Transcript Gravitational Waves, Dark Energy and Inflation ---

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 NI
Department of Physics
National Tsing Hua University
2009.11.21. Tsing Hua U.
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Dedicated to H C Yen – a
devoted physicist and educator
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OUTLINE
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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
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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 γ-ray etc. LOWER Frequency: Bigger events
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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(1aHz–10fHz), cosmic microwave
background experiments are most sensitive to this band.
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在荷兰Leiden建造的MiniGRAIL低温共振球形引力波侦测器。左图为实
体照片，右图为实验结构图。侦测球为直径65cm的铜铝(6%)合金，其共
振频率为3250Hz，频宽230Hz。运作温度将为20mK。在罗马和圣保罗将
各建造一个类似的球形侦测器──Sfera和Graviton。三个侦测器共同侦测
3250Hz附近频率引力波的目标灵敏度将比LIGO II的目标灵敏度好上几倍。
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Gravitational Wave Detectors on Ground and in Space
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LIGO
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LIGO instrumental sensitivity for science runs S1
(2002) to S5 (present) in units of gravitationalwave 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
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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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2009.11.21. Tsing Hua U.
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2009.06.28. ICGA9, Wuhan
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Massive Black Hole Systems:
Massive BH Mergers &
Extreme Mass Ratio Mergers (EMRIs)
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2009.06.28. ICGA9, Wuhan
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2009.06.28. ICGA9, Wuhan
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Space GW detectors as dark
energy probes
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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
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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 & Potential
slow-roll inflationary model（Linde；Albrecht &
Steinhardt, 1982）(from Kolb & Turner 1990)
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Barrier penetration
Slow-roll
Coherent oscillation
around potential
minimum
If the parameters at
the beginning of
inflation is
M=10^14 GeV
H^(-1)=10^(-34) sec and
T=100 H^(-1)=10^(-32) s
Tc=T_RH=10^14 GeV
H^(-1)=10^(-23) cm（initial
size） 3 ×10^20 cm（
after inflation）
S (entropy)=T^3 (H^(3))=10^14  10^144
(10^130 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_0^2(1/ρ_c) dρ_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
IRD
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RDMD
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3 predictions of inflation
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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)
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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 < 0.22 (95% CL)
Planck
0.5 % in n_s (0.957)
r>~0.0046
For Coleman-Weinberg
inflation 
>~1.61×10^(-17)
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arXiv:astro-ph/9704062v1
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Primordial Gravitational Waves
[strain sensitivity  (ω^2) energy sensitivity]
0.0
-2.0
-4.0
-6.0
bar-intf
2 intf
Nv = 3.2
(c) cosmic
strings
(b) String
-10.0
Log [h
Ωgw]
2
-16.0
(a)
inflation
‘Average’
ASTROD
DECIGO/BBO-grand
(correlation detection)
Super-ASTROD
*ASTROD
-20.0
(correlation detection)
-22.0
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LIGO II/LCGT/VIRGO II
(2 adv intf)
Extragalactic
Extrapolated
WMAP
-18.0
-24.0
-18.0
LISA
cosmology
-12.0
-14.0
(single intf)
Nv = 4
-8.0
0
LIGO or VIRGO
ms pulsars
* Super-ASTROD (correlation detection)
-14.0
-10.0
-6.0
Log f
-2.0
2.0
6.0
10.0
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[[[ [f(Hz)]
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WMAP 3 year Polarization Maps
TT
TE
foreground
EE
BB(r=0.3)
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BB(lensing)
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B-Pol: detecting primordial GWs
generated 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
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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 Binaries
Alison 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) singlearm Michelson combination
sensitivity curve. The‘unresolved’
Galactic close WD–WD 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
MS–MS signal at low frequencies.
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ASTROD-GW &
Super-ASTROD
Region
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DECIGO
BBO Region
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Primordial GW and Space Detectors
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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 102-10-3 Hz. To measure the properties of massive black hole binaries also
requires good sensitivity down at least to 10-4 Hz. (>2018)
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LISA
Pathfinder
in Assembly
Clean Room
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ASTROD
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ASTROD I
ASTROD
ASTROD-GW
Super-ASTROD
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ASTROD I (Cosmic Vision 2015-25)
submitted to ESA by H. Dittus (Bremen)
arXiv:0802.0582 v1 [astro-ph]
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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)
Inner Orbit
Earth Orbit
1
.
Earth L1 point S/C
(700 days after 1*
launch)
Outer Orbit
-V1
L3
U2
n̂3
.
U1
Launch
Position
2*
S/C 2
2
.
Sun
n̂2
-V3
n̂1
L2
L1
U3
-V2
.
3 3*
S/C 1
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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
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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.
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S/C 1 (L4)
(L3)
S/C 2
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Sun
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球地
L1 L2
60
S/C 3 (L5)
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Heliocentric Distance of 3 S/C
in 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
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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 引力波探测
任务轨道优化图
航天器S/C2
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This configuration
is optimized for
the correlation
detection of GW
background
太 30
阳
60
航天器S/C
60
30
航天器S/C (L5)
航天器S/C3
地球
6 S/C ASTROD引力波探测任务轨道优化图
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6 S/C ASTROD optimized
for correlation detection
航天器S/C *3
航天器S/C2
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This configuration
is optimized for
the correlation
detection of GW
background
太 30
阳
60
航天器S/C *1
60
航天器S/C1
30
航天器S/C *2
航天器S/C3
地球
6 S/C ASTROD GW mission orbit
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BIG BANG OBSERVATORY
BBO; http://universe.gsfc.nasa.gov/be/roadmap.htm
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The Big Bang Observatory is a follow-on mission to LISA, a vision mission of
NASA’s “Beyond Einstein” theme.
BBO will probe the frequency region of 0.01–10 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 LISA’s
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 < 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
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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
(52^3) better sensitivity due to this reason, while
Super-ASTROD has an additional 125 (5^3) times
better sensitivity.
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Primordial Gravitational Waves
[strain sensitivity  (ω^2) energy sensitivity]
0.0
-2.0
-4.0
-6.0
bar-intf
2 intf
Nv = 3.2
(c) cosmic
strings
(b) String
-10.0
Log [h
Ωgw]
2
-16.0
(a)
inflation
‘Average’
ASTROD
DECIGO/BBO-grand
(correlation detection)
Super-ASTROD
*ASTROD
-20.0
(correlation detection)
-22.0
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LIGO II/LCGT/VIRGO II
(2 adv intf)
Extragalactic
Extrapolated
WMAP
-18.0
-24.0
-18.0
LISA
cosmology
-12.0
-14.0
(single intf)
Nv = 4
-8.0
0
LIGO or VIRGO
ms pulsars
* Super-ASTROD (correlation detection)
-14.0
-10.0
-6.0
Log f
-2.0
2.0
6.0
10.0
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[[[ [f(Hz)]
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Outlook
(i)
(ii)
Tensor mode may first be detected
in CMB polarization observation
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)
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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 @ 1000 s
Laser pulse timing system: T2L2 (Time Transfer by Laser
Link) on Jason 2
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Single photon detector
Jason 2 S/C
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Drag-free AOC requirements
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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
Thrust noise
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Proof mass
Proof massS/C coupling
Control loop
gain
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Two GOCE sensor heads (flight models) of the
ultra-sensitive accelerometers (ONERA’s 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 γ, β, 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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Anchoring
Dummy
telescope
Outgoing Laser beam
Proof
mass
LASER
Metrology
Capacitive
readout
Housing
Telescope
Optical readout
beam
Telescope
Incoming Laser
beam
Dummy telescope
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Proof mass
Large gap
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ASTROD-GW Mission Orbit
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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.
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S/C 1 (L4)
(L3)
S/C 2
Sun
Earth
60
球地
L1 L2
60
S/C 3 (L5)
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6 S/C ASTROD optimized
for correlation detection
航天器S/C *3
航天器S/C2
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This configuration
is optimized for
the correlation
detection of GW
background
太 30
阳
60
航天器S/C *1
60
航天器S/C1
30
航天器S/C *2
航天器S/C3
地球
6 S/C ASTROD GW mission orbit
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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.
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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
(2×5 AU) and the spacecraft would be in
orbits similar to Jupiter's. Four spacecraft
would be ideal for a dedicated gravitationalwave mission (Super-ASTROD).
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Orbit Design
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3-5 large-orbit spacecraft (~5 AU), 1
Earth-Sun L1/L2 point spacecraft
Earth departure: ~10 km/s
Direct to Jupiter orbit orΔV-EGA orbit
for Jupiter swingby
(Launch opportunity: every year)
Propulsion module
2009.11.21. Tsing Hua U.
Probing the inflationary physics empirically
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71
Payload and Spacecraft
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15 W CW lasers
Pulsed laser & event timer
Optical clock, optical comb & freq. syn.
Telescope (40-50 cm φ) & 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
2009.11.21. Tsing Hua U.
Probing the inflationary physics empirically
W.-T. Ni
72
Mapping the outer solar system for
testing the current models of cosmology
Example: DGP (Dvali, Gabadadze & Porrati) gravity
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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_c^2)^(1/3). For r_g = 3 km, r* = 130 pc.
For planetary motions, (Lue & Starkman, PRD 2003)
|dω/dt| = 3c/8(r_c) = 5▪10^(-4) (5Gpc/rc) ”/century
Iorio, CQG 2005, 2nd order in eccentricity, Iorio 2006,7
2009.11.21. Tsing Hua U.
Probing the inflationary physics empirically
W.-T. Ni
73