Cosmology with Longhorn High - z Galaxy Surveys: HETDEX &
HETDEX CIP
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=2.5-5m, z=3-6.5 (H )
=0.34-0.57m, z=1.8-3.8 (Ly )
•Gary Hill
•Phillip McQueen
•Karl Gebhardt
•Dan Jaffe
•Karl Gebhardt
•Volker Bromm
•Eiichiro Komatsu
PI: Gary Melnick (SAO)
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?
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 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)
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)
• The cosmological effects of dark energy are basically determined by the expansi on rate as a function of redshift:
• This function determines
• Power Spectrum of Primordial Fluctuations
• Growth Rate of Density Fluctuations
• 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 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%.
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!
High Sensitivity Calls for
Better Theory
Modeling Non-linearity:
Analytical Approach
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
256/h Mpc Box with 2563 particles 10 simulations are averaged
Z=6 Z=5
Z=4 Z=3
Z=2 Z=1
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
Parameter Forecast
•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 (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
Cosmic Inflation Probe Will Nail the Inflation Model
V()
HETDEX Will Nail the DE
P/
Gebhardt (2006) Cosmological Const.
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!
