilot run on Calar Alto in Dec saw 4 hrs data i n 8 nights, but we will go back
• Full VIRUS is in design phase; with full fundi ng expect completion 2008-2009
• HETDEX will then take 3 years, finishing 2011 -2012
• $30M project (including operation cost and d
ata analysis): $15M has been funded.
Neutrino Mass
•Free-streaming of non-relativisticneutrinos suppress the amplitude of the matter power spectrum at small scales.
•The total suppression
depends only on the total neutrino mass.
•The free-
streaming scale depends on
individual
neutrinos mass.
High Sensitivity Calls for
Better Theory
Modeling Non-linearity:
Analytical Approach
PT Works Very Well!
Z=4
Jeong & Komatsu, astro-ph/0604075
z=1,2,3,4,5,6 from top to bottom
Rule of Thumb:
2<0.4
Z=4
Jeong & Komatsu, astro-ph/0604075
Modeling Non-linear BAO
Z=4
Jeong & Komatsu, astro-ph/0604075
Parameter Forecast
•CIP, in combination with the CMB data from Planck, will determine the tilt 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 (0.8-1.2) 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 20-40 times better than the current limit.
Takada, Komatsu & Futamase, astro-ph/0612374
HETDEX CIP
Neutrinos don’t affect the
determination of P(k)
Cosmic Inflation Probe Will Nail the Inflation Model
V(
)
HETDEX Will Nail the DE
P/
Gebhardt (2006) Cosmological Const.
Redshift Space Distortion
Since we are measuring redshifts, the measured cl ustering length of galaxies in z-direction will be affe cted 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-directi on appears shorter than actually is.
This is not the “finger-of-god”! The finger-of-god is the no n-linear effect.
z direction
angular direction No peculiar motion Peculiar motion
Work in Progress…
Z=6 Z=5
Z=4 Z=3
Z=2 Z=1
Work to be done (1): Non- linear Bias
The largest systematic error is the effect of galax y bias on the shape of the power spectrum.
It is easy to correct if the bias is linear; however, i t won’t be linear when the underlying matter clust ering is non-linear.
How do we deal with it?
Non-linear Bias: Analytical
Approach
Powerful Test of Systematics
Work to be done (2):
Three-point Function
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 hi ghly complementary in redshifts, and address two diff erent (but potentially related) questions.
The nature of early & late dark energy.
Timeline?
HETDEX
Half-funded ($15M/$30M)
Begin a proto-type observation this Fall
The full survey begins in 2010
CIP
Up to NASA…
Expected Number Counts
Sensitivity of VIRUS (5-)
2e-17 erg/cm2/s at z=2
1e-17 erg/cm2/s at z=3
0.8e-17 erg/cm2/s at z=4
Detected # LAEs approximately constant with redshift
sensitivity tracks distance modulus
predict ~5 / sq. arcmin = 18,000 / sq. deg. per z = 1
With z~1 and 1/9 fill factor, expect 3,000 LAEs/sq. degr ee
0.6 million in 200 sq. degrees
Sufficient to constrain the position of the BO peaks to <1%
HETDEX will require ~1100 hours exposure or ~110 goo d dark nights
Needs 3 Spring trimesters to complete (not a problem: HET is O UR telescope!)
Why LAEs?
Target-selection for efficient spectroscopy is a challenge in measu ring DE with baryonic oscillations from ground-based observations
LRGs selected photometrically work well to z~0.8
High bias tracer already used to detect B.O. in SDSS
Higher redshifts require large area, deep IR photometry
Probably can’t press beyond z~2
Spectroscopic redshifts from absorption-line spectroscopy
[OII] and H emitters can work to z~2.5 with IR MOS
But difficult to select photometrically with any certainty
Lyman Break Galaxies work well for z>2.5
Photometric selection requires wide-field U-band photometry
Only ~25% show emission lines
Ly- emitters detectable for z>1.7
Numerous at achievable short-exposure detection limits
Properties poorly understood (N(z) and bias)
