Probing Dark Energy with Black Hole Binaries Laura Mersini-Houghton UNC / DAMTP Cambridge U. Firenze, March 2009

Equation of State of Dark Energy W[z] Too many models, too little data. Knowledge of W[z] seems the most important step for progress at present. Problem 1: Data Analysis Depends Heavily on Parameterization of W[z], (i.e. assuming Prior Models). Popular one is polynomial: W[z] = W0 + Wa * z +… Problem 2: Most of our Experiments ‘Contaminated’ by Noise of structure, foreground and background through which signals propagate . Tough since Noise comparable to “Wa”! Measuring W[z] in a Model-Independent Way is the Highest Priority

This New Method Complements Large Scale Efforts on Measuring W[z]. The Main Idea Black Holes (BH) Accrete Dark Energy. Their Mass Changes Depend on W[z]. (T.Jacobson, Babichev et al.). Gravitational Waves (GW) of the Binary Depend on the Masses of BH, thus on Dark Energy, W[z]. Energy Losses from the Emission of GW Reduce the Orbital Radius. This effect was discovered as predicted by Hulse-Taylor for CDM universe, (in the absence of Dark Energy). WHAT’S NEW: GW Emission is different in LCDM! Binary is Modified by Dark Energy. Thus Changes in GW and Orbital Separation carry direct information on Dark Energy W[z]. (For Phantom Energy Orbit is Ripped Apart, Binary Does Not Merge). BENEFITS: Can Be Observed! Avoids Noise from Large Scale Averaging since BH’s Are Compact Objects and GW propagate Unaffected. This New Method Complements Large Scale Efforts on Measuring W[z].

Black Holes Accrete Dark Energy Dark Energy Density Evaporation Lifetime: Solar Mass Time =10^{32} yrs BH Mass Before DE Accretion

Gravitational Waves Emitted by the Binaries Depend on Dark Energy, W[z] GW Power emitted by 2 BH’s with mass, m1 and m2 is: and frequency: The energy carried away by GW’s induces a loss in the Gravitational Mass ‘M’ of Binary: BUT BH Mass is: Equating the Energy Loss of the System to Power carried in GW tells us how the orbital separation ‘R’ changes as a result: PGW = d(M) / dt Eq.1

Binaries in LCDM Background Let’s take Equal Mass BH’s for simplicity. Then Orbit “R” obtained from Eq.1: Notice that all the terms in the solution R[t] are due to DE, except the last one which is the well known Hulse-Taylor term: Y2 Y1

Time (yrs) R[t] (m) W[z] W[z] Time (yrs)

Can it be observed? Y1 / Y2 = For Supermassive Black Holes (SBH), m = a Msun and large separation R0 = b Rschwarzchild, the DE correction terms, Y2, dominates over the standard Hulse-Taylor term, Y1, for 2ba >10^18: Y1 / Y2 = Such Binaries Exist! Two already observed.

GALAXY 0402 +379: 2007 VLBA R0 =40 pc, T=10^14 s, a=2 10^8, O =10^(-14) Hz, dR1=(1+w)10^6 m, dR2 = 10^10 m (merge in 1000yrs, 2 orders of magnitude) - Radio GALAXY OJ287: 2008 VLBA R=10 Mpc, T=12yrs, a=10^10, (merging accelerated by 3 orders of magnitude). Notice that if : W[z] < -1, then Merging does Not occur. Orbits Increase, they are Ripped Apart!