Probing the speed of gravity with LVK, LISA, and joint observations
I. W. Harry, Johannes Noller
Abstract
Abstract Theories of dark energy that affect the speed of gravitational waves $$c_{\textrm{GW}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> </mml:math> on cosmological scales naturally lead to a frequency-dependent transition of that speed close to the LIGO/Virgo/KAGRA (LVK) band. While observations such as GW170817 assure us that $$c_{\textrm{GW}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> </mml:math> is extremely close to the speed of light in the LVK band, a frequency-dependent transition below the LVK band is a smoking-gun signal for large classes of dynamical dark energy theories. Here we discuss (1) how the remnants of such a transition can be constrained with observations in the LVK band, (2) what signatures are associated with such a transition in the LISA band, and (3) how joint observations in the LVK and LISA bands allow us to place tight constraints on this transition and the underlying theories. We find that deviations of $$c_{\textrm{GW}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> </mml:math> can be constrained down to a level of $$\sim 10^{-17}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> in the LVK and LISA bands even for mild frequency-dependence, much stronger than existing bounds for frequency-independent $$c_{\textrm{GW}}\ne c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> <mml:mo>≠</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:math> . We use the strain data from GW170817 to bound the deviation of $$c_{\textrm{GW}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>GW</mml:mtext> </mml:msub> </mml:math> to be less than $$10^{-17}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:msup> </mml:math> at 100 Hz and less than $$10^{-18}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>18</mml:mn> </mml:mrow> </mml:msup> </mml:math> at 500 Hz. We also identify a particularly interesting type of transition in between the LVK and LISA bands and show how multi-band observations can constrain this further. Finally, we discuss what these current and forecasted constraints imply for the underlying dark energy theories.