Geometric Phase of Linear Cosmological Perturbations in Two-Field Inflation

As a footprint of primordial perturbations in cosmological observations, the Berry phase of cosmological perturbations can serve to probe the cosmological inflation. Considering linear perturbations in two-field slow-roll inflation, we derive the Hamiltonians of the scalar and tensor Fourier modes in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use these invariants to calculate the Berry phase for sub-horizon scalar and tensor modes in the adiabatic limit.