A New Approach for Transfer Function in Inhomogeneous Universe: Linear-Time Varying (LTV) System
Fargiza A. M. Mulki, Hesti R. T. Wulandari, M. Rafif Rabbani

Astronomy Research Group, FMIPA, ITB-
Bosscha Observatory, FMIPA, ITB

Abstract

A transfer function is a mathematical function that provides a lot of physical information about the state of a system. Matter transfer function describes the change of density contrast of mass over time so that it becomes the density contrast observed today. The square of the matter transfer function is proportional to its power spectrum which denotes the number of formed structures at each scale or size, which is certainly plausible to be observed. Most of the transfer function used today is extracted empirically from the known structures distribution, meanwhile the formal formulation is still very limited in terms of quantity. In this work, a matter transfer function will be built based on the linear-time varying (LTV) system approach, which is a continuation of the previous work, namely the development of the transfer function through a control theory approach for the linear-time invariant (LTI) system.
Mathematically, a transfer function is a ^field^ whose properties are clear and definite. The mathematical properties possessed will be elaborated to obtain profound understanding of the transfer function. By employing the block diagrams used in engineering physics, the physical properties of the perturbations of the universe will be investigated through the analogy of a control machine.
The formulation of the transfer function through the LTV system approach gives very good results with advantages in terms of processes and mechanisms through the block diagrams- therefore, it provides better understanding about the formation of the structure in the universe. The modular or ^plug and play^ property of this formalism makes it easier to be controlled, verified, and modified.

Keywords: matter power spectrum, transfer function, inhomogeneous universe, control theory, cosmology

Topic: Modelling and Computational Physics