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Cosmology with High-z Galaxy Survey

Cosmology with High-z Galaxy Survey. PI: Gary Melnick (SAO). HETDEX. l =0.34-0.57 m m, z=1.8-3.8 (Ly a ). l =2.5-5 m m, z=3-6.5 (H a ). Eiichiro Komatsu University of Texas at Austin U. of Florida, October 13, 2006. Dan Jaffe Karl Gebhardt Volker Bromm Eiichiro Komatsu. Gary Hill

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Cosmology with High-z Galaxy Survey

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  1. Cosmology with High-z Galaxy Survey PI: Gary Melnick (SAO) HETDEX l=0.34-0.57mm, z=1.8-3.8 (Lya) l=2.5-5mm, z=3-6.5 (Ha) Eiichiro Komatsu University of Texas at Austin U. of Florida, October 13, 2006 • 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? (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?

  3. How much we don’t know about the universe ~10-34 sec InflationEarly Dark Energy Log(Time) <30,000 yrs Radiation EraPhoton, Neutrino <8 billion yrs Matter EraDark Matter <now Dark Energy EraLate 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 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)

  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) • Dark energy affects cosmology mainly through the expansion rate as a function of redshift: 1/2 • This function determines • Power Spectrum of Primordial Fluctuations • (Approximately) 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 early 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)toP(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. Homogeneous INFLATION x 100,000 Inhomogeneous

  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. 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

  20. Ha is an ideal line due to its strength

  21. CIP is stationed at L2 to achieve proper passive cooling.

  22. HETDEX: Late Dark Energy 1/2

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

  24. “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 oscillation in Fourier space: baryonic oscillations.

  25. 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). 1/2

  26. The Current State-of-the-Art P/r Seljak et al., PRD 71, 103515 (2005) [Baryonic oscillations not used]

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

  28. Hobby-Ebery Telescope (9.2m) HET Mt. Fowlkes west Texas

  29. 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)

  30. Ly-a 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 Dz=1 at z~3 • But significant cosmic variance between surveys • 5000 – 10000 per sq. deg. Per Dz=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

  31. 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-a emitting galaxies as tracers, will measure the galaxy power spectrum to 1% • Prototype observation • Will start this month!

  32. Layout of 145 IFUs w/ 1/9 fill New HET wide field corrector FoV • 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 (HETDEX is sampling variance limited) • Well-defined window function • Dithering of pointing centers removes aliasing 0.22 sq. arcmin (20’ dia field)

  33. Experimental Requirements • A LAE DE survey reaching <1% precision requires: • large volume to average over sample variance • 200-500 sq. degrees and Dz ~ 2 • this is 6-15 Gpc3 at z~2-4 • surface density ~3000 per sq. degree per Dz=1; ~1 M galaxies • LAEs have 18,000 /sq. deg./Dz=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 l3400 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

  34. 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.

  35. 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. Neutrino Mass

  36. High Sensitivity Calls for Better Theory

  37. Modeling Non-linearity: Analytical Approach

  38. Jeong & Komatsu, ApJ, 651 (2006), astro-ph/0604075 PT Works Very Well! z=1,2,3,4,5,6 from top to bottom Z=4

  39. Jeong & Komatsu, ApJ, 651 (2006), astro-ph/0604075 Rule of Thumb: D2<0.4 Z=4

  40. Jeong & Komatsu, ApJ, 651 (2006), astro-ph/0604075 Modeling Non-linear BAO

  41. Parameter Forecast Takada, Komatsu & Futamase, PRD 73, 083520 (2006) HETDEX CIP • 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.

  42. Neutrinos don’t affect the determination of P(k)

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

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

  45. Comparison of various DE projects (for w=w0+wa[1-a]) Curvature assumption is very important for HETDEX (high-z) HETDEX + 3% Flat prior

  46. 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

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

  48. 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?

  49. Non-linear Bias: Analytical Approach

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