Relations between Newtonian and relativistic cosmology

TL;DR

This paper explores the connection between Newtonian mechanics and relativistic cosmology by reformulating the Friedmann equations using a Lagrangian approach and attempting to unify classical and relativistic gravitational equations.

Contribution

It introduces a novel Lagrangian formulation of the Friedmann equations and seeks to bridge Newtonian and relativistic descriptions of cosmic dynamics.

Findings

Reformulation of Friedmann equations using Lagrangian mechanics.

Insights into the interplay between Newtonian and relativistic gravity.

Framework for extending classical equations to include relativistic effects.

Abstract

We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe's dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations - namely, the conservation, Euler, and Poisson equations - with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.