Is there something wrong with the way that we search for gravitational waves from bumpy neutron stars?

Isolated, deformed neutron stars are expected to emit quasi-monochromatic, infinite-duration gravitational waves as they slowly spin down. Over the last few decades, a multitude of searches has been carried out for such systems, ranging from analyses targeting known pulsars like Crab and Vela, to pointing to specific interesting areas in the sky like the Galactic Center and supernova remnants, and to blindly looking everywhere for the billions of such systems that should exist in our Galaxy. No detection has been made, which means the possible deviations from spherical symmetry become smaller and smaller, as tiny as 10µm in some cases. As an added concern, gravitational-wave energy loss has been constrained to be much less than 1% for some known pulsars. We do not know whether it is true that such neutron stars are really that spherical, or if there is a problem in the assumptions made in the analyses that are performed. In this project, we propose to question the underlying assumptions that are made in the searches for gravitational waves from neutron stars, study the impact of these assumptions on the prospects for detectability, and develop new ways of probing these systems that are robust against theoretical uncertainties in the signal model. Furthermore, we propose to go beyond just a ``detection'' and ask ``what can we learn from a detection of a continuous wave''?