The fate of (phantom) dark energy universe with string curvature corrections

TL;DR

This paper investigates the late-time fate of a phantom-dark-energy universe by incorporating higher-order string curvature corrections to the Einstein-Hilbert action with a fixed dilaton. By comparing type II, heterotic, and bosonic strings, it shows that de-Sitter fixed points do not arise for phantom fluids in type II and heterotic cases, while bosonic strings can admit an unstable de-Sitter state. Numerical analyses reveal that the cosmological outcome is string-model dependent: a Big Crunch for type II and a Big Rip for heterotic and bosonic corrections under phantom $w_m<-1$, with stable de-Sitter solutions emerging only when a cosmological constant is included for certain models. The work highlights how stringy corrections can drastically modify the ultimate fate of the universe and outlines future directions involving dynamical dilaton/modulus fields and ambiguities from higher-curvature terms.

Abstract

We study the evolution of (phantom) dark energy universe by taking into account the higher-order string corrections to Einstein-Hilbert action with a fixed dilaton. While the presence of a cosmological constant gives stable de-Sitter fixed points in the cases of heterotic and bosonic strings, no stable de-Sitter solutions exist when a phantom fluid is present. We find that the universe can exhibit a Big Crunch singularity with a finite time for type II string, whereas it reaches a Big Rip singularity for heterotic and bosonic strings. Thus the fate of dark energy universe crucially depends upon the type of string theory under consideration.

Figures (3)

• Figure 1: The phase portrait for heterotic string in the case of $\rho_m\equiv \Lambda=1$ for several different initial conditions. The stable fixed point $x_c \equiv H_c=0.408$ corresponds to a de-Sitter solution which is a stable spiral.
• Figure 2: The evolution of the Hubble rate $H$ in the presence of string curvature corrections and a phantom fluid with an equation of state: $w_m=-1.5$. For the type II correction, the solution approaches $H=-\infty$ by crossing $H=0$, whereas in the heterotic and bosonic cases the Hubble rate grows toward infinity.
• Figure 3: The phase portrait for bosonic string in the presence of a cosmological constant ($\rho_m \equiv \Lambda=1$) with $A=1/2$ and $B=3/4$. There exist two de-Sitter fixed points. The point A [$x_c=0.417$] corresponds to a stable spiral, whereas the point B [$x_c=0.652$] is a saddle.