Cosmology with High-z Galaxy Survey

Eiichiro Komatsu

University of Texas at Austin

U. of Florida, October 13, 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 CosmologyThe nature of dark energyWhat is it?

Modification to gravity? (e.g., brane world) Another form of energy? (e.g., vacuum energy)

The physics of inflationDid it happen at all? If so, how did it happen? What powered inflation?

The origin of baryonsPhysics of Baryogenesis?

The nature of dark matterWhat 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 Photon, Neutrino

<8 billion yrs Matter Era Dark Matter<now Dark Energy Era Late Dark Energy

Log

(Tim

e)

The Proposal: High-z Galaxy Survey

The nature of (late) dark energyEquation of state of dark energy

The physics of inflationSpectrum of primordial fluctuations

The origin of baryonsMass of neutrinos

The nature of dark matterMass of dark matter particles

Dark EnergyDark 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 UniverseThe second derivative of scale factor with 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 through the expansion rate as a function of redshift:

• This function determines

• Power Spectrum of Primordial Fluctuations

• (Approximately) Growth Rate of Density Fluctuations

• Distance-redshift Relations

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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 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)

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 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 EnergyScalar fields (whatever they are) are attractive early dark energy candidates, as they can have negative pressure.

Observe InflationInflation generates primordial fluctuations in spacetime. (a) Fluctuations inherited in radiationCosmic Microwave Background

Temperature AnisotropyPolarization Anisotropy

(b) Fluctuations inherited in matterDark Matter Distribution (Gravitational Lensing)Galaxy Distribution (Redshift Surveys)Gas Distribution (Lyman-alpha clouds)

(c) Fluctuations in spacetime itselfPrimordial Gravitational Waves

V(phi)to

P(k)V()

V()

V()

k

k3P(k)

From Primordial Fluctuations to Observed

FluctuationsPrimordial 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”.

P(k) of Density FluctuationsDifferent wave-numbers probe different parts of H(t). Thus, it probes the sh

ape of V()

We need to cover many decades in wave-number to determine the 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 ModelWhat is necessary?More accurate measurements of P(k)

Not just statistical error! Minimum systematic errorSample more k-modes

One solution = A galaxy survey at high-zWhy 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 theobserving 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

CIP is stationed at L2 to achieve proper passive cooling.

HETDEX: Late Dark Energy

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Baryonic Features: The Standard Ruler

Eisenstein et al., ApJ 633, 560 (2005)

“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 = 147 +- 2 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 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 the 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 the angular diameter distance and H(z).

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The Current State-of-the-Art

Seljak et al., PRD 71, 103515 (2005) [Baryonic oscillations not used]

P/

Toward “the” DE ModelOne solution = A galaxy survey at high-zWhy high-z? Once again. Less non-linear power!

HETMt. Fowlkes west Texas

Hobby-Ebery Telescope (9.2m)

Goals for HETDEX

• HETDEX measures redshifts for about 1 million LAEs from 1.8<z<3.8

•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 percent• Tightest constraints on evolving w at z=0.4 (to a few percent)

Ly- emitters as tracersProperties 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. degree 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 observation Will start this month!

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 (H

ETDEX is sampling variance limited) Well-defined window function

Dithering of pointing centers removes aliasing

Experimental RequirementsA 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 specifications of VIRUS

Status of HETDEX

• The prototype VIRUS observation will verify performance and test the engineering

• Full VIRUS is in design phase; with full funding expect completion 2009-2010

• HETDEX will then take 3 years, finishing 2012-2013

• $33M project (including operation cost and data analysis): $15M has been funded.

Neutrino Mass •Free-streaming of non-relativistic neutrinos 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

z=1,2,3,4,5,6 from top to bottom

Jeong & Komatsu, ApJ, 651 (2006), astro-ph/0604075

Rule of Thumb: 2<0.4

Z=4

Jeong & Komatsu, ApJ, 651 (2006), astro-ph/0604075

Modeling Non-linear BAOJeong & Komatsu, ApJ, 651 (2006), 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, PRD 73, 083520 (2006)

HETDEXCIP

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.

HETDEX + 3% Flat prior

Comparison of various DE projects (for w=w0+wa[1-a])Curvature assumption is very important for HETDEX (high-z)

Redshift Space DistortionSince 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 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 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?

Non-linear Bias: Analytical Approach

Powerful Test of Systematics

Work to be done (2): Three-point Function

SummaryHigh-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

Half-funded ($15M/$33M) Begin a proto-type observation this month The full survey begins in 2010

CIP Up to NASA…

Expected Number CountsSensitivity 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. degree 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 good 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 measuring 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)