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Primordial black holes (PBHs) provide a unique probe of the early Universe. Their cosmological evolution is governed by the competition between mass accretion and Hawking evaporation. In this paper we look into the details impact of accretion. Most of the earlier analysis relied on non-relativistic accretion models. In this work, we reinvestigate this in a fully relativistic framework for Kerr PBHs in the radiation-dominated era. We derive relativistic accretion rate and compute spin-dependent efficiency λ<SUB>Kerr</SUB>(a <SUB>*</SUB>). Using this result, we construct coupled evolution equations for the PBH mass and spin that include both relativistic accretion and spin-dependent evaporation. Our analysis shows that relativistic accretion significantly increases PBH masses and consequently suppresses their spins, causing all PBHs to become effectively Schwarzschild well before evaporation. These effects strengthen the Big Bang Nucleosynthesis (BBN) bound on the initial PBH mass by a factor of ∼4─5, reduce the mass required for survival to the present epoch to ∼2.7 × 10<SUP>14</SUP> g, and shift the viable particle like DM parameter space. Notably the early accretion induced spin-down effect further washes out the well known high-frequency, spin-induced feature in the high frequency stochastic gravitational-wave background, modifying predictions for future detectors.

The inflationary <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals encode invaluable information about the origin of our Universe, and searching for potential signatures of primordial gravitational waves (PGWs) is one of the major science goals for future precision observations of cosmic microwave background (CMB) polarization. However, dominant <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals of both Galactic foreground contamination and gravitational lensing effects prevent direct measurements of the PGW <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals. There are existing proposals which can effectively eliminate these two contaminants but issues remain for future high-sensitivity and multifrequency CMB polarization observations, such as spatially varying spectral energy distribution (SED) of polarized foreground and cosmological <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals due to primordial magnetic fields. In this work, we investigate inference of PGW <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals in the presence of both complexities. We employ a constrained moment internal linear combination method to remove polarization signals arising from spatially varying SEDs. Also, we employ a power-spectrum-based approach to extracting both the Galactic and cosmological <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode components. Two methods have been validated by mock data and different consistency tests have been performed. We apply these two methods to end-to-end simulations for future high-sensitivity and multifrequency polarization observations and investigate the detectability of different <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signals in the presence of complex polarized foregrounds under different scenarios. This study will be important for new physics studies with <inline-formula><mml:math><mml:mi>B</mml:mi></mml:math></inline-formula>-mode signatures.