Brian C. Seymour Introduction Testing General Relativity with Black Orbital Decay Rate Bounds Hole-Pulsar Binaries Formulation Varying G Lorentz-violating Massive Gravity Cubic Galileon Massive Gravity Brian C. Seymour General Screen Modified Gravity Quadrupole University of Virginia Moment Bounds bcs8dn@virginia.edu Formulation Dynamical Chern-Simons Gravity November 1, 2018 Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Overview Introduction 1 Brian C. Seymour Orbital Decay Rate Bounds 2 Introduction Formulation Orbital Decay Varying G Rate Bounds Formulation Lorentz-violating Massive Gravity Varying G Lorentz-violating Cubic Galileon Massive Gravity Massive Gravity Cubic Galileon General Screen Modified Gravity Massive Gravity General Screen Modified Gravity Quadrupole Moment Bounds 3 Quadrupole Moment Formulation Bounds Dynamical Chern-Simons Gravity Formulation Dynamical Chern-Simons Einstein-dilaton Gauss-Bonnet Gravity Einstein-dilaton Gauss-Bonnet Conclusion 4 Conclusion Appendix Appendix 5
Motivation for Testing General Relativity Brian C. Seymour Introduction General relativity is currently the most well-tested theory Orbital Decay Rate Bounds of gravity. Formulation Varying G Nevertheless, it must be an effective field theory of some Lorentz-violating Massive Gravity Cubic Galileon quantum theory of gravity. Massive Gravity General Screen Modified Gravity Gravity has been tested very stringently in the weak field Quadrupole through solar system and cosmological observations. Moment Bounds It has been tested less however in the strong field regime. Formulation Dynamical Chern-Simons Gravity Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Tests with Pulsar Timing Brian C. Seymour Introduction Radio observations of pulsar binaries can be used to find Orbital Decay Rate Bounds their system and orbital properties through pulsar timing. Formulation Varying G Pulsar timing provides precision tests of gravity and has Lorentz-violating Massive Gravity Cubic Galileon placed stringent bounds on a broad class of theories Massive Gravity General Screen beyond general relativity. Modified Gravity Quadrupole Typically this is done with binary pulsar systems such as Moment Bounds double pulsar, pulsar-neutron star, and pulsar-white dwarf. Formulation Dynamical Chern-Simons Gravity Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Black Hole-Pulsar Binary Brian C. Seymour So far, neither gravitational wave or electromagnetic Introduction observations have found a black hole-neutron star binary. Orbital Decay Rate Bounds The Five-hundred-meter Aperture Spherical radio Formulation Varying G Telescope (FAST) under construction or the Lorentz-violating Massive Gravity next-generation Square Kilometer Array (SKA) may find a Cubic Galileon Massive Gravity binary with a millisecond pulsar orbiting a black hole. General Screen Modified Gravity We will consider the possibility of testing general relativity Quadrupole Moment if a radio telescope finds a black hole-pulsar binary. Bounds Formulation Dynamical If found, a black hole-pulsar binary would be a powerful Chern-Simons Gravity test of general relativity. Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Measurable Quantities Brian C. Seymour Pulsar timing can be used to measure binary parameters Introduction such as masses, orbital period, et cetera. Orbital Decay Rate Bounds Specifically, two quantities are of particular importance for Formulation Varying G this presentation. Lorentz-violating Massive Gravity The orbital decay rate is the time derivative of the orbital Cubic Galileon Massive Gravity period ˙ General Screen P . Modified Gravity The black hole quadrupole moment Q . Quadrupole Moment I will denote the δ and δ Q to be the fractional error of the Bounds Formulation orbital decay rate and black hole quadrupole moment Dynamical Chern-Simons Gravity respectively. Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Methodology Brian C. Seymour Measurements of the orbital decay rate and quadrupole moment place constraints on the upper bound of theory Introduction parameters. Orbital Decay Rate Bounds Essentially, the maximum possible upper bound on Formulation Varying G violation from general relativity is constrained by the Lorentz-violating Massive Gravity measurement error. Cubic Galileon Massive Gravity General Screen Since a black hole binary has not been found yet, we must Modified Gravity Quadrupole instead rely on simulated measurement uncertainties to Moment Bounds test gravity. Formulation Dynamical Chern-Simons Gravity Einstein-dilaton Simulations of Binary Parameter Theory Constraints Gauss-Bonnet ˙ black hole-pulsar observations Measurabilities: δ , δ Q e.g. G , m g Focus of talk Conclusion Appendix
Utility of Black Hole-Pulsar Tests Brian C. Seymour Black hole-pulsar binaries are powerful tests of general Introduction relativity due to their slower relative velocity (compared to Orbital Decay other pulsar binaries). Rate Bounds Formulation The relative velocity of a binary is given by Varying G Lorentz-violating v = (2 π M / P ) 1 / 3 . Although the mass is larger, the slower Massive Gravity Cubic Galileon Massive Gravity orbital period more than compensates for larger total mass. General Screen Modified Gravity The result is a relative velocity smaller that neutron-pulsar Quadrupole Moment binaries by about a factor of 2. Bounds Formulation As I will show later, this makes black hole-pulsar binaries Dynamical Chern-Simons advantageous for constraining theories which have a Gravity Einstein-dilaton Gauss-Bonnet dependence on velocity to a negative power. Conclusion Appendix
Orbital Decay Rate Bounds Introduction 1 Brian C. Seymour Orbital Decay Rate Bounds 2 Introduction Formulation Orbital Decay Varying G Rate Bounds Formulation Lorentz-violating Massive Gravity Varying G Lorentz-violating Cubic Galileon Massive Gravity Massive Gravity Cubic Galileon General Screen Modified Gravity Massive Gravity General Screen Modified Gravity Quadrupole Moment Bounds 3 Quadrupole Moment Formulation Bounds Dynamical Chern-Simons Gravity Formulation Dynamical Chern-Simons Einstein-dilaton Gauss-Bonnet Gravity Einstein-dilaton Gauss-Bonnet Conclusion 4 Conclusion Appendix Appendix 5
Orbital Decay Rate in General Relativity Brian C. Seymour Orbital decay rate in general relativity is described by the Introduction following equation. Orbital Decay Rate Bounds For the rest of this presentation, a subscript with GR Formulation Varying G represents the quantity in general relativity. Lorentz-violating Massive Gravity Cubic Galileon Massive Gravity � P General Screen � − 8 / 3 ˙ Modified Gravity P GR = − 96 � 5 G 5 / 3 µ M 2 / 3 F GR ( e ) (1) � Quadrupole 2 π P � Moment Bounds Formulation 1 � 1 + 73 24 e 2 + 37 � Dynamical 96 e 4 F GR ( e ) ≡ (2) Chern-Simons Gravity (1 − e 2 ) 7 / 2 Einstein-dilaton Gauss-Bonnet Conclusion Appendix
Simulated Orbital Decay Rate Fractional Error � P − ˙ ˙ � P P P | GR Brian C. � � The orbital decay rate fractional error is given by � < δ . Seymour � � ˙ P P | GR � Introduction Orbital Decay Rate Bounds -1 10 Formulation Varying G Lorentz-violating Massive Gravity -2 Cubic Galileon 10 Massive Gravity General Screen δ Modified Gravity Quadrupole -3 10 Moment . Measurability (FAST) Bounds P . Measurability (SKA) Formulation P Dynamical -4 10 PSR-WD Chern-Simons Gravity Double Pulsar (J0737) Einstein-dilaton Gauss-Bonnet -5 Conclusion 10 0 1 2 3 4 5 6 P [day] Appendix
Generic Formalism for Orbital Decay Rate We use the following formula characterizing orbital decay Brian C. Seymour rate in modified theories of gravity. Introduction ˙ ˙ � P P � 1 + γ v 2 n � � Orbital Decay P = (3) � Rate Bounds P � Formulation GR Varying G Lorentz-violating Massive Gravity The γ v 2 n term gives the leading correction to general Cubic Galileon Massive Gravity relativity where γ is theory dependent and v is the General Screen Modified Gravity relativity velocity. Quadrupole Moment The n gives the post-Newtonian order (PN) of the theory. Bounds Formulation Dynamical Since the relative velocity of a black hole-pulsar binary is Chern-Simons Gravity lower than other pulsar binaries, it constrains theories with Einstein-dilaton Gauss-Bonnet negative post-Newtonian order more stringently. Conclusion δ Combining this with the previous slide, we have | γ | < v 2 n . Appendix
Astrophysical System Bounds by Post-Newtonian Order Brian C. 24 Seymour BH-PSR (FAST) 10 BH-PSR (SKA) Introduction Double Pulsar (J0737) Orbital Decay GW150914 12 10 Rate Bounds GW151226 Formulation Varying G Lorentz-violating Massive Gravity | γ | 0 Cubic Galileon 10 Massive Gravity General Screen Modified Gravity Quadrupole -12 Moment 10 Bounds Formulation Dynamical Chern-Simons Gravity -24 Einstein-dilaton 10 Gauss-Bonnet Conclusion -4 -2 0 2 4 Appendix n [PN]
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