Stochastic Group Summary and Plans

1. Stochastic Group Summary and Plans Vuk Mandic LSC Meeting MIT, 11/05/06

2. Stochastic Background of Gravitational Waves • Energy density: • Characterized by log-frequency spectrum: • Related to the strain power spectrum: • Strain scale:

3. Detection Strategy • Cross-correlation estimator • Theoretical variance • Optimal Filter Overlap Reduction Function For template: Choose N such that:

4. Analysis Details • Data divided into segments: • Yi and i calculated for each interval i. • Weighed average performed. • Sliding Point Estimate: • Avoid bias in point estimate • Allows stationarity (Δσ) cut |σi±1 – σi| / σi <  • Data manipulation: • Down-sample to 1024 Hz • High-pass filter (~40 Hz cutoff) • 50% overlapping Hann windows: • Overlap in order to recover the SNR loss due to windowing. i Yi i i+1 i+2 i-1

5. S4 H1L1 Isotropic • Combined H1L1 + H2L1: • Ω0 σΩ = (-0.8 4.3) × 10-5 • 90% UL: 6.5 × 10-5 • H0 = 72 km/s/Mpc • 51-150 Hz (includes 99% of inverse variance) • Paper submitted to ApJ. • Resubmit with minor revisions. • 1st S4 paper • 1st ApJ paper

6. S4 H1L1 Radiometer Flat spectrum in Ω • Design optimal filters for point-like sources on the sky: • Avoid overlap reduction at high frequencies. • S4 H1L1 result nearly completed (S. Ballmer): • Review Committee approved preliminary results to be presented at the Texas Symposium in December 2006. • Goal for the paper: final draft to be circulated to the LSC by the end of 2006. • Paper geared toward PRD. • Successfully injected and recovered 5 point-sources at SNR=10. • Isotropic search could not detect these sources! S. Ballmer Simulated Sources

7. S4: ALLEGRO-LLO • Cross-correlating ALLEGRO and LLO: • Strain sensitivity similar around 915 Hz. • Overlap reduction very small. • 90% upper limit: Ω0 < 1.02 • Strain < 1.5 × 10-23 • ~100× better than the previous limit at these frequencies. • Review committee approved preliminary results to be presented at GWDAW XI. • Paper is still under review, should be available to the LSC by the end of the year. • Paper geared toward CQG. • At the moment, there are no plans to repeat this experiment during S5.

8. S4 H1H2 FSR • Strain sensitivity of interferometers at free-spectral-range (FSR) frequency is similar to low-frequency region. • Cross-correlate H1 and H2 at (Rochester group): • 37.5 kHz: H1 sensitivity similar to DC, H2 ~130× worse than DC. • 75 kHz: H1, H2 sensitivities similar to DC. • Acquire at 262 kHz, heterodyne to FSR frequencies, use 200 Hz around FSR. • Results are nearly finalized: • Internal review to start in 2-3 weeks. • First draft of the paper should be available soon. • Remaining issues: • Calibration to be reviewed. • Estimate of the time-jitter in the fast channels. Very Preliminary Results 1 FSR S4 ALLEGRO-LLO 2 FSR S4 LHO-LLO A. Melissinos

9. S5 H1L1 Isotropic Coh = CSD2 / PSD1 / PSD2 • First pass at H1L1: • Time-shift: defining cuts blindly. • Analyzed up to Apr 3, 2006. • σΩ = 1.67 × 10-5(H0 = 72 km/s/Mpc) • Coherence much cleaner than S4. • Online H1L1 analysis • Also done with time-shift. • Calibration and DQ cuts not optimal. • As of Oct 11 2006: • σΩ = 4.75 × 10-6 • BBN integral bound:1.5 × 10-5 Frequency (Hz) σ Days into the run

10. S5 H1H2 Isotropic • Attempts to estimate and suppress instrumental and environmental correlations • PEM coherence method • Time-shift method • Independent and complementary methods. • Promising in terms of identification of “bad” frequency bands, but it is not clear yet how successful these approaches will be. • Hope to achieve sensitivity within a factor of 2-3 of the best possible. • Analysis of 11/05 – 04/06 data may give σΩ~ 2-3 × 10-6 • S5 H1H2 potential: few × 10-7

11. S5 H1L1 Radiometer Effect of Deconvolution • R. Ward is taking the lead in this analysis. • Repeat the H1L1 radiometer analysis, but also deconvolve the antenna pattern and estimate errors on the deconvolved map. • Deconvolution of the antenna pattern (S. Mitra, Ph. D. Thesis): • Solved problem. • Also developed a method for calculating the covariance matrix of the deconvolved map. • Goal: Have first results by the March LSC meeting. S. Mitra

12. Potential LIGO-only S5 papers • S5 H1H2 isotropic, 40-220 Hz • Potentially including results up to ~ 1 kHz. • S5 H1L1 radiometer • Including deconvolution and errors on deconvolved map. • Including S5 LHO-LLO isotropic result. • S5 H1H2 FSR • Relatively straightforward repetition of the S4 FSR analysis. • Better control of the time-jitter. • Efforts toward understanding the noise budget at the FSR.

13. LSC-VIRGO • Motivation • Multiple comparable all-sky stochastic searches above 200 Hz • Possible improvements over the H1L1 search in the “zeros” of the overlap reduction function. • Better resolution for anisotropic stochastic searches • Bi-weekly telecons • Comparing different (LSC and VIRGO) codes on simulated data. • Recovering software injections with different codes.

14. Implications: Cosmic Strings • X. Siemens, V. Mandic, and J. Creighton, astro-ph/0610920 • Modified the work of Damour & Vilenkin to include more accurate Universe model and to allow different cosmic string models • Explore accessibility of cosmic string models to different experiments. • Conclusions: • Already exclude some models, with great future potential. • Already more sensitive than BBN for a few models. • Experiments are complementary. • Burst and stochastic LIGO searches: overlap partly, partly complementary. • 1/p dependence. Pulsars CMB BBN LISA S5 Burst S5 H1L1 AdvLIGO S5 H1H2 S4

15. Implications: Cosmic Strings • X. Siemens, V. Mandic, and J. Creighton, astro-ph/0610920 • Modified the work of Damour & Vilenkin to include more accurate Universe model and to allow different cosmic string models • Explore accessibility of cosmic string models to different experiments. • Conclusions: • Already exclude some models, with great future potential. • Already more sensitive than BBN for a few models. • Experiments are complementary. • Burst and stochastic LIGO searches: overlap partly, partly complementary. • 1/p dependence. CMB Pulsars LISA S5 Burst BBN AdvLIGO S5 H1H2 S5 H1L1

16. Implications: Cosmic Strings • X. Siemens, V. Mandic, and J. Creighton, astro-ph/0610920 • Modified the work of Damour & Vilenkin to include more accurate Universe model and to allow different cosmic string models • Explore accessibility of cosmic string models to different experiments. • Conclusions: • Already exclude some models, with great future potential. • Already more sensitive than BBN for a few models. • Experiments are complementary. • Burst and stochastic LIGO searches: overlap partly, partly complementary. • 1/p dependence. Pulsars LISA S5 Burst AdvLIGO S5 H1H2

17. Implications: Cosmic Strings • In some models, loops are large at formation and long lived • Models preferred by some. • Again, exclude parts of the parameter space. • But, pulsar limit is more constraining in this case. • AdvLIGO and LISA will eventually surpass the pulsar bound.

18. Conclusions • S4 isotropic paper to be published in ApJ soon. • S4 radiometer and ALLEGRO-LLO results approved for conference presentations. • Papers largely reviewed, should be submitted to journals by the March LSC meeting. • S4 FSR results almost finalized • Review should start in 2-3 weeks • S5 H1L1 online analysis already surpassed the BBN integral bound. • Potential LIGO-only S5 papers: • H1H2 isotropic • H1L1 Radiometer, with deconvolution of antenna pattern • S5 H1H2 FSR • Efforts toward LIGO-VIRGO joint stochastic analysis have started • Already excluding some theoretical models. • Intend to continue such studies.

19. Reach as a Function of Spectral Slope • S3 H1L1: Bayesian 90% UL. • S4 H1L1+H2L1: Bayesian 90% UL. • Expected S5: design strain sensitivity and 1 year exposure. • For H1L1, sensitivity depends on frequency band.

20. S4 Injections Hardware Injections • Software injections: • Signal added to data in software. • Successfully recovered down to Ω~5×10-5. • Theoretical error agrees with the standard error over 10 trials. • Hardware injections: • Physically moving the mirrors. • Successfully recovered (within errors). Software Injections Hardware Injection

21. Interferometer Sensitivity • Sensitivity steadily improved over time. • Reached design sensitivity. • Started 1-year long run in November 2005.

22. Summary of Analyses H1L1 • “conversion”: Bad data segments defined in 60-sec analysis, then converted to 192-sec analysis H2L1

23. Landscape Cosmic Strings models and Pre-Big-Bang models: - can easily escape other experimental bounds - accessible to LIGO.

24. Cosmic Strings: Model • Cosmic strings are: • Topological defects formed in the early Universe. • Fundamental strings (in string theory). • Cosmic string cusps, with large Lorentz boosts, can create large GW signals. Integrating over all directions and redshift yields a stochastic background. • Calculation done by Damour & Vilenkin, PRD71, 063510 (2005) • Uncertainties exist. • Some of them can be resolved by improving the calculation (ongoing work with X. Siemens et al). • Three parameters: • String tension: 10-12 < G < 10-6 • Reconnection probability: 10-3 < p < 1 • Efficiency of damping perturbations with GW radiation: 10-13 <  < 10-2

25. Cosmic Strings: Results

26. Cosmic Strings: Results

27. Cosmic Strings: Results

28. Cosmic Strings: Results

29. Pre-Big-Bang: Model • Amplification of vacuum fluctuations: • Universe transitions between different regimes. • Super-horizon modes of vacuum fluctuations are amplified. • Inflation: Inflationary phase  RD  MD • Pre-Big-Bang Models: • Dilaton-dominated phase • Stringy phase • Radiation, followed by matter phase. • Three parameters: •  < 1.5 • fs – unconstrained • f1 – high-frequency cutoff ~f3-2 ~f3 fs

30. Pre-Big-Bang: Results AdvLIGO H1H2 S5 H1L1 S3 • Scan f1 -  plane for fs=30 Hz. • For each model, calculate ΩGW(f) and check if it is within reach of current or future expected LIGO results. • Beginning to probe the allowed parameter space. • Currently sensitive only to large values of f1. • Sensitive only to spectra close to flat at high-frequency. • But, not yet as sensitive as the BBN bound: BBN S5 H1H2 S4 Mandic & Buonanno, PRD73, 063008, (2006).

31. Pre-Big-Bang: Results • Can also define: • zs = f1/fs is the total redshift in the stringy phase. • gs/g1 = (fs/f1), where 2 = |2 - 3| • gs (g1) are string couplings at the beginning (end) of the stringy phase • Probe fundamental, string-related parameters, in the framework of PBB models. • Assumed f1 = 4.3 × 1011 Hz (relatively large).