# A Closed Universe with Maximum Life-Time

## TL;DR

This paper constructs a model of a closed universe with maximum lifetime using optimal control theory, involving Einstein's equations and a variable cosmological constant, with the Hubble parameter's second derivative as the control.

## Contribution

It introduces a novel optimal control approach to model a closed universe with maximum lifetime by varying the cosmological constant and analyzing the Hubble parameter.

## Key findings

- Derived conditions for maximum universe lifetime.
- Established a control framework using Einstein's equations.
- Proposed a model with a variable cosmological constant.

## Abstract

A closed universe with maximum life-time is constructed using optimal control. Einstein's field equations are used with varying cosmological "constant". The second time derivative of the Hubble parameter acts as the control function in the optimal control model.