astronomy with gravitational-wave detectors vuk mandic university of minnesota 04/02/09

Astronomy with Gravitational-Wave Detectors

Vuk MandicUniversity of Minnesota

04/02/09

Outline

Gravitational Waves:» What are they?

LIGO - Laser Interferometer Gravitational-wave Observatory: » Overview and Status

Recent results highlights:» Crab pulsar» GRB search» Stochastic background of gravitational waves

Outlook for the future:» Enhanced and Advanced LIGO» Underground interferometers?

Einstein's General Relativity:» Mass/Energy and Space-Time are related.

Presence of mass distorts the fabric of space-time.» Straight lines not always shortest distances.

Gravity is an effect of curved space-time.

General Relativity

Gravitational Waves

Newtonian gravity: instantaneous action at a distance. General Relativity: the “signal” travels at the speed of light. Weak field limit: Einstein’s field equations reduce to the wave equation:

Two polarizations:a,b ~ f(t - k·x)

Gravitational Waves

Two Polarizations:

“+” Polarization “x” Polarization

Sources: Binary Coalescence

Compact binary objects:» Two neutron stars, ~1.4 Solar

Masses each.» Two black holes, large mass

ranges.» Neutron star and a black hole.

Inspiral toward each other.» Emit gravitational waves as they

inspiral. Amplitude and frequency of the

waves increases over time, until the merger.

Waveform relatively well understood.

Sources: Bursts

Various other transients exists:» Supernova explosions: e.g.

collapse of massive stars.» Gamma Ray Bursts:

collapse of rapidly rotating massive stars or neutron star mergers.

» Pulsar glitches: acretion. Physics not entirely

understood. Waveform not known – search

for power excess in the data.

Sources: Periodic

Pulsars with mass non-uniformity:» Small “mountain”.» Density non-uniformity.» Dynamic processes inside

neutron star. Produce gravitational-waves at

twice the rotational frequency. Waveform well understood:

» Sinusoidal, but Doppler-modulated.

Continuous source!

Sources: Stochastic Background

Incoherent superposition of many unresolved sources.

Cosmological:» Inflationary epoch» Cosmic strings» Alternative

cosmologies Astrophysical:

» Supernovae» Magnetars

Potentially could probe physics of the very-early Universe.

Interferometers as Gravitational Wave Detectors

Gravitational wave effectively stretches one arm while compressing the other.

Time


Interferometer measures the arm-length difference.» Suspended mirrors act as

“freely-falling”.» Dark fringe at the detector.

Time





Fabry-Perot cavities in the arms» Effectively increase arm length

~100 times.

Time





Fabry-Perot cavities in the arms» Effectively increase arm length

~100 times. Power-recycling mirror

» Another factor of ~40 in power.

Time


LIGO Sensitivity

Rough sensitivity estimate» Input laser power: ~5 Watt

Sensitivity (ΔL) ~ (~ 10-6 m)/ Number of Bounces in Arm (~100)/ Sqrt(Number of Photons (~1021))

~ 3 × 10-19 m Strain Sensitivity:

» h = ΔL / L ~ 10-22

» L = 4 km

Seismic Noise

LIGO Sensitivity

Seismic Noise» Active and passive isolation

LIGO Sensitivity

Seismic Noise» Active and passive isolation» Suspensions» Effective “Seismic Wall” at 40 Hz

LIGO Sensitivity

Seismic Noise (<40 Hz)» Active and passive isolation» Suspensions» Effective “Seismic Wall” at 40 Hz

Thermal Noise (40-150 Hz)» Suspension wires» Internal mirror modes

Shot noise (>150 Hz)

Substrates: SiO2

» 25 cm Diameter, 10 cm thick

» Internal mode Q’s > 2 x 106

Polishing

» Surface uniformity < 1 nm rms ( / 1000)

LIGO Sensitivity

LIGO Noise Budget

Fundamental noise sources:» Seismic noise, <40 Hz» Thermal noise, 40-150 Hz» Laser-power shot noise, >150 Hz

Many technical, noise sources:» Electronics, 60 Hz harmonics» Angle-to-length couplings» Auxiliary length degrees of freedom» Laser frequency noise» Laser intensity noise» Oscillator phase noise

LIGO Observatories

4 km + 2 km

4 km L1

H2

H1

Brief History of LIGO

Inauguration

1999 2000 2001 2002 20033 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

E2Engineering

E3 E5 E9 E10E7 E8 E11

First Lock Full Lock all IFO

10-17 10-18 10-20 10-21

2004 20051 2 3 4 1 2 3 4 1 2 3 4

2006

First Science Data

S1 S4Science

S2 RunsS3 S5

10-22

4K strain noiseat 150 Hz Strain [Hz-1/2]3x10-23

20071 2 3 4

Sensitivity History

~4 orders of magnitude over ~4 years.

LIGO reached the design sensitivity in Nov. 2005.

Science run S5 completed in Oct. 2007.

~2-year long run at design sensitivity, 1-year of H1-H2-L1 coincident data.

Data analysis in progress.

S5 Results: Pulsar Searches

Crab pulsar:» One of the most promising known local

sources, one of the LIGO “targets”.» Spin down 3.710-10 Hz/s.» Maximum strain of 1.410-24.» Model: <40% of the spin-down is due to

gravitational waves. Two analyses performed, using data up to August

2006.» Time domain: using E-M timing.» Frequency domain: spans small range in

frequency and spin-down. Final results (time domain):

» 95% UL h0<3.410-25, ellipticity < 1.810-4

» Less than 6% of the lost energy goes into gravitational waves.

Major Milestone: Beating the Crab spin-down limit!Ap. J. Lett. 683, 45 (2008)

S5 Results: Transient Searches

Short Gamma Ray Bursts (GRBs): intense flashes of gamma rays, lasting <2s.» Nearby: soft gamma-ray repeaters (SGRs).» Distant: neutron star and/or black hole merger.

GRB 070201 was observed in the direction of Andromeda galaxy (M31) by several spacecraft (Konus-Wind, Integral, Messenger, Swift).

H1 and H2 operational at the time.» Search -120/+60 sec around the GRB time.» No gravitational-wave candidate was found

(Astrop. J. 681, 1419 (2008)). Inspiral search for compact binary merger

(M⊙<m1<3M⊙, M⊙<m

2<40M⊙):

» In M31 (770 kpc) excluded at 99% confidence.» Excluded at 90% confidence out to 3.5 Mpc.

Un-modeled burst: SGR in M31 not excluded.IPN3 error box overlaps with M31

Stochastic Background of Gravitational Waves

Energy density:

Characterized by log-frequency spectrum:

Related to the strain power spectrum:

Strain scale:

Detection Strategy Cross-correlation estimator

Theoretical variance

Optimal Filter

Overlap Reduction Function

For template:

Choose N such that:

Preliminary S5 Result

Use S5 data up to Jan 22, 2007.» 140 days of effective observing

time. Preliminary S5 H1L1 result:

» Ω σΩ = (1.0 5.2) × 10-6

» H = 72 km/s/Mpc The frequency band is selected to

include 99% of sensitivity, as measured by the integrand of σ-2.» 41.5-177.5 Hz

Bayesian 90% UL:» Prior on Ω: S4 Posterior» Marginalize over calibration

uncertainties

» 90% UL: 9.0 × 10-6

Signal Injections

Software injections:» Signal added to data in

software.» Successfully recovered

down to Ω ~ 4 × 10-5. Hardware injections:

» Physically moving the mirrors.

» Successfully performed and recovered three injections (within errors).

HardwareInjections

0.6 x 10-30.3 x 10-20.2Calibration Uncertainty

0.2 x 10-30.1 x 10-20.04Statistical Uncertainty

7.0 x 10-32.3 x 10-21.8Recovered Amplitude

6.3 x 10-31.7 x 10-21.9Injected amplitude

2152913Duration (min)

3 21Injection

Future Stochastic Searches Analysis of full S5 data in progress. H1H2 pair offers potentially 10x better sensitivity, but susceptible to instrumental

correlations.» Study coherence with auxiliary (environmental etc.) channels to identify

“bad” frequencies.» Time-shift one detector with respect to the other by ~1-sec. GW correlations

should disappear, but instrumental correlations may survive. Search at the higher resonance frequencies of the arm cavities (37.5, 75 kHz). Include non-LIGO interferometers in the search (VIRGO, GEO). Directional searches:

» Search for point-sources (S4 run)» Generate stochastic GW map (analogous to CMB maps).» Spherical-harmonic decomposition.

Landscape

- Surpassed BBN bound

- Beginning to probe models.

- Window around 1 Hz.

BBN Bound

Big-Bang Nucleosynthesis model and observations constrain the total energy at the time of BBN:

In our frequency band, 41.5-177.5 Hz, and assuming frequency independent spectrum, this becomes:

» Ω0 < 1.0 × 10-5

We have now surpassed this bound.» Another important LIGO milestone!

Landscape




Cosmic (Super)Strings String cusps moving at the speed of light

produce bursts of gravitational waves. Integrating over the entire Universe gives a

stochastic background. Parameters (small-loop scenario):

» loop-size parametrized by: 10-13 < < 1

» String tension: 10-12 < G < 10-6

» Reconnection probability: 10-3 < p < 1

Expected Future Timeline

Year

LIGO

2007 2009 2010 2011 2012 2013 20142008

S5Enhanced LIGOCommissioning S6 AdvLIGO Commissioning

Enhanced LIGO» Relatively small upgrade over the Initial LIGO.» Improve strain sensitivity of 4-km interferometers 2-3 times.» Test some of the Advanced LIGO concepts.» NSF support: $150M over 2009-2013 for LIGO Lab operation!

Advanced LIGO» Major upgrade: essentially every aspect of the experiment will be

significantly improved.» Improve strain sensitivity of all interferometers >10 times.» Widen the sensitive band down to 10 Hz.» Substantial increase in the number of expected accessible sources.» NSF support: $205M over 2008-2015 for ALIGO construction!

Hardware installation nearly complete.

More powerful laser (35 W instead of 6 W), with upgraded input optics.

New, active seismic isolation platform in the output port.

Output mode cleaner, suspended, in vacuum.

New locking scheme. New earthquake stops (SiO

2) to

suppress charging of the mirrors. New magnets (SmCo instead of

NdFeB) to minimize non-linear, up-conversion effects.

Enhanced LIGO

Enhanced LIGO

Modifications only planned for 4-km interferometers: H1 and L1.

H2 will not be upgraded, currently running in Astrowatch mode.

Astrowatch:» Stay “ON”, just in case...» Run by students, when there is no

interference from H1 commissioning.» Excellent training for students, while

experts can focus on H1. H2 maintains the S5 strain sensitivity,

with about 50% duty cycle.

Advanced LIGO Keep the same facilities, but redesign

all subsystems.» Improve sensitivity over the whole

frequency range.



frequency range. Increase laser power in arms.



frequency range. Increase laser power in arms. Better seismic isolation.

» Quadruple pendula for each mass




» Quadruple pendula for each mass Larger mirrors to suppress thermal

noise. Silica wires to suppress suspension

thermal noise.




» Quadruple pendula for each mass Larger mirrors to suppress thermal

noise. Silica wires to suppress suspension

thermal noise. “New” noise source due to increased

laser power: radiation pressure noise. Signal recycling mirror

» Allows tuning sensitivity for a particular frequency range.

Advanced LIGO

Three 4km interferometers.» Two at Hanford, one at Livingston.

Significantly larger expected number of GW sources.

Project started in April 2008. Presently finalizing designs, placing

orders.» Preliminary tests of various

subsystems.» Some of the hardware and

concepts to be tested by Enhanced LIGO.

Installation expected to start in 2011.» First results: ~2014.

Beyond Advanced LIGO

Third generation GW interferometers will have to confront (and beat) the Standard Quantum Limit» Shot noise ~ P-1/2 » Radiation pressure noise ~ P1/2

» Together define an optimal power and a maximum sensitivity for a “conventional” interferometer

» Require non-classical states of light, special interferometer configurations, …

Underground interferometers?» Significant reduction in seismic noise and gravity gradient could

allow exploring low frequencies (~1 Hz)» Further suppression of thermal noise

– Cryogenic?– Larger mirror masses?

» Lower power?

Probing ~1 Hz

Since

probing lower frequencies quickly improves sensitivity to ΩGW.

Astrophysical stochastic foregrounds appear to be minimized in this band.» Could pursue the most interesting

cosmological sources, such as inflationary models etc.

Other scientific motivation:» Most pulsars are below 10 Hz

(periodic sources).» Inspirals: larger total mass, longer

observations, possibly a dark energy probe.

ATNF Pulsar Catalogue,The Astronomical Journal 129, 1993 (2005)

Pulsar Period Distribution

Landscape




Probing ~1 Hz

Since

probing lower frequencies quickly improves sensitivity to ΩGW.

Astrophysical stochastic foregrounds appear to be minimized in this band.» Could pursue the most interesting

cosmological sources, such as inflationary models etc.

Other scientific motivation:» Most pulsars are below 10 Hz

(periodic sources).» Inspirals: larger total mass, longer

observations, possibly a dark energy probe.

ATNF Pulsar Catalogue,The Astronomical Journal 129, 1993 (2005)

Pulsar Period Distribution

47

Gravity Gradient Noise

Saulson (PRD30, 732, (1984)) made first estimates.» At 1 Hz, predicts equivalent

strain of ~10-20 Hz-1/2.» Also predicts seismic and

atmospheric contributions to be similar.

Later, more detailed calculations agree with Saulson:

– Hughes and Thorne, PRD58, 122002 (1998).

– Beccaria et al, CQG15, 3339 (1998).

We need ~103x suppression at 1 Hz.

48

Why Underground?

Atmospheric fluctuations are irrelevant. Local disturbances much more

controlled:» Limited access, no passers-by... » Controlled use of machinery.» Ventilation well understood and

controllable. Much more stable environment.

» Temperature, pressure, humidity... Seismic noise is reduced exponentially.

» At 1 Hz expect ~10x suppression» Depends on depth and rock

structure.Depth (m)

Seismic suppression due to depth (Cella)

49

Why Underground?

Correlation lengths are significantly longer (several km at 1 Hz):» Speed of sound is ~5 km/s, compared to ~500 m/s on surface.» Uniform medium, not very dissipative.

– Depends on location, rock composition, geological history... Two consequences:

» Gravity gradients correlated between mirrors, depending on frequency (at 0.1 Hz, expect ~50 km wavelength...)

» Track the seismic noise with a relatively few instruments spanning the entire detector.

– Active suppression may be more plausible.– And the requirement is a bit more relaxed: need ~100x.

Generation of gravity gradient noise is different:» Not surface waves!» Bulk waves, within probably several wavelength away... » Developing finite-element models to understand this better.

50

What Do We Know About Underground?

Not much! How does seismic noise amplitude depend on depth and frequency?

» How deep should we go?» How much does rock content matter?» How much does rock non-uniformity matter?

How does correlation length change as a function of depth and frequency? » How deep should we go?» How much does rock content matter?» How much does rock non-uniformity matter?

How much can we gain by building large cavities?» Less sensitive to tilts?

What does this mean for the gravity gradient noise? How does this constrain the design of an underground GW detector? Many questions!

» Need detailed underground measurements and finite-element models to answer these questions!

DUSEL at Homestake Mine

Homestake mine, SD, chosen to host Deep Underground Science and Engineering Laboratory (DUSEL).» Expected to be operational in ~2013.

Driven by low radioactive background requirements (dark matter, neutrino experiments etc).

DUGL at DUSEL

Deep Underground Gravity Lab at DUSEL:» Benefit from the low gravitational and vibrational background.» Developing a collaboration to characterize the gravitational field noise

underground.» Minnesota, Caltech, U of Florida, Carleton, Louisiana State.

First trip in February 2008.» Preliminary measurements, established contacts.

Initiated a more detailed campaign in the summer 2008.» Build an array of seismic stations.» Monitor environmental conditions (magnetometers, thermometers...)» Combine with theoretical models to estimate gravity gradient noise.» Goal: inform the design of a multi-km gravitational-wave interferometer.

Seismic Stations

*

*

*

*N

- 300 ft Station- Ellison Formation- 250 ft from shaft

Ross Shaft

- 800 ft station- Tip of Homestake formation ledge-600 ft from shaft

- 2000 ft station- Homestake formation ledge- 2600 ft from shaft

Stations:- Concrete slabs on bedrock.- Leveled granite plates supportseismometers.- Nested rigid-foam huts to suppress ambient noise.- DAQ in a separate hut.

300ft Station

2000ft Station

First Results

In the summer 2008, operated STS-2 and two T240's next to each other at 2000ft level.

Nanometrics provided the T240's and the data acquisition for them.

Simultaneous data:» Instrument self-noise.

Good measurement of the seismic noise level at 2000 ft.» ~10x quieter than LLO at 1 Hz.

Residual microseismic peaks in the self-noise spectra probably indicate imperfections in the set-up.» Made improvements since.

LLO

2000 ft

Homestake Low Noise Model

Minimize over time for each frequency bin.

Similar (or even quieter) than the USGS New Low Noise Model (Peterson 1993)!

300 ft level also has quiet times, although not quite as good as 2000 ft.

Conclusion

LIGO achieved design sensitivity and completed a year-long science run.

Searches beginning to have astrophysical implications:» New upper limit on stochastic

background: ΩGW < 9.0×10-6

Significant improvements expected in the coming years:» Enhanced LIGO nearly

completed.» Advanced LIGO construction

under way.» Already thinking about third

generation. Stay tuned...

Environment Stability

Analyzed about 12 days of 2000ft data in Jan/Feb 2009 (Jan Harms).

Environment very stable!

Relative Humidity

Pressure

Temperature

Magnetic Field at 2000 ft

Ground Velocity

300 ft: Guralp not reliable below 50 mHz

2000 ft: above 0.7 Hz dominated by digitizer noise.

Note: 300 ft is NOT surface!

Horizontal

Vertical

300 ft

2000 ft

300 ft

2000 ft

Homestake Horizontal Motion

300ft appears to have significantly more local disturbances.Possibly due to proximity of the shaft and the hoist?

Homestake Vertical Motion

300ft appears to have significantly more local disturbances.Possibly due to proximity of the shaft and the hoist?

Coherence Between Levels

Microseismic peak appears coherent, especially in horizontal DOF.

Elsewhere the coherence is strongly reduced:» Reliable range is: 50 mHz –

0.7 Hz.» Effect of local disturbances at

300 ft?» Effect of the rock structure

between 300ft and 2000ft? Of course, we really care about

coherence at a given level.» Hopefully soon...

Horizontal

Vertical

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

Data manipulation:» Down-sample to 1024 Hz» High-pass filter (32 Hz cutoff)

50% overlapping Hann windows:» Overlap in order to recover the

SNR loss due to windowing.

ii

iii Y

Y2

2

opt

i

i22

opt

i-1 i i+1 i+2

Yi

i

Science Run S5

LIGO science run S5 started on November 4 (14), 2005 at Hanford (Livingston) and ended on September 30, 2007.

One year of coincidence running at LIGO design sensitivity.

New result uses data up to Jan 22, 2007.» About 140 days of effective

observing time. Currently analyzing the rest of the

run:» Duty cycle and sensitivity

improved during the run.» Expect 2x more data and ~2x

better final sensitivity.

Typical strain sensitivitiesduring S5.

S5: H1L1 Coherence

Calculated using S5 data up to 04/07.» Using the same data segments as in

stochastic analysis. Very clean:

» 48.0 Hz (3rd harmonic of 16 Hz).» 108.85 Hz – simulated pulsar.» 60 Hz (only 0.1 Hz resolution).» Additional very weak lines at 46.45

Hz and 47.58 Hz (10 mHz resolution).– Likely instrumental.– Notching them has negligible

effect on the final result.– Currently still included.

No sign of the 1 Hz harmonics, which were present in the S4 search.

1 mHz resolution

0.1 Hz resolution

Coh = CSD2 / PSD1 / PSD2

S5: H1L1 Coherence

Calculated using S5 data up to 04/07.» Using the same data segments as in

stochastic analysis. Very clean:

» 48.0 Hz (3rd harmonic of 16 Hz).» 108.85 Hz – simulated pulsar.» 60 Hz (only 0.1 Hz resolution).» Additional very weak lines at 46.45

Hz and 47.58 Hz (10 mHz resolution).– Likely instrumental.– Notching them has negligible

effect on the final result.– Currently still included.

No sign of the 1 Hz harmonics, which were present in the S4 search.

Coh = CSD2 / PSD1 / PSD2

Data Quality

Frequency notches:

» 48.0 Hz

» 60 Hz harmonics

» Simulated pulsar lines Data Quality Cuts:

» Require |σi±1 – σi| / σi < 20% (removes 4-5% of the segments).

» Reject a handful of segments identified to contain glitches in coherence studies.

All cuts defined blindly (with unphysical time-shift).

Residual distribution consistent with gaussian.

» Passes the Kolmogorov-Smirnov test.

Residual distributionis Gaussian.

S5 H1L1 Results (1)

Point estimate integrand Y(f) reveals no signal.

S5 H1L1 Results (2)

Inverse FFT of Y(f): - Shows no signal. - Gaussian behavior.

S5 H1L1 Results (3)

Preliminary S5 H1L1 result: » Ω σΩ = (1.0 5.2) × 10-6

» H = 72 km/s/Mpc The frequency band is selected to

include 99% of sensitivity, as measured by the integrand of σ-2.» 41.5-177.5 Hz

Bayesian 90% UL:» Prior on Ω: S4 Posterior» Marginalize over calibration

uncertainties– Gaussian priors with standard

deviation 8% for L1, 13% for H1.

» 90% UL: 9.0 × 10-6

Reach as a Function of Spectral Slope

- S3 H1L1: Bayesian 90% UL.- S4 H1L1+H2L1: Bayesian 90% UL.- S5 H1L1 preliminary: Bayesian 90% UL.

- Expected S5: design strain sensitivity and 1 year exposure.

- AdvLIGO: sensitivity optimized for binary neutron star search, and 1 year exposure.

Cosmic Strings: Model Topological defects formed during phase

transitions in the early Universe. Or, fundamental or Dirichlet strings (in

string theory). Cosmic string cusps, with large Lorentz

boosts, can create large GW signals. Look for the stochastic background

created by superposing cusp signals throughout the Universe.

Calculation done by Siemens, Mandic & Creighton, PRL98, 111101 (2007).» Update on Damour & Vilenkin,

PRD71, 063510 (2005).» There are uncertainties in the

calculation.» Some of them can be resolved by

improving simulations of cosmic strings networks.

Small-loop Casep = 5× 10-3

Gµ = 10-7

Small Loop Case If loop-size at formation is determined by

gravitational back-reaction, the loops are small and of the same size.

Parameters:

» loop-size parametrized by: 10-13 < < 1


– Upper bound from CMB observations.

» Reconnection probability: 10-3 < p < 1

– Determines the density of strings. Spectrum has a low-frequency cutoff.

» Determined by the string length and the angle at which we observe the cusp.

Small or G push the cutoff to higher frequencies.

Spectrum amplitude increases with G and with 1/p.

Large Loop Case Recent simulations indicate that loops

could be large at formation, and therefore long-lived.

Loop distribution more complex.» Larger amplitudes of gravitational-

wave spectra. Free parameters:


» Reconnection probability: 10-4 < p < 1 Assuming that loop-size is 10% of the

horizon at the formation time. » Some simulations indicate that a

more complicated distribution would be more accurate, involving both small and large loops.

Interferometer Controls

6 mirrors: many degrees of freedom» Length» Angular

Input field is phase modulated:» Ein = E0 ei**cos(t)

» Carrier + sidebands at ±25 MHz.

» Carrier resonates in arms, sidebands do not!

Sample the beam at several locations, measure with photodiodes.» Output voltage is demodulated.» Pound-Drever-Hall locking.

Reflected Port

Pick-off Port

Antisymmetric Port

Example: White Noise

Define: si(f) = ni(f) + h(f) ni(f) – white gaussian noise h(f) – gaussian, colored, signal

Q(f) = 1 Coherence – “normalized” cross spectrum, averaged over N samples: Coh = CSD2 / PSD1 / PSD2

Running Point Estimate

Pre-Big-Bang: Model

Mechanism similar to inflation:» Amplification of vacuum fluctuations» Super-horizon modes are amplified

during transitions between phases. Universe goes through several phases:

» Dilaton-dominated phase» Stringy phase» Radiation, followed by matter phase.

2 free parameters:» 1 < < 1.5

» fs – essentially unconstrained But: High-frequency amplitude goes as f1

4.

» f1 depends on string related parameters, which are not well known.

» We vary it by factor of 10 around the most “natural” value.

~f3

~f3-2

fs

Mandic & Buonanno, PRD73, 063008, (2006).

Pre-Big-Bang: Results

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:

S3

S4

S5 H1L1

S5 H1H2

AdvLIGO H1H2

BBN

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).

astronomy with gravitational-wave detectors vuk mandic university of minnesota 04/02/09

Documents

time slide

arm length

general relativity slide

arm length difference

wave equation

time interferometers

f t kx slide

neutron stars