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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 NI Department of Physics National Tsing Hua University 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 1 Dedicated to H C Yen – a devoted physicist and educator 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 2 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 3 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 4 Importance of Gravitational Wave Detection Explore fundamental physics and cosmology; As a tool to study Astronomy and Astrophysics 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 5 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 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. 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 6 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。 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 7 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 8 LIGO 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 9 LIGO instrumental sensitivity for science runs S1 (2002) to S5 (present) in units of gravitationalwave strain per Hz1/2 as a function of frequency 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 10 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 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 11 Evolution of the Virgo strain sensitivity 2009.11.09. Gravitational Wave Detectors on Ground and in Space W.-T. Ni 12 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 13 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 14 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 15 Massive Black Hole Systems: Massive BH Mergers & Extreme Mass Ratio Mergers (EMRIs) 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 16 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 17 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 18 2009.06.28. ICGA9, Wuhan Primordial GWs and their detectablity W.-T. Ni 19 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 20 3 Focused Issues in Cosmology Dark Matter Issue Dark Energy Issue What is the Physical Mechanism of Inflation 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 21 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 22 Inflation Scenario & Potential slow-roll inflationary model(Linde;Albrecht & Steinhardt, 1982)(from Kolb & Turner 1990) 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) 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 23 A Comparison (from Kolb & Turner 1990) Standard Cosmology vs. Inflationary Cosmology Can we probe the inflationary physics? 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 24 Inflationary GW Background = h_0^2(1/ρ_c) dρ_gw/d(logf) ~ 10^(-13) (H/10^(-4)M_pl) De Sitter 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 25 Ressel & Turner Primordial GW Model (1989) : Compare with the numerical values nowadays IRD 2009.11.21. Tsing Hua U. RDMD Probing the inflationary physics empirically W.-T. Ni 26 3 predictions of inflation Flat Universe Nearly scale-invariant spectrum of Gaussian density perturbations Nearly scale-invariant spectrum of Gravitational Waves 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 27 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 28 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) 2009.11.21. Tsing Hua U. arXiv:astro-ph/9704062v1 Probing the inflationary physics empirically W.-T. Ni 29 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 2009.11.21. Tsing Hua U. 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 Probing the inflationary physics empirically [[[ [f(Hz)] W.-T. Ni 30 WMAP 3 year Polarization Maps TT TE foreground EE BB(r=0.3) 2009.11.21. Tsing Hua U. BB(lensing) Probing the inflationary physics empirically W.-T. Ni 31 B-Pol: detecting primordial GWs generated during inflation (Exp. Astron.) Paolo de Bernardis · Martin Bucher · Carlo Burigana · Lucio Piccirillo · For the B-Pol Collaboration 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 32 The sensitivity goal of B-Pol 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 33 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 34 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 35 The sensitivity goal of LiteBIRD 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 36 B modes From tensor mode of polarization (GW) From electromagnetic propagation with pseudoscalar-photon interaction From lensing effects From magnetic field 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 37 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. 2009.11.21. Tsing Hua U. ASTROD-GW & Super-ASTROD Region Probing the inflationary physics empirically DECIGO BBO Region W.-T. Ni 38 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. 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 39 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 40 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) 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 41 LISA Pathfinder in Assembly Clean Room 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 42 ASTROD 2009.11.21. Tsing Hua U. ASTROD I ASTROD ASTROD-GW Super-ASTROD Probing the inflationary physics empirically W.-T. Ni 43 ASTROD I (Cosmic Vision 2015-25) submitted to ESA by H. Dittus (Bremen) arXiv:0802.0582 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 44 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 45 Summary of the scientific objectives in testing relativistic gravity of the ASTROD I and ASTROD missions 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 46 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. 2009.11.21. Tsing Hua U. S/C 1 (L4) (L3) S/C 2 Probing the inflationary physics empirically Sun Earth 60 球地 L1 L2 60 S/C 3 (L5) W.-T. Ni 47 Heliocentric Distance of 3 S/C in 10 years 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 48 Armlenth in 10 years 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 49 Difference of Armlengths in 10 years 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 50 Angle between Arms in 10 Years 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 51 Velocity in the Line-of-Sight Direction (Men & Ni) 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 52 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. 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 53 6 S/C ASTROD 引力波探测 任务轨道优化图 航天器S/C2 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 54 6 S/C ASTROD optimized for correlation detection 航天器S/C *3 航天器S/C2 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 55 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 56 BIG BANG OBSERVATORY BBO; http://universe.gsfc.nasa.gov/be/roadmap.htm 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. 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 57 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 (52^3) better sensitivity due to this reason, while Super-ASTROD has an additional 125 (5^3) times better sensitivity. 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 58 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 2009.11.21. Tsing Hua U. 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 Probing the inflationary physics empirically [[[ [f(Hz)] W.-T. Ni 59 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 60 Thank you ! 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 61 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 @ 1000 s Laser pulse timing system: T2L2 (Time Transfer by Laser Link) on Jason 2 Single photon detector Jason 2 S/C 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 62 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 Thrust noise 2009.11.21. Tsing Hua U. Proof mass Proof massS/C coupling Control loop gain Probing the inflationary physics empirically W.-T. Ni 63 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 64 A comparison of the target acceleration noise curves of ASTROD, LISA, the LTP and ASTROD 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 65 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 66 Anchoring Dummy telescope Outgoing Laser beam Proof mass LASER Metrology Capacitive readout Housing Telescope Optical readout beam Telescope Incoming Laser beam Dummy telescope 2009.11.21. Tsing Hua U. Proof mass Large gap Probing the inflationary physics empirically W.-T. Ni 67 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. 2009.11.21. Tsing Huathe U.inflationary physics empirically Probing W.-T. Ni S/C 1 (L4) (L3) S/C 2 Sun Earth 60 球地 L1 L2 60 S/C 3 (L5) 68 6 S/C ASTROD optimized for correlation detection 航天器S/C *3 航天器S/C2 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 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 69 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 (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). 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 70 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 orΔV-EGA orbit for Jupiter swingby (Launch opportunity: every year) Propulsion module 2009.11.21. Tsing Hua U. Probing the inflationary physics empirically W.-T. Ni 71 Payload and Spacecraft 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 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