SPEC & GEN RELATIVITY
SPEC & GEN RELATIVITY PHZ 6607
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Date Created: 09/18/15
Outline III Introduction What is LISA Gravitational waves I Characteristics I Detection LISA design 1 Sources Stochastic Monochromatic Chirping What is LISA I Laser Interferometer Space Antenna LISA Planned spacebased gravitational wave detector I Why in space Dramatically reduced environmental noise compared to terrestrial detectors ie LIGO VIRGO GEO OO TAMA3000 Longer leg length 5000000 km vs 4 km i Better strain sensitivity Sensitive at lower frequencies 005 mHz 01 Hz New sources I Complications Solar winds Radiation pressure Gravitational Waves III Plane wave solution in weak field limit GR is extremely nonlinear near source Far from source we use a perturbation gm may hm Solution to wave equation with CW 0000 hm lMezkml 0 0 0 h h 0 h 4 0 k0 w00w 0 0 0 GW Characteristics III Tends to stretch 0 distribution of matter in orthogonal directions in an oscillating fdshion buy 0 Polarizations n Polarized n Ellipticclly polarized Three separate spacecraft with 2 incoming beams and 2 outgoing beams each Define two independent Michelson interferometers for redundancy Three sepdrdte spacecraft with 239 incoming beams and 2 outgoing beams each Define two independent Michelson interferometers for redundancy Sources III Four classifications Stochastic I Backgrounds Monochromatic I Galactic binaries Chirping I Massive black hole binaries I EMRIs Inflationary Waves a Arose from quantum fluctuations in early universe El Amplified by cosmic inflation Inflationary Waves II Random essentially white over wide range 10 16 Hz lt f lt 1010 Hz El Very interesting Wave amplitudes determined by potential driving inflation I Direct probe of inflationary physics El TOUGH to detect Drowned out by foreground sources Current estimates suggest amplitudes 45 orders of magnitude lower than LISA sensitivity El Side note GWs have a distinct effect on CMB photons may be detected indirectly using this method Phase Changes III Additional backgrounds known to have been produced during universal phase changes Phase Changes III Example 15 At Tumverse 10 K electroweak force separates into electromagnetic and weak nuclear forces Not spatially homogenous I Background Estimated that waves borne at this time will have frequencies f m 10 2 Hz right in LISA band I Good chance of detection Monochromatic Sources III Compact galactic binaries Trillions of binary systems in our galaxy Tens of millions compact enough I Radiate GWs in LISA band GUARANTEED source I Not truly monochromatic but sllloooww 48 f EMM2Sl27iflll3 MA MB M0 gt 92 X 10 18Hzsec Monochromatic SOUI CGS III Overguaranteed I I I I L I I I I I I I I I log h log f HZ T 1 yr I l I II nl I I I I I I l I I I Chirping Sources II Massive black hole binaries f ELMawn For appreciabigrfrequency increase chirp need high mass For a system with MA 1 Msystem 104MCD 107MCD M B GWs produced start in LISA band and sweep out in a period of between a few months and a few years Chirping Sources ann uuu 700 400 300 200 39 100 5 1 3 gt2 1 A m mi III Monte Carlo simulation showing mass and spin measurement errors nnn I UU I000 800 toquot 0quot 10 II for a set of 10000 binaries randomly distributed on the sky C Solid line m1 El Dashed line m2 3 X Churpmg ggwmgg Martin G Hoehnel r Even a pessimisf who assumes a rcfher long quasisfellar obiecf lifefime and only one binary coalescence per newlyformed halo should expecf a couple of supermassive black hole binary coalescences during fhe lifefime of LISA while an opfimisf mighf expecf 0 see up 0 several hundred of fhese excifing evem squot Chirping Sources u Extreme Mass Ratio Inspirals EMRI Formation I Compact obiect stellar mass scattered onto highly eccentric orbit about supermassive galactic black hole Waveform l Strongfield effects a Complicated chirps Event Rates Estimates predict 1000 events over LISA s lifetime Chirping Sources D EMRI nfaing obiect executes 10000 100000 orbits before coalescence z Three periods converge in Newtonian limit W T axial T9 poloidal Tr radial Unique GW signature I I I I I I I I I I I I I I I I Provides unprecedented description of spacetime near SMBH I IF orbit can be tracked throughout infall difficult Coalescence of Massive Black H 0193 I39ISNS and BH EH f Resolved 39 Galactic Binaries f 2 E lt1 0 3 Inquot 5 F a O vs 4 4 5 I 7 39a 3 10 2 10U Frequrencr Hz LISA will embody an unprecedented tool 39For the study of important and exotic processes of the universe Together with the family of terrestrial detectors such as LIGO it represents an entirely new probe of the sky Acknowledgements 1 References 5 came spawnquot and Geomelry s A Hughes USA Source and Scrence arXiv 071 1 m saw grrqc a AHen The duckedquot gruvvlyrwuve background source sand derecrmn armz V50AD33V3 We 9 6 NE EMGHSWmmLampLamamemr Mmm r H gt u Image credivs H e Many athersl Gaug e mage Search a Professor Dr Bernard Whiting Cosmology and Large Scale Structure of Universe PHZ 6607 Nimit Agarwal Prof Bernard Whiting Outline Cosmological Probes and ACDM Model Redshift Surveys as Large Scale structure Observations Statistical tools for analysis Results from Observations Redshift Distortions Correlation functions Baryonic Acoustic Oscillations Cosmological Probes CMB gt Geometry of Universe is Flat universe Large Scale Matter Distribution gt There is less than critical density of matter Distant supernovae gt Expansion of Universe is accelerating ACDM Cosmological Model Flat Universe Q1 Dark Energy cosmological constant for expanding universe QDE 7 Dark Matternon relativistic noninteracting QCDM 22 Qb O4 Six Cosmological parameters H Qm Qb Optical depth to reionization scalar fluctuation amplitude and scalar spectral index Hubble Law All galaxies are moving away from us Isotropic expansion of Universe Hubble law vH0d at low rdshift Measuringzgives 1 k 39 dczHo Redshift Surveys A redshift survey of strip of sky is a slice through 3D galaxy distribution riglrlnrcmxian Redshift Surveys 2df Galaxy Redshift Survey contains 63000 galaxies 4 s r8 4 Statistical tools Correlation function P12n21 r CIV1dV2 r gt 0 more clustered than random DDr 1 I I r RRO Datadata pairs Randomrandom pairs Power spectrum Pk J reik39rd3r Statistical tools Data points are in redshift space Correlation function rpTr Projected correlation function wprp2 I rp7rd7r 0 Cosmology by eye Redshift space distortions Small scale Fingers of God effect 2c Large scale Kaiser effectFlattening due to coherent infall a 42c Separation along the line oFsr ght 7 Mpch 720 o 20 Separation on the sky 0 Mpch 5 Redshift Distortions Distortion parameter BQm b 4707 galaxies b 6dark matter 0 27 for b1 Qm 3 for b12 Correlation Function Correlation decreases with scale Acoustic Peak at large scale 01 Power law rrro391398 on small scales Correlation function Deviations on small scales rlt10h1 Mpc Fitted to two power functions two clustering regimes Small scales from V same halo Large scales from different halo logm Fik h 3Mpca 35 Power spectrum 4 k h Mpc 1 001 002 005 0 1 02 100000 FIm models h 07 LN HM 10000 H n 1000 x 100 72 715 71 705 logw k h Mpcquot Q m at 1 looking at the turnaround point Q m 2204 Baryonic Acoustic OscillationslBAO Peak in r at 100 h1 quot i Mpc at Oscillations in Pk BAO No peak for 0 b 0 Apeak a 0 b Small peak amplitude from CMBnon photon baryon interacting matter CDM Mass Pro le of PerlurbaLion a a o 5 o m Origin of BAD I Dark Matter Gas Photon 110 yrs 252507 7 Radius Mpc I 150 200 Mass Profile of Perturbation m Origin of BAD Dark Matter Gas I Photon I 14433 yrs 26824 Radius Mpc I 150 200 Mass Profile of Perturbation 0 Origin of BAD I Dark Matter Gas Photon O 03933 Myrs 21051 7 Radius Mpc I 150 200 Origin of BAD Recombination takes place w I I 30 Dark Matter Gas Photon 145 Myrs 2475 Mass Profile of Perturbation Mass Profile of Perturbation 1000 Origin of BAD Dark Matter Gas I Pho on 234 Myrs 279 Radius Mpc a o o o 4000 2000 Mass Profile of Perturbation Origin of BAD I Dark Matter Gas Photon I 4745 Myrs 2710 Radius Mpc I 150 200 0001 0 Origin of BAD Radius Mpc I 150 BAO as standard ruler At particular redshift it gives angular distance Hence Dez Compare Dez1 De22 from BAO with Drz1Dr22 from cosmological model BAO as standard ruler For z135 and 222 ratio from BAO18 ratio from modelQm25167 not close May be inherent curvature or wz Cosmology from CMB and 2dfGRS 054225 n 125 115 a m M as g k W Em Combining OMB and 2dfGRS reduces degeneracy and improves constraints