Stringent Constraints on

Brans-Dicke Parameter using DECIGO

Kent Yagi (Kyoto-U.)

LISA/DECIGO Workshop @ Sagamihara

Nov. 2008

Collaborators: T.Tanaka(YITP)

N.Seto (Kyoto-U.)

§1. Introduction

・ The aim of my work: Verification of G.R. in strong field region by

detecting G.W.s from NS/BH binaries using DECIGO.

・ There exist many modified theories of gravity. e.g. scalar-tensor, vector-tensor, f(R) gravity, massive graviton

・ scalar-tensor theory

gravity = metric + scalar

(i) KK theory （ dilaton ）(ii) superstring theory(dilaton)(iii) braneworld (radion)…Garriga&Tanaka(2000) (iv) inflation (inflaton)…Steinhardt&Accetta(1990)(v) dark energy (quintessence)…Perrotta&Baccigalupi(1999)

・ Why do we consider such theory? Because it appears in many situations.Here are some lists (+corresponding scalar fields):

・ For now, we consider the simplest scalar-tensor theory, the Brans-Dicke theory.

§2. Brans-Dicke Theory

・ Action of Brans-Dicke theory:

・ B.D.→G.R. (ωBD→∞) 　　 (in this case, φ becomes

const.)

・ The current strongest constraint on ωBD:

Shapiro time delay from Saturn probe Cassini.

(ωBD=const. )

ωBD >40000 (Cassini Bound)

・ EoM for the B.D. scalar field:

・ In the case of compact objects binary:

This characterises the gravitational dipole radiation.

Generating gravitational dipole radiation.

・ Gravitational Const. G:

G is not a constant in this theory.

T: trace of energy-momentum tensor

§3. Waveforms of NS/BH in B.D.

Assumptions:

・ Stationary phase approximation ・ Observation starts 1 year before the coalescence ⇒ We assume that the orbits are circular.

・ Neglect spin precessions (for simplicity)

・ Neglect the directions of binaries and the inclinations of the orbits

(assuming we have averaged over those angles.)

・ Gravitational waveform in Fourier component:

Amplitude: : chirp mass

DL: luminosity distance

Phase: (up to 2PN)

tc: coalescence time φc: coalescence phase

β ：　 spin-orbit coupling

S=s1-s2 ← φdependence of mass

B.D. dipole(-1PN)

G.R. quadrupole

§4. Parameter Estimation

・ We want to determine the binary parameters from G.W.

・ 6 parameters: θa = M, η, tc, φc, β, ωBD-1

・ Apply the usual matched filtering analysis.

Fisher Matrix:

Inner product ：

・ We assume the noise is stationary & Gaussian. ⇒the probability distributions of parameters are Gaussian.

Sn(f):noise spectrum

θa

θatrue

p(θa)

estimation error

・ constraint for ωBD: ωBD > 1/Δ(ωBD-1)

§5. Results

BH mass (M◉)

ωBD×(SN/10)

5000 6486

1000 21257

400 39190

・ Fix MNS=1.4M◉, tc=0, φc=0, β=0, ω=0, S=0.3

・ Change BH mass and see how strongly we can constraint ωBD.

LISA (Berti et al. 2004)

c.f. Cassini Bound

ωBD >40000

BH mass (M◉)

ωBD×(SN/10)

50 8.176×105

10 2.696×106

3 5.391×106

DECIGO・ DECIGO can put 100 times stronger constraint than Cassini and LISA.

・ This constraint can be made even stronger by considering larger SN binaries.

・ Why lower mass puts stronger constraint?

Lower the mass⇒ slower the velocity

⇒ greater the contribution of dipole rad.・ This result certainly becomes one of the big motivation for the DECIGO Project!

§6. Future Works

・ To take the direction dependence into account, we are working on Monte Carlo simulations.

We distribute 104 random direction of binaries and take the average of each error.

We expect the constraint would be weakened by a few factors.

・ Take the spin precession into account.(Vecchio 2004, Lang & Hughes 2006 for G.R.) This effect make the estimation errors lower. ⇒ We expect these make the ωBD constraint stronger.