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The observed gravitational-wave background (GWB) spectrum is higher in amplitude than model predictions by a factor of 2─3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation (M<SUB>BH</SUB>─M<SUB>bulge</SUB>) on models of the nanohertz GWB. By implementing an intrinsic scatter of the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at 4 &lt; z &lt; 6 without changing the M<SUB>BH</SUB>─M<SUB>bulge</SUB> normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as <inline-formula> <mml:math><mml:mi>∊</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>∊</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn>0.56</mml:mn><mml:mo>±</mml:mo><mml:mn>0.4</mml:mn><mml:mo>)</mml:mo><mml:msub><mml:mrow><mml:mi>log</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:math> </inline-formula> and normalization that evolves as α(z) = α<SUB>0</SUB>(1 + z)<SUP>0.84±0.35</SUP>. The results of this work imply that the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH─galaxy evolution.

Observations of the Cosmic Microwave Background (CMB) B-mode polarisation provide a unique probe of inflationary physics. Extracting a reliable constraint on the tensor-to-scalar ratio r nonetheless demands stringent suppression of diffuse Galactic foregrounds, whose residuals can bias the inferred signal. This work introduces and evaluates two extensions of the Needlet Internal Linear Combination (NILC) framework aimed at reducing foreground-induced biases on r. The first extension implements the deprojection of selected foreground moments directly within the component-separation step. The second performs a likelihood-level marginalisation over residual foreground power using a data-driven template. Using Simons Observatory Small Aperture Telescope (SO-SAT) - like simulations, we show that both methods effectively control residual contamination, yielding unbiased estimates of r and a consistent reconstruction of the lensing B-mode amplitude. These results indicate that enhanced foreground-mitigation strategies will be useful for next-generation CMB polarisation analyses seeking a robust detection of primordial B-modes.