A Search for Alternative Gravitational-Wave Polarizations in the Stochastic Background

Tom Callister (Caltech) for the LIGO Scientiﬁc Collaboration & Virgo Collaboration

PASCOS 2018 June 7, 2018 LIGO DCC# G1801143 Alternative theories of gravity predict alternative gravitational- wave polarizations.

The stochastic gravitational-wave background is a useful tool in hunting for alternative polarizations.

LIGO & Virgo collaborations looked for alternative polarizations in the gravitational-wave background in O1 data.

We didn’t ﬁnd any. Six possible gravitational-wave polarizations

y y x y y x or y

z z z “Tensor” x x z z x z

Plus Cross Vector-x Vector-y Breathing Longitudinal y y x y y x or y

z z z x “Vector” x z z x z

Plus Cross Vector-x Vector-y Breathing Longitudinal y y x y y x or y

z z z x x z “Scalar” z x z

Plus Cross Tom CallisterVector-x Vector-y Breathing Longitudinal 3 Six possible gravitational-wave polarizations

y y x y y x or y

z z z “Tensor” x x z z x z

Plus Cross Vector-x Vector-y Breathing Longitudinal y y x y y x or y

z z z x “Vector” x z z x z

Plus Cross Vector-x Vector-y Breathing Longitudinal y y x y y x or y

z z z x x z “Scalar” z x z

Plus Cross Tom CallisterVector-x Vector-y Breathing Longitudinal 4 LIGO has different responses to different polarizations

Maximal response to waves from z- No response direction

Fb/Fl Plus mode|F+| antenna Breathing mode antenna pattern pattern

Tom Callister 5 Generally have insufﬁcient information for polarization measurements

• Six unknowns require six measurements

• Need six gravitational wave detectors to fully measure a transient’s polarization!

• Three detectors allow limited statements about polarization of transient signals (e.g. GW170814)

• LIGO & Virgo Collaborations (1709.09660)

Tom Callister 6 Other (hypothesized) sources may be more promising

• Long-duration sources: Measurements at many different times

• Rotating neutron stars • M. Isi et al. 2017 (1703.07530) • LIGO & Virgo Collaborations 2018 (1709.09203)

• Spatially-extended sources: Measurements in many different directions

• Stochastic gravitational-wave background

• T. Callister et al. 2017 (1704.08373) |F+| • LIGO & Virgo Collaborations 2018 (1802.10194)

Tom Callister 7 The stochastic gravitational-wave background

• Superposition of all gravitational-wave signals too weak to directly detect

• Contributions from: • Compact binary mergers • Supernovae • Rotating neutron stars • Cosmic strings? • Inﬂation?

Energy in GWs per • Parametrized by a dimensionless energy density: logarithmic frequency interval

Tom Callister 8 An Example Energy-Density Spectrum Energy Density Energy

The LIGO & Virgo Collaborations, Phys. Rev. Lett. 120, 91101 (2018).

Frequency (Hz)

Tom Callister 9 An Example Energy-Density Spectrum

Power-law at low frequencies Energy Density Energy

The LIGO & Virgo Collaborations, Phys. Rev. Lett. 120, 91101 (2018).

Frequency (Hz)

Tom Callister 10 Background induces correlated signal in multiple detectors

• Measured by cross-correlating data from widely-separated detectors

• Expected correlation due to a stochastic background:

Transfer functions Energy densities in (overlap reduction tensor (T), vector (V), functions) and scalar (S) modes

Tom Callister 11 Different transfer functions for different polarizations

Hanford-Livingston 0.4

0.2

0.0

0.2 ) f (

0.4

0.6 Tensor Vector 0.8 T. Callister, S. A. Biscoveanu, et al., Scalar Phys. Rev. X 7, 041058 (2017) 1.0 0 50 100 150 200 250 300 350 400 f (Hz)

Tom Callister 12 Measuring alternative polarizations in the background

• Assume a power-law form for each contribution to the background

• Given measured , ﬁt a model of the form

Tom Callister 13 Results from Advanced LIGO’s ﬁrst observing run

• Used data recorded during Advanced LIGO’s ﬁrst observing run (Sept. 2015 — Jan. 2016)

• No detection of the stochastic gravitational-wave background (of any polarization)

• Bayesian log-odds between Signal and Noise hypotheses

Tom Callister 14 Upper limits on alternative polarizations

1.0 Log Uniform Prior Uniform Prior 0.8

0.6 PDF 0.4

0.2 Posterior Probability Posterior

0.0 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 T V S log ⌦0 log ⌦0 log ⌦0 Tensor Log-Amplitude Vector Log-Amplitude Scalar Log-Amplitude

Tom Callister 15 Upper limits on alternative polarizations

1.0 Log Uniform Prior LIGO & Virgo Collaborations Uniform Prior 0.8 PRL 120, 201102 (2018)

0.6

PDF 0.4

0.2 Posterior Probability Posterior

0.0 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 T V S log ⌦0 log ⌦0 log ⌦0 Tensor Log-Amplitude Vector Log-Amplitude Scalar Log-Amplitude

• At 95% credibility (with log-uniform priors):

Tom Callister 16 Summary

• The stochastic gravitational-wave background is a useful tool for studying gravitational-wave polarizations

• At present, no background (of any polarization) has been detected

• First upper limits on the presence of alternative polarizations in the stochastic background

• Additional reading:

• T. Callister, S. A. Biscoveanu, N. Christensen et al., Phys. Rev. X 7, 041058 (2017). ArXiv: 1704.08373

• The LIGO Scientiﬁc Collaboration & Virgo Collaboration, Phys. Rev. Letters 120, 201102 (2018). ArXiv: 1802.10194

Tom Callister 17 Extras LIGO has different responses to different polarizations

Plus mode Vector-x mode Breathing mode

Tom Callister 19 LIGO/Virgo Antenna Responses

Fx Fy |F+| F× Plus Cross Vector-x Vector-y

Fb/Fl Breathing & Longitudinal Tom Callister 20 Effect of different overlap reduction functions

7 10 1.0 ⇥ Tensor Injected Scalar Measured 0.5 ) f

( 0.0 ˆ C

0.5

T. Callister, S. A. Biscoveanu, et al., Phys. Rev. X 7, 041058 (2017) 1.0 101 102 f (Hz)

Tom Callister 21 Effect of different overlap reduction functions

8 10 2.0 ⇥

1.5 Tensor Injected Scalar Measured 1.0

0.5 ) f

( 0.0 ˆ C 0.5 1.0 1.5 T. Callister, S. A. Biscoveanu, et al., Phys. Rev. X 7, 041058 (2017) 2.0 101 102 f (Hz)

Tom Callister 22 Past searches could have missed a vector/scalar background

6 10 T. Callister, S. A. Biscoveanu, et al., Phys. Rev. X 7, 041058 (2017) a 0 7 10

8 10

9 10 Tensor Optimal

Detectable Amplitude ⌦ Vector Naive Scalar 10 10 2 1 0 1 2 3 4 Spectral Index ↵

Tom Callister 23 Past searches could have missed a vector/scalar background

Vector Scalar 101 Optimal /T Naive T

T. Callister, S. A. Biscoveanu, et al., Phys. Rev. X 7, 041058 (2017) 100 2 1 0 1 2 3 4 Spectral Index ↵a

Tom Callister 24 Full O1 Parameter Estimation Results

5 6 7

V 0 8 9 95 log ⌦ 10 68 11 12 13 5 6 7 95

S 0 8 68 9 68 LIGO & Virgo Collaborations

95 log ⌦ 10 11 PRL 120, 201102 (2018) 12 13 8 6 95 95 95 4 68 2 T 0 ↵ 2 4 68 68 6 8 8 6 95 4 95 95 68 95 2 V 0 ↵ 2 4 68 68 68 6 8 8 6 4 95 95 68 68 68 2 68

95 S 0 ↵ 2 4 68 6 95 95 8 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 13 12 11 10 9 8 7 6 5 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 T V S ↵T ↵V ↵S log ⌦0 log ⌦0 log ⌦0

Tom Callister 25 Full O1 Parameter Estimation Results

7 10 5 ⇥ 4

3 95 V 0

⌦ 2 68 1 0

6 10 1.8 ⇥ 1.5 1.2

S 0 0.9 LIGO & Virgo Collaborations ⌦ 0.6

0.3 68 95 68 95 PRL 120, 201102 (2018) 0.0

8 6 4 68 95 2 95 68 T 0 ↵ 2 4 6 95 68 8

8 6 4 95 2 68

V 68 0 95 95 ↵ 2

68 4 68 6 95 8

8 6 4 2 95 68 S 0 68 ↵ 95 2 4 68 6 68 68 8 95 95 95 0 1 2 3 4 5 0 1 2 3 4 5 0.0 0.3 0.6 0.9 1.2 1.5 1.8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 7 7 6 T 10 V 10 S 10 ↵T ↵V ↵S ⌦0 ⇥ ⌦0 ⇥ ⌦0 ⇥

Tom Callister 26