Bounds on gravitational wave backgrounds from large distance clock comparisons

Our space-time is filled with gravitational wave backgrounds that constitute a fluctuating environment created by astrophysical and cosmological sources. Bounds on these backgrounds are obtained from cosmological and astrophysical data but also by analysis of ranging and Doppler signals from distant spacecraft. We propose here a new way to set bounds on those backgrounds by performing clock comparisons between a ground clock and a remote spacecraft equipped with an ultrastable clock, rather than only ranging to an on-board transponder. This technique can then be optimized as a function of the signal to be measured and the dominant noise sources, leading to significant improvements on present bounds in a promising frequency range where different theoretical models are competing. We illustrate our approach using the SAGAS project which aims to fly an ultrastable optical clock in the outer solar system.

Figure 1

Principle of a general two-way link with $t_2\ne t_3$.

Figure 2

$b$ (red, dotted line) and $c$ (blue, solid line) as functions of $x\equiv \omega T/\pi$.

Figure 3

$b_r$ (blue, solid line), $b_t$ (green. dashed line) and $b_{\mathrm{opt}}$ (red, dotted line, see Sec. 3c) as functions of $x\equiv \omega T/\pi$.

Figure 4

Power spectral densities of the dominant noise sources on a one-way link: $S_{y_s}$ (magenta, crosses), $S_{y_g}$ (light blue, dashed line), $S_{v_s/c}$ (dark blue, solid line), $S_{v_g/c}$ (red, dotted line), $S_{y_{\mathrm{tropo}}}$ (green. dashed-dotted line).

Figure 5

PSD of the noise affecting the two observables $y_t$ (upper graph) and $y_r$ (lower graph) for the special cases $T_{23}=0$ (blue, solid line) and $T_{14}=0$ (red, dotted line), and for a spacecraft to ground distance of 10 AU.

Figure 6

${\Omega }_{\mathrm{GW}}$ versus $f$, for a probe to Earth distance of 6 AU (left) and 53 AU (right). The three curves show the limits on ${\Omega }_r$ (blue, solid line), ${\Omega }_t$ (green, dashed line), and ${\Omega }_{\mathrm{opt}}$ (red, dotted line).

Figure 7

${\Omega }_{\mathrm{opt}}$ versus $f$, for probe to Earth distances (top to bottom) of 20 AU (light blue), 30 AU (magenta), 53 AU (green), 100 AU (red), and 200 AU (dark blue). The horizontal black line indicates the BBN bound.