Unified Framework for Space-Time Fabric Formation from the space chunks and it’s interaction with mass to emit gravitational waves: A theoretical Exploration

Considering the formation of space-time fabric and its sophisticated relation- ship with mass and gravitational waves is crucial to work out on the mysteries of the universe. In this paper, we delve into a hypothetical scenario where space emerge from a fundamental unit termed as a space chunk, exploring its evolution over time. By considering space as a function of time denoted as X(t), incorporating phenomena like quantum fluctuations, 4-D expansion of space, total energy change over a time interval , topology changes, multidimensional extensions, cosmic evolutions, observable consequences etc we discover the dynamics commanding its development. Moreover, we explore the manifestation of quantum fluctuations through the energy density operator pˆ(t) interpreting its fluctuations over time and its inherent role in the fabric of space-time. Four- dimensional expansion of space is characterised by the (FLRW) metric. Through mathematical derivations, we as- certain the rate of change of energy with respect to the expanding volume of space, focusing on the evolving nature of the vacuum.Subsequently, we reconnoitre the interaction between mass and space-time fabric, postulating the emission of gravitational waves as a consequence of mass interacting with the space-time fabric. By proposing hypothetical gravitational wave observables, we find out their joint observable state and its relationship with the mass-space- time interaction. Through rigorous mathematical formulations, we establish the mass as the eigenvalue of the universal gravitational operator, highlighting its fundamental role in shaping the fabric of the universe.