  We investigate the possibility of measuring the primordial gravitational wave
(GW) signal across 21 decades in frequencies, using the cosmic microwave
background (CMB), pulsar timing arrays (PTA), and laser and atomic
interferometers. For the CMB and PTA experiments we consider the LiteBIRD
mission and the Square Kilometer Array (SKA), respectively. For the
interferometers we consider space mission proposals including the Laser
Interferometer Space Antenna (LISA), the Big Bang Observer (BBO), the
Deci-hertz Interferometer Gravitational wave Observatory (DECIGO), the
$\mu$Ares experiment, the Decihertz Observatory (DO), and the Atomic Experiment
for Dark Matter and Gravity Exploration in Space (AEDGE), as well as the
ground-based Einstein Telescope (ET) proposal. We implement the mathematics
needed to compute sensitivities for both CMB and interferometers, and derive
the response functions for the latter from the first principles. We also
evaluate the effect of the astrophysical foreground contamination in each
experiment. We present binned sensitivity curves and error bars on the energy
density parameter, $\Omega_{GW}h^2$, as a function of frequency for two
representative classes of models for the stochastic background of primordial
GW: the quantum vacuum fluctuation in the metric from single-field slow-roll
inflation, and the source-induced tensor perturbation from the spectator
axion-SU(2) inflation models. We find excellent prospects for joint
measurements of the GW spectrum by CMB and space-borne interferometers mission
proposals.
