Standard sirens cosmography with LISA

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1 Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

2 The concept of standard siren The luminosity distance can be inferred directly from the measured waveform produced by a binary system h = 4 ( ) 5 ( ) 2 GMc 3 πf 3 cos ι sin[φ(t)] d L c 2 c GW sources are standard distance indicator (standard sirens) The problem with GW is to obtain the redshift of the source through the detection of an EM counterpart such as EM emission at merger Hosting galaxy

3 The distance-redshift relation d L (z) = c [ 1 + z Ωk z sinh H 0 Ωk 0 The distance-redshift relation connects the luminosity distance (d L ) to the redshift (z) at any point in the universe and depends on the cosmological parameters if for some astrophysical object both d L and z are known, one can fit the distance-redshift relation and obtain constraints on the cosmological parameters Example: Supernovae type-ia (standard candles) ] H 0 H(z ) dz

4 What sources can be used as standard sirens for LISA? How many standard sirens will be detected by LISA? What type of sources can be used? For how many it will be possible to observe a counterpart?

5 The LISA mission Laser Interferometric Space Antenna Proposed design: [arxiv: ] Near-equilateral triangular formation orbiting around the Sun 6 laser links (3 active arms) Armlength: 2.5 million km [lisamission.org] Mission duration: 4 years Main target sources: MBHBs: M Stellar mass BHBs: M Stochastic background: astrophysical & cosmological origin Extreme mass ratio inspirals (EMRIs)

6 The Gravitational Wave Landscape

7 Standard sirens for LISA Possible standard sirens sources for LISA: Massive BHBs ( M ) Stellar mass BHBs ( M ) EMRIs

8 Standard sirens for LISA Possible standard sirens sources for LISA: Massive BHBs ( M ) Stellar mass BHBs ( M ) EMRIs Characteristics of Massive BHB mergers: High SNR High redshifts (up to 10-15) Merger within LISA band Gas rich environment EM counterparts expected!

9 Standard sirens for LISA Possible standard sirens sources for LISA: Massive BHBs ( M ) Stellar mass BHBs ( M ) EMRIs Characteristics of StMBHBs and EMRIs: Low redshifts ( 0.1 for StBHBs and 1 for EMRIs) Merger outside the LISA band (StMBHBs) Gas poor environment No EM counterparts expected!

10 Standard sirens for LISA Example of possible LISA cosmological data 100 EMRIs dl Gpc 10 1 Stellar mass BHBs MBHBs 0.1 CDM StMBHBs: [Del Pozzo et al, ; Kyutoku & Seto, ] EMRIs: [MacLeod & Hogan, ] MBHBs: [Tamanini et al, ; Petiteau et al, ]

11 Standard sirens for LISA: stellar mass BHBs Redshift range: z 0.1 Method: without counterparts Expected detections: 50/yr Useful standard sirens: 5/yr Average LISA errors: d L /d L < 20% Ω 1 deg 2 Results: H 0 to few % [Del Pozzo et al, ] [Kyutoku & Seto, ]

12 Standard sirens for LISA: EMRIs Redshift range: 0.1 z 1 Method: without counterparts Expected detections: /yr Average LISA errors: dl /d L few % Ω few deg 2 Useful standard sirens:? Results: H 0 to 1% with 20 EMRIs at z 0.5 (obsolete) [MacLeod & Hogan, ] [Babak et al, ]

13 Standard sirens for LISA: massive BHBs Events 5 years 10 8 L6A2M5N Light seeds popiii 26.4 Heavy seeds delay 40.4 Heavy seeds no delay Redshift range: 1 z 8 Method: with counterparts dl Gpc z z Expected detections: /yr Average LISA errors: d L /d L few % (inc. lensing) Ω < 10 deg 2 Useful standard sirens: 6/yr (with counterpart) Results: H0 to 1% w0 to 15% [Tamanini et al, ]

14 MBHBs: data simulation approach To obtain cosmological forecasts, we have adopted the following realistic strategy: [NT, Caprini, Barausse, Sesana, Klein, Petiteau, arxiv: ] Start from simulating MBHBs merger events using 3 different astrophysical models [arxiv: ] Light seeds formation (popiii) Heavy seeds formation (with delay) Heavy seeds formation (without delay) Compute for how many of these a GW signal will be detected by LISA (SNR>8) Among these select the ones with a good sky location accuracy ( Ω < 10 deg 2 ) Focus on 5 years LISA mission (the longer the better for cosmology)

15 MBHBs: data simulation approach I To model the counterpart we generally consider two mechanisms of EM emission at merger: (based on [Palenzuela et al, ]) I I A quasar-like luminosity flare (optical) Magnetic field induced flare and jet (radio) I Magnitude of EM emission computed using data from simulations of MBHBs and galactic evolution I EM transients expected long after the merger (up to weeks/months)

16 MBHBs: data simulation approach Finally to detect the EM counterpart of an LISA event sufficiently localized in the sky we use the following two methods: LSST: direct detection of optical counterpart SKA + E-ELT: first use SKA to detect a radio emission from the BHs and pinpoint the hosting galaxy in the sky, then aim E-ELT in that direction to measure the redshift from a possible optical counterpart either Spectroscopically or Photometrically

17 MBHBs: standard sirens rate Example of simulated catalogue of MBHB standard sirens: dl Gpc z Events 5 years L6A2M5N Light seeds popiii 26.4 Heavy seeds delay 40.4 Heavy seeds no delay z Note 1: LISA will be able to map the expansion at very high redshifts (data up to z 6), while SNIa can only reach z 1.5 Note 2: Few MBHBs at low redshift bad for DE (but on can use SNIa and other GW sources)

18 MBHBs: cosmological parameter constraints RESULTS: [NT et al, arxiv: ] 1σ constraints with 5 million km armlength: { Ω M (8%) ΛCDM: h (2%) Ω M (18%) ΛCDM + curvature: Ω Λ 0.15 (21%) h (5%) { w Dynamical DE: w a 0.83 Similar results with 1 or 2 million km armlength

19 MBHBs: cosmological parameter constraints RESULTS: [NT et al, arxiv: ] 1σ constraints with 5 million km armlength: { Ω M (8%) ΛCDM: h (2%) < 1% (with Planck) Ω M (18%) ΛCDM + curvature: Ω Λ 0.15 (21%) h (5%) { w Dynamical DE: w a 0.83 Similar results with 1 or 2 million km armlength

20 LISA forecasts: alternative cosmological models Investigation of alternative cosmological models: [C. Caprini & NT, arxiv: ] Same approach to construct standard sirens catalogues and analyse data Focus on interesting and simple phenomenological models: Early dark energy (EDE): non-negligible amount of DE at early times [arxiv: ] Interacting dark energy (IDE): mild indications for a non-vanishing late-time dark interaction [arxiv: ] Deviations from ΛCDM allowed only up to a determined redshift (z e, z i )

21 LISA forecasts: alternative cosmological models de EDE 0.03 ze 6 EDE 0.03 ze Pettorino et al 2013 CDM Early dark energy: non negligible DE energy density at early times: Ω de (z) Ω e de 0 as z Ω de (z) = Ω0 de [ ] Ωe de 1 (z + 1) 3w 0 Ω 0 de + Ω0 m(z + 1) 3w + Ω e [ ] de 1 (z + 1) 3w 0 0

22 LISA forecasts: alternative cosmological models Results for EDE: [C. Caprini & NT, arxiv: ] ede Light seeds popiii Heavy seeds delay Heavy seeds no delay z e 1 z e 2 z e 3 z e 4 z e 6 z e 6 If z e 10 then strong constraints from CMB: Ω ede = [Planck, 2015] However if z e 10 then CMB results do not apply and only LISA can constrain deviations from ΛCDM

23 LISA forecasts: reconstructing the dark sector interaction Using Gaussian processes to reconstruct the interaction in a model independent way [Cai, NT, Yang, arxiv: ] 4 4 LISA-popIII-5 years q q q 4 LISA-Q3d-5 years LISA-Q3nod-5 years 3 ΛCDM 3 ΛCDM 3 ΛCDM D ΛCDM Redshift(z) D ΛCDM Redshift(z) D ΛCDM Redshift(z) Redshift(z) Redshift(z) Redshift(z) LISA MBHB standard sirens reconstruct the interaction well for 1 z 3 (5 yr) and 1 z 5 (10 yr)

24 Future work Future perspectives for LISA cosmology: Check the cosmological potential of EMRIs Improve MBHB standard siren models (formation and counterpart models) Combine all LISA sources into a single cosmological analysis Combine LISA forecasts with future EM forecasts Analyse other alternative cosmological models Investigate the potential of LISA to constrain modified gravity at high redshift

25 Summary Standard sirens are excellent distance indicators: Do not require calibration and are not affected by systematics Can be used with or without an EM counterpart Standard sirens for LISA: Three possible sources: SOBHBs (no EM counterpart) EMRIs (no EM counterpart) MBHBs (EM counterpart) Probing the cosmic expansion from z 0.01 to z 10 Useful to constrain H 0 and test alternative cosmological models