K. K. Venkataratnam

We study the role of domain walls and their relics in the very early Universe within the framework of the mode-matching technique. Domain walls formed during the spontaneous breaking of discrete symmetries are modelled as a short lived contribution to the background energy density, leading to a controlled deviation from standard slow-roll inflation. Solving the modified Friedmann equation, we obtain a smooth, time-dependent Hubble parameter that asymptotically approaches the standard inflationary value. We analyze the evolution of scalar perturbations using the gauge-invariant Mukhanov variable and perform mode matching across the transition between the domain wall affected phase and standard inflation. We find that only modes exiting the horizon near the transition experience a modified evolution, while modes far from the transition remain unaffected. As a result, the primordial scalar power spectrum exhibits localized, scale-dependent deviations from scale invariance, while preserving the overall success of inflation. These results demonstrate that unstable domain-wall relics can leave subtle imprints on primordial fluctuations, potentially providing a probe of early-Universe phase transitions.