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

Testing gravity with cosmic variance-limited pulsar timing array correlations