LISA 1

Fundamental Physics with LISA

Bernard Schutz

Albert Einstein Institute, Golm

School of Physics and Astronomy, Cardiff

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Verifying gravitational waves

Testing GR in strong field domain

Cosmogony

New fundamental physics

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Testing GR’s GW model

Do GWs exist?– Verification binaries, good SNR. Given Hulse-Taylor binary pulsar, hard to

imagine that LISA will see no GWs. But observations will test quadrupole radiation formula, look for extra polarizations.

Do GWs travel at the speed of light? – If LISA finds an edge-on CWDB that can be observed optically for eclipses,

then phasing of GW should match phasing of light. – Not as strong as ground-based observations of γ-bursts from NS-NS

coalescence. Are there other associated gravitational radiation fields (eg scalar-

tensor theories), polarization states?– By observing thousands of resolved CWDBs over 5 years, LISA can look for

residuals from standard GR fits to waveforms. Dispersion?

– Fitting inspiral signal to PN model, with high SNR, may reveal unexpected phasing if higher frequencies travel faster than lower (graviton mass).

– For inspirals or EMRIs, orbital plane might show anomalous precession due to parity failure (right- and left-hand polarizations propagate differently in some string theory models).

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Verifying gravitational waves

Testing GR in strong field domain

– SMBH binaries

– EMRI as Probes of the Metric

– EMRIs in Binary SMBH Systems

– EMRIs as Tests of Gravitation Theory

Cosmogony

New fundamental physics

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SMBH Mergers: Strong-field Dynamics

Verifying that black holes exist– Probably the observation that will create the biggest impression in physics and

astronomy: listening to their merger and ringdown will be our only direct test of black holes. (Ground-based detectors may do this earlier than LISA, but with lower SNR.)

Test Cosmic Censorship Hypothesis– Remember: still a hypothesis, so there is potential for something new!

– Look for compact object with a/m > 1.

– Might come from comparing mergers with numerical simulations, or from EMRI observations. Since accretion-fed holes may have a/m > 0.98, EMRIs with high SNR will be needed to be sure.

Test Hawking Area Theorem– Genuine theorem, but deeply linked to thermodynamics, quantum theory,

probably quantum gravity – strong motivation for testing it.

– Equal-mass mergers generate a lot of entropy, but in simulations they are very far from limiting case of Afinal = ΣAinitial.

– EMRI and IMRI mergers do not seem promising either.

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Probing Strong Curvature with EMRIs

EMRIs are one of LISA’s strongest tools for studying fundamental physics, and they set the LISA noise requirement at mid-range frequencies.

Very sensitive because of large number of cycles: chirp time

Null test of uniqueness of Kerr metric: fit EMRI waveforms to signal, determine if errors are consistent with noise/confusion background.

Testing for non-Kerr metric: existing studies (Glampedakis & Babak 2005, Barak & Cutler 2007, Barausse et al 2007) examine how EMRIs could test if metric is non-Kerr but still GR: eg due to accretion disk or tidally distorting nearby body.

– They do not look for evidence for non-GR theories, because they assume GR to generate waveforms in the distorted metric.

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EMRIs from Binary SMBH Systems

An EMRI might come from a compact object falling onto a SMBH that is itself in a binary. Would notice a gradual drift in f due to acceleration of central SMBH.

In 3 yr observation, Δf = 10-8 Hz. At f = 1 mHz, LISA could resolve Δv/c = 10-5, or an acceleration a = 3x10-5 ms-2.

If both SMBHs were 106 M, then they should be closer than 0.3 pc to one another.

The acceleration parameter should be part of the signal fit.

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Using EMRIs to Test Gravity Theory

To compare GR with an alternative theory, need to compute EMRI waveforms self-consistently in the other theory, including EOM.

– For Hulse-Taylor Binary Pulsar, the limits on Brans-Dicke ω come from a calculation that includes scalar radiation and its back-reaction (Will).

– In Hulse-Taylor system, scalar effects are anomalously small (test anomalously weak) because stars have nearly equal mass, reducing scalar dipole radiation.

Black holes radiate away massless fields when formed, so in Brans-Dicke, BHs are the same as in GR.

– EMRI signals from stellar-mass BHs falling into SMBHs will not test such theories. Weaker EMRI signals from NS’s or WD cores of giant stars will provide tests.

We lack a “Parametrized Post Kerr” framework that includes other theories – hard to quantify the meaning of a null result when looking for violations of GR.

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Verifying gravitational waves

Testing GR in strong field domain

Cosmogony

– Dark energy measurement

– Redshift-distance relation

– Dark energy mission

New fundamental physics

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LISA and Dark Energy We have known for 22 years that binary inspirals are standard candles

(standard sirens).– Ground-based detectors will use them to perform an independent measurement of the

Hubble constant.

LISA’s SMBHs permit it to measure the acceleration of the universe.– The so-called Dark Energy is possibly the biggest challenge to fundamental theoretical

physics today.

The Dark Energy Task Force (DOE/NSF 2006) did not treat LISA’s capability seriously:

A year later, the BEPAC committee (NAS 2007) took a different view:

Other techniques …, such as using … gravitational waves from coalescing binaries as standard candles, merit further investigation. At this time, they have not yet been

practically implemented, so it is difficult to predict how they might be part of a dark energy program. We do note that if dark energy dominance is a recent cosmological

phenomenon, very high-redshift (z 1) probes will be of limited utility.

LISA also has the potential to measure the dark energy equation of state, along with the Hubble constant and other cosmological parameters. Through gravitational wave form measurements LISA can determine the luminosity distance of sources directly. If

any of these sources can be detected and identified as infrared, optical or x-ray transients and if their redshift can be measured, this would revolutionize cosmography

by determining the distance scale of the universe in a precise, calibration-free measurement.

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Measuring Redshift-Distance Relation

Any binary system that chirps during observation has intrinsic distance information in signal. Chirp time measures chirp mass M = (m1m2)3/5/(m1+m2)1/5. Amplitude depends just on M/DL, where DL is the luminosity distance, so measuring it gives DL.

Converting detector response into signal amplitude requires measurement of polarization, sky position. Strong covariance of errors among these and the chirp mass.

Getting the redshift normally requires identifying the host galaxy or cluster and obtaining an optical redshift. Small error box is key to this.

– Since 2006 LISA community has made better estimates of errors by implementing full TDI in data analysis and using better signal models.

– Talks by Cutler, Cornish, van den Broeck, Porter, Babak, Husa address this. NB: identification reduces error in DL. Weak lensing produces random errors in DL. Not clear how much

can be removed by lensing studies of signal field. Using EMRI spirals, Hogan & McLeod (2007) show that LISA can

measure H0 to 1% accuracy (needs 20 events to z = 0.5).

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LISA as a Dark-Energy Mission

LISA has 3 capabilities that complement existing dark energy proposals

1. Calibration-free. No distance ladder, binary sources are clean systems. Even G is not involved: DL is measured in seconds.

2. Not statistical: each event gives a measurement of DL.

3. Potentially long range: LISA will see coalescences out to z = 20, although identifications are probably not likely beyond z = 3. Most dark-energy methods, even with dedicated missions, stop around z = 1.

If we take the dark energy EOS as the conventional P = wρ, and look for evolution in w by defining w = -1 + w1z + O(z2), then one can show that in the recent past, if our universe is flat,

Then if there is no evolution (w1 = 0), dark energy is 25% of H2 at z = 1, 7% at z = 2, and 3% at z = 3. (Recall DETF comment on high-z behavior.) If w1 = 0.2, then at z = 2 dark energy is 10% of H2. LISA may well be able to make this measurement, but it will need errors of order 1% to distinguish w1 = 0.2 from w1 = 0.

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Verifying gravitational waves

Testing GR in strong field domain

Cosmogony

New fundamental physics

– Fundamental physics and gravity

– New physics

– Brane physics

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Fundamental Physics and Gravity

Physics beyond the standard model should provide ways of:– unifying the strong and electroweak interactions (GUTs),

– showing why there is a non-zero baryon number (CP violation),

– explaining why the universe is so well fine-tuned for life to exist (multiverse, Everitt-Wheeler, …)

Because we expect GR to give way to a quantum theory, we expect corrections. Naïvely they should be at the Planck scale, but new ideas suggest other ways of looking for new physics.

– Branes. Since string theory is renormalizable only if the full theory is written in 11 dimensions, there is plenty of freedom for new physical ideas. Instead of compactifying the extra dimensions, Nature could allow them to be large and just confine us to the 3+1 brane. Only gravity leaks out into the “bulk”. But LISA observes gravity, so LISA can touch the bulk.

– Emergent gravity. Gravity may not be the fundamental interaction we think it is. It might be an effective theory based in some other kind of microphysics, emerging at low energies the way superfluidity emerges from molecular dynamics.

– Loops and topology. Gravity may be the long length-scale limit of a theory that is not based on a continuous manifold but rather on some topological structure. Already loop quantum gravity has found a way through the Big Bang to an earlier epoch. Some topological theories predict that Λ maintains a constant proportion to the matter energy density at all times.

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Where is the new physics?

Cosmic strings (see talk by Siemens): distinctive signature in GWs. Ground-based detectors already searching for them. May be a consequence of superstring theory (Damour & Vilenkin 2001)

Stochastic GW background: LISA sensitive at level Ωgw ~ 10-10. Too strong for standard slow-roll inflation. But f ~ 0.1 mHz is in the band of radiation emitted during the electroweak transition, when T ~ 1 TeV:

The EW transition is normally thought of as second-order (no density perturbations), but if baryon-antibaryon asymmetry arose there, then it could have resulted in strong density perturbations (Megewand & Astorga 2006)

String theory could make many modifications in gravity, including adding extra fields (talk by Yunes) and f(R) action terms. In principle, the best chance for observing these fields may be in EMRIs where R is large and δR comes from inspiral. (But recall that massless fields get radiated away in collapse.)

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Physics on branes

The brane paradigm (Maartens, Living Reviews) offers plenty of scope for new gravitational effects

– Larger amounts of stochastic gravitational radiation (eg Randall & Servant 2006)

– Radiation in our universe from “shadow matter” on a nearby brane connected to us by a black string that looks to us like a black hole (Maeda & Wands 2000, Clarkson & Searha 2006)

– No stochastic background radiation: the Ekpyrotic Universe (Steinhardt & Turok)