Wei-Tou NI Department of Physics

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Gravitational Waves, Dark Energy and Inflation
---Classification of gravitational waves, dark
energy equation, and probing the inflationary
physics using space gravitation-wave detectors 

• Wei-Tou NIDepartment of Physics
• National Tsing Hua University

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Dedicated to H C Yen a devoted physicist and
educator
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OUTLINE

• Classification of Gravitational Waves
• Space GW detector as dark energy probe
• Inflation Primordial Gravitational Waves
• CMB Polarization Detection of Tensor Modes
• Two potential frequency regions to detect
  primordial GWs in Space by Interferometers
• General Concept of --- ASTROD I, ASTROD,
  ASTROD-GW, Super-ASTROD
• Outlook

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Importance of Gravitational Wave Detection

• Explore fundamental physics and cosmology
• As a tool to study Astronomy and Astrophysics

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Frequency Classification of Gravitational Waves-
similar to frequency classification of
electromagnetic waves to radio wave,
millimeter wave, infrared, optical, ultraviolet,
X-ray and ?-ray etc. LOWER
Frequency Bigger events

• Very high frequency band (100 kHz 1 THz)
  high-frequency ground resonators are most
  sensitive to this band.
• High frequency band (10 Hz 100 kHz)
  low-temperature and laser-interferometric ground
  detectors are most sensitive to this band.
• Middle frequency band (0.1 Hz 10 Hz) space
  detectors of short armlength (1000-100000 km).
• Low frequency band (100 nHz 0.1 Hz)
  laser-interferometer space detectors are most
  sensitive to this band.
• Very low frequency band(300 pHz 100 nHz)
  pulsar timing observations are most sensitive to
  this band.
• Ultra low frequency band (10 fHz 300 pHz)
  astrometry of quasars.
• Extremely low frequency band(1aHz10fHz), cosmic
  microwave background experiments are most
  sensitive to this band.

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???Leiden???MiniGRAIL????????????????????,????????
???????65cm???(6)??,??????3250Hz,??230Hz???????20
mK??????????????????????--Sfera?Graviton??????????
3250Hz???????????????LIGO II???????????
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LIGO
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LIGO instrumental sensitivity for science runs S1
(2002) to S5 (present) in units of
gravitational-wave strain per Hz1/2 as a function
of frequency
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The displacement sensitivity of the three LIGO
interferometers across the gravitational-wave
frequency band of interest to LIGO. The solid
curve is the optimum sensitivity predicted in
1995 Science Req.s Document
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Evolution of the Virgo strain sensitivity
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No detection yet

• Advanced LIGO completion 2014-15
• 12-13 times more sensitive
• Chance by volume 2000 times
• Now 0.05 per year for ns-ns inspirals
• To 100 per year for ns-ns inspirals

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Massive Black Hole Systems Massive BH Mergers
Extreme Mass Ratio Mergers (EMRIs)
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Space GW detectors as dark energy probes

• Luminosity distance determination to 1 or
  better
• Measurement of redshift by association
• From this, obtain luminosity distance vs
• redshift relation, and therefore equation of
  state of dark energy

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3 Focused Issues in Cosmology

• Dark Matter Issue
• Dark Energy Issue
• What is the Physical Mechanism of Inflation

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Issues in the Standard Cosmology

• Large-Scale Smoothness
• Small-Scale Inhomogeneity
• Spatial Flatness
• Unwanted Relics (monopoles ? Guth 1981,
  Inflation)
• Cosmological Constant
• Except for the last one Explained by Inflation

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Inflation Scenario Potentialslow-roll
inflationary model(LindeAlbrecht Steinhardt,
1982)(from Kolb Turner 1990)

• Barrier penetration
• Slow-roll
• Coherent oscillation around potential minimum
• If the parameters at the beginning of inflation
  is
• M1014 GeV
• H(-1)10(-34) sec and
• T100 H(-1)10(-32) s
• TcT_RH1014 GeV
• H(-1)10(-23) cm(initial size)? 3 1020
  cm(after inflation)
• S (entropy)T3 (H(-3))1014 ? 10144 (10130
  fold increase)

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A Comparison (from Kolb Turner 1990)
Standard Cosmology vs. Inflationary Cosmology Can
we probe the inflationary physics?
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Inflationary GW Background
h_02(1/?_c) d?_gw/d(logf)
10(-13) (H/10(-4)M_pl)
De Sitter
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Ressel Turner Primordial GW Model (1989)
Compare with the numerical values nowadays
RD?MD
I?RD
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3 predictions of inflation

• Flat Universe
• Nearly scale-invariant spectrum of Gaussian
  density perturbations
• Nearly scale-invariant spectrum of Gravitational
  Waves

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Amplification of vacuum fluctuations of GWs for
wavelengths larger than transition time (Hubble
time)

• Sudden (Instantaneous) Transition
• Transition between an inflationary phase and the
  radiation-dominated phase (RD) I ? RD
• Transition between radiation-dominated phase and
  the matter dominated phase (MD) RD ? MD

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Spectral energy density in gravity waves produced
by inflation (for T/S 0.018, dnT/dlnk
-10(-3), 0, 10(-3). T/S 0.18 (heavy curve)
maximizes the energy density at f 100 microHz)
WMAP5 Data Scalar spectral index n_s 0.960
0.013, r lt 0.22 (95 CL) Planck 0.5 in n_s
(0.957)? rgt0.0046 For Coleman-Weinberg inflation
? gt1.6110(-17)
arXivastro-ph/9704062v1
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Primordial Gravitational Wavesstrain
sensitivity ? (?2) energy sensitivity
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WMAP 3 year Polarization Maps
TT
TE
foreground
EE
BB(lensing)
BB(r0.3)
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B-Pol detecting primordial GWsgenerated during
inflation (Exp. Astron.) Paolo de Bernardis
Martin Bucher Carlo Burigana Lucio Piccirillo
For the B-Pol Collaboration
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The sensitivity goal of B-Pol
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The sensitivity goal of LiteBIRD
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B modes

• From tensor mode of polarization (GW)
• From electromagnetic propagation with
  pseudoscalar-photon interaction
• From lensing effects
• From magnetic field

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The Gravitational Wave Background from
Cosmological Compact BinariesAlison J. Farmer
and E. S. Phinney (Mon. Not. RAS 2003)
Optimistic (upper dotted), fiducial (Model A,
lower solid line) and pessimistic (lower dotted)
extragalactic backgrounds plotted against the
LISA (dashed) single-arm Michelson combination
sensitivity curve. Theunresolved Galactic close
WDWD spectrum from Nelemans et al. (2001c) is
plotted (with signals from binaries resolved by
LISA removed), as well as an extrapolated total,
in which resolved binaries are restored, as well
as an approximation to the Galactic MSMS signal
at low frequencies.
ASTROD-GW Super-ASTROD Region
DECIGO BBO Region
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Primordial GW and Space Detectors

• For detection of primordial GWs in space. One may
  go to frequencies lower or higher than LISA
  bandwidth where there are potentially less
  foreground astrophysical sources to mask
  detection.
• DECIGO and Big Bang Observer look for
  gravitational waves in the higher range
• ASTROD-GW, Super-ASTROD look for gravitational
  waves in the lower range.
• Super-ASTROD 3-5 spacecraft with 5 AU orbits
  together with an Earth-Sun L1/L2 spacecraft and
  ground optical stations to probe primordial
  gravitational-waves with frequencies 0.1 µHz - 1
  mHz and to map the outer solar system.

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LISA
LISA consists of a fleet of 3
spacecraft 20º behind earth in solar orbit
keeping a triangular configuration of nearly
equal sides (5 106 km). Mapping the space-time
outside super-massive black holes by measuring
the capture of compact objects set the LISA
requirement sensitivity between 10-2-10-3 Hz. To
measure the properties of massive black hole
binaries also requires good sensitivity down at
least to 10-4 Hz. (gt2018)
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• LISA Pathfinder in Assembly Clean Room

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ASTROD

• ASTROD I
• ASTROD
• ASTROD-GW
• Super-ASTROD

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ASTROD I (Cosmic Vision 2015-25) submitted to ESA
by H. Dittus (Bremen)arXiv0802.0582 v1
astro-ph

• Scaled-down version of ASTROD
• 1 S/C in an heliocentric orbit
• Drag-free AOC and pulse ranging
• Launch via low earth transfer orbit to solar
  orbit with orbit period 300 days
• First encounter with Venus at 118 days after
  launch orbit period changed to 225 days (Venus
  orbit period)
• Second encounter with Venus at 336 days after
  launch orbit period changed to 165 days
• Opposition to the Sun shortly after 370 days,
  718 days, and 1066 days

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ASTROD configuration (baseline ASTROD after 700
days from launch)
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Summary of the scientific objectives in testing
relativistic gravity of the ASTROD I and ASTROD
missions
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ASTROD-GW Mission Orbit

• Considering the requirement for optimizing GW
  detection while keeping the armlength, mission
  orbit design uses nearly equal arms.
• 3 S/C are near Sun-Earth Lagrange points
  L3?L4?L5,forming a nearly equilateral triangle
  with armlength 260 million km(1.732 AU).
• 3 S/C ranging interferometrically to each other.

Earth
Sun
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Heliocentric Distance of 3 S/Cin 10 years
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Armlenth in 10 years
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Difference of Armlengths in 10 years
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Angle between Arms in 10 Years
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Velocity in the Line-of-Sight Direction (Men Ni)
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Time delay interferometry Technology common to
LISA and ASTROD-GW

• Although the velocity in the Doppler shift
  direction for ASTROD-GW (40 of LISA) is smaller
  than LISA, LISA and ASTROD-GW both need to use
  time delay interferometry.
• For ASTROD-GW, the Doppler tracking technology
  developed in LISA could be used.
• Telescope pointing of LISA could also be used.

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6 S/C ASTROD ????????????

• This configuration is optimized for the
  correlation detection of GW background

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6 S/C ASTROD optimized for correlation detection
???S/C 3

• This configuration is optimized for the
  correlation detection of GW background

???S/C1
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BIG BANG OBSERVATORY BBO http//universe.gsfc.nas
a.gov/be/roadmap.htm

• The Big Bang Observatory is a follow-on mission
  to LISA, a vision mission of NASAs Beyond
  Einstein theme.
• BBO will probe the frequency region of 0.0110
  Hz, a region between the measurement bands of the
  presently funded ground- and space-based
  detectors. Its primary goal is the study of
  primordial gravitational waves from the era of
  the big bang, at a frequency range not limited by
  the confusion noise from compact binaries
  discussed above.
• In order to separate the inflation waves from the
  merging binaries, BBO will identify and subtract
  the signal in its detection band from every
  merging neutron star and black hole binary in the
  universe. It will also extend LISAs scientific
  program of measuring wavesfrom the merging of
  intermediate-mass black holes at any redshift,
  and will refine the mapping of space-time around
  supermassive black holes with inspiraling compact
  objects.
• The strain sensitivity of BBO at 0.1 Hz is
  planned to be 10-24, with a corresponding
  acceleration noise requirement of lt 10-16 m/(s2
  Hz1/2). These levels will require a considerable
  investment in new technology, including
  kilowatt-power level stabilized lasers,
  picoradian pointing capability, multi-meter-sized
  mirrors with subangstrom polishing uniformity,
  and significant advances in thruster,
  discharging, and surface potential technology.

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Sensitivity to Primordial GW

• The minimum detectable intensity of a stochastic
  GW background is proportional to
  detector noise spectral power density Sn(f) times
  frequency to the third power
• with the same strain sensitivity, lower frequency
  detectors have an f (-3)-advantage over the
  higher frequency detectors.
• compared to LISA, ASTROD has 140,000 times (523)
  better sensitivity due to this reason, while
  Super-ASTROD has an additional 125 (53) times
  better sensitivity.

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Primordial Gravitational Wavesstrain
sensitivity ? (?2) energy sensitivity
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Outlook

1. Tensor mode may first be detected in CMB
   polarization observation
2. Direct detection by space GW detector may probe
   deeper into inflationary physics

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Thank you !
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Laser ranging / Timing 3 ps (0.9 mm)

• Pulse ranging (similar to SLR / LLR)
• Timing on-board event timer ( 3 ps)reference
  on-board cesium clock
• For a ranging uncertainty of 1 mm in a distance
  of 3 1011 m (2 AU), the laser/clock frequency
  needs to be known to one part in 1014 _at_ 1000 s
• Laser pulse timing system T2L2 (Time Transfer by
  Laser Link) on Jason 2
• Single photon detector

Jason 2 S/C
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Drag-free AOC requirements

• Atmospheric (terrestrial) air column exclude a
  resolution of better than 1 mm
• This reduces demands on drag-free
• AOC by orders of magnitude
• Nevertheless, drag-free AOC is needed for
• geodesic orbit integration.

Thruster requirements
Proof mass-S/C coupling
Control loopgain
Proof mass
Thrust noise
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Two GOCE sensor heads (flight models) of the
ultra-sensitive accelerometers (ONERAs courtesy)
2 10-12 m s-2 Hz-1/2 resolution in presence
of more than 10-6 m s-2 acceleration
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A comparison of the target acceleration noise
curves of ASTROD, LISA, the LTP and ASTROD
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Uncertainties of ?, ß, J2 and G?/G as functions
of epoch for a 2015 launch orbit choice.The unit
of ordinate in the G?/G diagram is yr-1
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Incoming Laser beam
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ASTROD-GW Mission Orbit

• Considering the requirement for optimizing GW
  detection while keeping the armlength, mission
  orbit design uses nearly equal arms.
• 3 S/C are near Sun-Earth Lagrange points
  L3?L4?L5,forming a nearly equilateral triangle
  with armlength 260 million km(1.732 AU).
• 3 S/C ranging interferometrically to each other.

Earth
Sun
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6 S/C ASTROD optimized for correlation detection
???S/C 3

• This configuration is optimized for the
  correlation detection of GW background

???S/C1
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Super-ASTROD (1st TAMA Meeting1996)W.-T. Ni,
ASTROD and gravitational waves in Gravitational
Wave Detection, edited by K. Tsubono, M.-K.
Fujimoto and K. Kuroda (Universal Academy Press,
Tokyo, Japan, 1997), pp. 117-129.

• With the advance of laser technology and the
  development of space interferometry, one can
  envisage a 15 W (or more) compact laser power and
  2-3 fold increase in pointing ability.
• With these developments, one can increase the
  distance from 2 AU for ASTROD to 10 AU (25 AU)
  and the spacecraft would be in orbits similar to
  Jupiter's. Four spacecraft would be ideal for a
  dedicated gravitational-wave mission
  (Super-ASTROD).

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Orbit Design

• 3-5 large-orbit spacecraft (5 AU), 1 Earth-Sun
  L1/L2 point spacecraft
• Earth departure 10 km/s
• Direct to Jupiter orbit or?V-EGA orbit for
  Jupiter swingby
• (Launch opportunity every year)
• Propulsion module

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Payload and Spacecraft

• 15 W CW lasers
• Pulsed laser event timer
• Optical clock, optical comb freq. syn.
• Telescope (40-50 cm f) optics
• Inertial sensor/accelerometer
• Drag-free control and micro-Newton thrusters
• Radioisotope Thermoelectric Generators (RTGs)
• LEOP (Launch early orbit phase) 2 low-gain
  attennas
• X-band or Ka band communication
• Propulsion module

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Mapping the outer solar system for testing the
current models of cosmologyExample DGP (Dvali,
Gabadadze Porrati) gravity

• Dark matter, dark energy or modified gravity?
• DGP gravity able to produce cosmic acceleration
  without invoking dark energy
• DGP gravity has a crossover scale r_c, above
  which gravity becomes 5-d. Cosmic acceleration ?
  r_c 5 Gpc ? universal rate of periapse
  precession for bodies in nearly circular orbits
  below below r (r_g?r_c2)(1/3). For r_g 3
  km, r 130 pc.
• For planetary motions, (Lue Starkman, PRD
  2003)
• d?/dt 3c/8(r_c) 5?10(-4) (5Gpc/rc)
  /century
• Iorio, CQG 2005, 2nd order in eccentricity, Iorio
  2006,7