Probing Primordial Power Spectrum and Non-Gaussianities With Fast Radio Bursts

We use the precision measurements of the arrival time differences of the same fast radio burst (FRB) source along multiple sightlines to measure the primordial power spectrum and Non-Gaussianities. The anticipated experiment requires a sightline separation of 100 AU, achieved by sending three or more radio telescopes to the outer solar system. The Shapiro time delays, measured relatively between different telescopes, are sensitive to the gradient field of the gravitational potential between different sightlines. Since the arrival time difference is independent of when the transient signal is emitted from the source, every measurement of the detected FRB source can be correlated. With enough FRB sources discovered, we can map the gravitational potential across the sky. We further calculate the two-point and three-point correlation function of the arrival time difference between telescopes for different FRB sources in the sky. If $10^4$ FRBs were to be detected, our results suggest that this technique can test the inflationary scale-invariant power spectrum down to $\sim 10^3\,\rm Mpc^{-1}$ and primordial Non-Gaussianities at a level of $f_{\rm NL}\sim 1$.