Constraints on Deflation from the Equation of State of Dark Energy

TL;DR

This paper explores how the dark energy equation of state constrains the number of causal patches in cyclic cosmology, providing bounds on critical density based on dark energy properties and universe conditions.

Contribution

It establishes a lower bound on the number of causal patches in cyclic cosmology based on dark energy parameters and introduces bounds on critical density tied to the size of bound states.

Findings

Lower bound on causal patches depends on dark energy equation of state.

Critical density has a lower bound related to bound state size.

More precise measurements of dark energy parameter $\

Abstract

In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/\rho = -1 - \phi$ with $\phi > 0$. More accurate measurement of $\phi$ will constrain $N_{\rm cp}$. The critical density $\rho_c$ in the model has a lower bound $\rho_c \ge (10^9 {\rm GeV})^4$ or $\rho_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.