A new variable in scalar cosmology with exponential potential

TL;DR

This paper introduces a new variable to describe scalar cosmology with exponential potential, simplifying the analysis of universe evolution and its equation of state in flat FRW space-time.

Contribution

It proposes a novel time variable, L, that clearly characterizes the universe's state and evolution in scalar cosmology with exponential potential.

Findings

Universe inflates when |L|<1/√3

End states depend on β: at L=β for β≤1, at L=1 for β≥1

Initial state always has equation of state w=1

Abstract

We present a new way describing the solution of the Einstein-scalar field theory with exponential potential $V\propto e^{\sqrt{6}\beta \phi/M_{Pl}}$ in spatially flat Friedmann-Robertson-Walker space-time. We introduced a new time variable, $L$, which may vary in $[-1,1]$. The new time represents the state of the universe clearly because the equation of state at a given time takes the simple form, $w= -1+ 2L^2$. The universe will inflate when $|L|<1/\sqrt{3}$. For $\beta\leq 1$, the universe ends with its evolution at $L=\beta$. This implies that the equation of state at the end of the universe is nothing but $w=-1+2\beta^2$. For $\beta \geq 1$, the universe ends at L=1, where the equation of state of the universe is one. On the other hand, the universe always begins with $w=1$ at $L=\pm 1$.