Toward self-consistent calculations of CS gravity in the solar system test Hideki Asada Hirosaki U

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1 GWastro Symposium, , YITP Toward self-consistent calculations of CS gravity in the solar system test Hideki Asada Hirosaki U with Yuya Nakamura (M1), Riko Yamada (M1) Kei Yamada (Kyoto) Nicolas Yunes (Montana)

2 Introduction many theories of modification to GR e.g. Mukoyama-san s talk 1) Theoretical tests self-consistency, stability, well-posed initial value etc. 2) Experimental tests cosmology, solar-system, GW etc. (weak-field)(strong-field)

3 PPN (Parameterized post-newton) Formalism slow motion (v/c << 1) weak field (U << 1) Eddington (1922) Will and Nordtvedt (1972) The coefficients at 1PN metric depend on a theory that we wish to test Assume(explicit): Potentials obey Poisson equation Assume(implicit): Potentials do not violate parity (exclude pseudo-scalars) 10 parameters

4 PPN metric g 00 = 1+2GU 2 G 2 U 2 2 G 2 W +( )G 1 +2( )G (1 + 3 )G 3 ( 1 2 )GA +2( )G 4 g 0i = 1 2 ( )GV i 2 ( )GW i g ij = (1+2 GU) ij.

5 Will, LRR

6 Alexander & Yunes, (2007) EH action + Chern-Simons(CS) term S = c4 16πG g d 4 x [ R + f ] RR 4, R = R αβγδ, R = 1 2 ϵαβµν R γδ µν. See also Witten(1989) and Ashtekar+(1989)

7 Experimental CS test using Gravity Probe B (GPB) (launched in 2004) Everitt et al. PRL (2011) Frame-dragging detection with 20% precision Geodetic effect with 0.3% precision See Focus Issue: Gravity Probe B, Classical and Quantum Gravity (2016) for the full technical and data analysis details of GPB.

8 CS makes a parity-violating PPN term Alexander & Yunes (2007) e.g. V V (V i ) 1PN vector potential

9 PN approximation (Slow motion + Weak field) N point-like objects g 0i 2 X A f_ r A ma r A v A n A i Ji A 2r 2 A 3 2 J A n A r 2 A n i A ; (12 CS correction (Parity-violating)

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11 However, the calculations of CS in the PN so far rely on simplistic assumptions (especially for a scalar field...)

12 e.g. Alexander and Yunes(2007) assume a priori spatially homogeneous and slowly varying with time They assume df/dt = const. This is taken as a new PPN parameter. Their model is non-dynamical. Smith, Erickcek, Caldwell, Kamionkowski(2008) dv d 1 12 R ~R: (4) By restricting θ to be spatially homogenous, we are effectively treating θ as a nondynamical field,...

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14 Z S d 4 p x ffiffiffiffiffiffiffi g g R þ 4 #R R 2 r #r # þ L mat : ð Þ G þ C ¼ 1 g h# ¼ 4 R R : ðt mat þ T Þ; # 2 g

15 θ = [ i i h h 0i 0 i h ij i j 1 ( h 00 2,0 +2h 0i,i h i 0) i, 0 1 ( 2h i0,0 +2h ij,j 2 h0 0, i h j i) j, i + 1 ( 2 h00 2h 0 0,0 +2h i 0,i h i ) i, ( 2 h00 2h i 0,0 h00, i ) i + 1 ( ) 2 h0i 2h 0 i,0 +2h j i,j hj j,i + h0 0,i ( ) 2 h0i h 0 0,0 +2h j 0,j hj j,0 i + 1 ( 2 h0i h j 0,i + hj i,0 h j 0i, ) j hij ( 2h 0 i,0 +2h k i,k h k k,i h 0 0,i) j hij ( 2h 0 i,j h 0 ij, ) ( 2 hij 2h k i,j hij, k ) k +h 00 h h i0 h i + h i0 h j 0 i j +h 0i h 0 i h ij h 0 i 0 j + h ij h k i j k ] θ + O(h 3 ) (32)

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18 Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes Toshiaki Ono, Tomohito Suzuki, and Hideki Asada Phys. Rev. D 94, Published 15 September 2016 ISCO = Last Stable Orbit This work was supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban C, No (H.A.) and Shingakujutsu, No. 15H00772 (H.A.).

19 Thank you!