You raise an interesting point. When discussing the very early moments of cosmic inflation, where extremely rapid expansion of the universe is believed to have occurred, the concept of time being relative becomes relevant.
In the framework of general relativity, which describes the behavior of spacetime, the passage of time is indeed relative and can vary depending on the observer's reference frame. This means that different observers, situated in different locations or moving at different velocities, may perceive time differently.
When we talk about the first nanoseconds of cosmic inflation, we typically discuss it from a reference frame that provides a useful and consistent perspective. This reference frame is often referred to as the "cosmic rest frame" or the "comoving frame." In this frame, observers are assumed to be at rest with respect to the average expansion of the universe.
Using the comoving frame as a reference allows scientists to describe the overall dynamics and evolution of the universe, including the early moments of cosmic inflation. It provides a way to discuss the behavior of matter and energy on large scales without getting entangled in the intricate details of individual observers or their relative reference frames.
While it is true that the specific experiences and measurements of a localized observer during the first nanoseconds of cosmic inflation may differ from the perspective of the comoving frame, the aim is to understand the broader behavior and characteristics of the universe as a whole during that time.
It's worth noting that our understanding of the very early moments of cosmic inflation is based on theoretical models and supported by observational evidence, such as the cosmic microwave background radiation. The intricacies of how time and reference frames precisely behave during that period are still active areas of research, and refining our understanding requires the integration of quantum mechanics with general relativity, which is a major goal of theoretical physics.