  The nanohertz stochastic gravitational wave background (SGWB) is an excellent
early universe laboratory for testing the fundamental properties of gravity. In
this letter, we elucidate on the full potential of pulsar timing array (PTA) by
utilizing cosmic variance-limited, or rather experimental noise-free,
correlation measurements to understand the SGWB and by extension gravity. We
show that measurements of the angular power spectrum play a pivotal role in the
PTA precision era for scientific inferencing. In particular, we illustrate that
cosmic variance-limited measurements of the first few power spectrum multipoles
enable us to clearly set apart general relativity from alternative theories of
gravity. This ultimately conveys that PTAs can be most ambitious for testing
gravity in the nanohertz GW regime by zeroing in on the power spectrum.
