Detecting Additional Polarization Modes with LISAmoriond.in2p3.fr/grav/2017/transparencies/3_tuesday/1...LISA with 3 arms 2 detectors Simultaneous detection of 2 polarizations How

Detecting Additional PolarizationModes with LISA

Lionel Philippoz

Department of PhysicsUniversity of Zurich

La Thuile, 28.03.2017

Moriond 2017 Polarization - LISA

Outline

1. Polarization of GW

2. LISA sensitivity to additional modes

3. Mode extraction

4. Comments on LISA


Motivation

Existence of scalar fields (e.g. Higgs)⇒ Extensions of GR

SGWB possible from unresolved sources⇒ Analyze the polarization content of such asignal


Polarization


Polarization (tensor modes from GR)


Polarization (tensor modes from GR)

eLISA/NGO Yellow Book, 2012


Polarization (additional modes)

GR: h+ and h×Metric theories of gravity: up to sixpolarizations

Not all of them disappear within the frame of agiven theory

2T, 2V, 2S





hij(ωt − k · x) =∑A

hA(ωt − k · x)eAij

e+ij =

1 0 00 −1 00 0 0

e×ij =

0 1 01 0 00 0 0

exij =

0 0 10 0 01 0 0

eyij =

0 0 00 0 10 1 0

ebij =

1 0 00 1 00 0 0

e lij =

0 0 00 0 00 0 1


Some examples

Theories Polarization modesGR +, ×Metric f (R) gravity +, ×, b, lPalatini f (R) gravity +, ×Scalar-tensor theory (massive) +, ×, b, lBrans-Dicke theory (massive) +, ×, b, lBrans-Dicke theory (massless) +, ×, bMassive bimetric +, ×, b, l , x , y

......

⇒ There is a way to discriminate those theories!


Several questions

Without any assumption, a SGWB would contain amixture of all modes:

Is LISA sensitive to additional modes?

SNR for each mode?

How to extract the information regarding theadditional modes?


Sensitivity


Sensitivity to additional modes

3 arms, 2.5 millionskm

TDI (X , α, ζ, E , P ,U)

LISA with 3 arms≡ 2 detectors

Simultaneousdetection of 2polarizations

How sensitive?


LISA: sensitivity to other modes

Noise power spectrum SX (f )

10-4 0.001 0.010 0.100 110-44

10-42

10-40

10-38

10-36

f/Hz

Noisepowerspectrum/Hz⁻¹



RMS GW response XRMS(f )

10−4 10−3 10−2 10−1 10010

−4

10−3

10−2

10−1

100

101

f(Hz)

XR

MS(f)

/H

Scalar T

TensorVector

Scalar L

Tinto, Alves, PRD 82, 122003 (2010)



X Sensitivity SNR ·√SX (f )B/XRMS

10−4 10−3 10−2 10−1 10010

−24

10−23

10−22

10−21

f(Hz)

X S

ensi

tivity

Scalar T

Tensor

Vector

Scalar L

Tinto, Alves, PRD 82, 122003 (2010) [SNR=5, T=1 year]


Extraction of the modesfrom a SGWB


SGWB with all polarization modes

SGWB from many unresolved sources (e.g.produced during inflation):

isotropic

independently polarized

stationary

Gaussian

⇒ Model-independant


h(t, x) =∑A

∫S2

dΩ

∫ ∞−∞

df hA(f , Ω)e2πif (t−Ωx/c)FA(Ω),

FA: antenna pattern function


Mode separation: recipe

1. Network of detectors: cross-correlation(to discriminate from stochastic detector noise)

2. Sensitivity to each mode

3. Correlation matrix

Nishizawa et al. PRD 79, 082002 (2009)Nishizawa, Taruya, Kawamura, PRD 81, 104043 (2010)


Network of detectors

Nishizawa, Ayama, 2013


Energy densities

ΩAGW(f ) =

1

ρcrit

dρAGWd ln(f )

∝ f 3SAh (f )

ΩTGW = Ω+

GW + Ω×GWΩV

GW = ΩxGW + Ωy

GW

ΩSGW = Ωb

GW + ΩlGW


Power-spectral density, noise spectrum

s(t) = h(t) + n(t)

〈h∗A(f , Ω)hA′(f ′, Ω′)〉 = δ(f − f ′)1

4πδ2(Ω, Ω′)δAA′ · 1

2SAh (|f |)

〈nI (f )nJ(f ′)〉 =1

2δ(f − f ′)δIJ · PI (|f |)


Optimal SNR for each mode

SNRM ∝∫ ∞0

df

[(ΩM

gw(f ))2 det F(f )

f 6FM(f )

](1/2),

FMM′ =∑

detector pairs (I , J)

∫ Tobs

0

dtγMIJ (t, f )γM

′

IJ (t, f )

PI (f )PJ(f ),


Overlap reduction functions γAIJ(f )

Nishizawa, Ayama, 2013


Mode extraction

Define the statistics

ZIJ ∝∣∣f 3∣∣ s∗I (f )sJ(f )

=∑M

ΩMGWγ

MIJ (f ) + noise

〈ZIJ〉 =∑M

ΩMGWγ

MIJ (f )


Mode extraction

〈Z12〉〈Z23〉〈Z31〉

=

γT12 γV12 γS12γT23 γV23 γS23γT31 γV31 γS31

ΩTGW

ΩVGW

ΩSGW

Z Π Ω

Ω = Π−1Z (det Π 6= 0)


Potential problems/solutions for LISA

Full polarization extraction: requires anetwork (future projects?)

Autocorrelation technique:(Tinto, Armstrong, 2013 (1205.4620))

1 single detector with correlated noise∼ 2 colocated/coaligned detectors withuncorrelated noise

But not yet for the full polarization content

Correlation at different times, noise problem tosolve


Conclusion

LISA sensitive to additional modes

Higher sensitivity to longitudinal scalar/vectormodes

Possible to extract the polarization contentfrom a SGWB signal

Single cluster: simultaneous detection of twopolarizations (3 arms)

Network: Separate detection of all modes

All modes with a single cluster?


Thank you for your attention!


Detecting Additional Polarization Modes with LISAmoriond.in2p3.fr/grav/2017/transparencies/3_tuesday/1...LISA with 3 arms 2 detectors Simultaneous detection of 2 polarizations How

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