Gravitational Bounce and Inflation Driven by the Exclusion Principle

We present a novel cosmological framework where cosmic expansion arises from the gravitational collapse and bounce of a uniform, spherically symmetric cloud of mass \( m \) with an initial comoving radius \( \chi_* \). Extending Lemaître's 1933 "atom universe," this model incorporates a perfect fluid with an evolving equation of state \( P = P(\rho) \), transitioning from pressureless dust \( P = 0 \) to a ground state with fixed energy density (\( \rho_G \)) as required by the quantum exclusion principle. This results in negative pressure (\( P_G = -\rho_G \)) and a gravitational bounce at the gravitational radius \( R_B \), associated with \( \rho_G \) (\( R_B \simeq 24 \) km for nuclear saturation density). The bounce triggers an expansion phase, with \( P(\rho) \) serving as the inflationary potential. This framework explains the cosmic cutoff scale (\( \chi_* \simeq 15.9 \) Gpc) which addresses key observed CMB anomalies. The bounce is trapped within the initial gravitational radius \( r_S = 2Gm \), which acts like a \( \Lambda \) term with \( r_S=\sqrt{3 /\Lambda} \simeq 5.1 \) Gpc. This approach provides a unified explanation of inflation and its observational signatures, offering new insights into cosmic expansion and the quantum origins of structures.