Accelerated Universes from type IIA Compactifications

TL;DR

The work addresses constructing slowly evolving, accelerating cosmologies within string theory by exploring geometric Type IIA compactifications on $T^{6}/(Z_{2}\times Z_{2})$ with O6/D6. It uses a genetic algorithm to locate quasi-de Sitter backgrounds with slow-roll parameters $\epsilon_V$ and $|\eta_V|$ around $\mathcal{O}(0.1)$ and then numerically evolves the full multi-field system to reveal a transient phase of acceleration with a few e-folds. The authors present four explicit backgrounds (Sol 1–4), analyze their time evolution, and discuss the issues of perturbative control, scale separation, and tadpole cancellation, showing that quasi-dS solutions require a negative net orientifold charge $N_6<0$. They provide scaling arguments indicating when large-volume, weak coupling regimes are possible and what finetuning is needed to achieve scale separation, highlighting both the promise and the challenges of embedding quasi-dS cosmologies in string theory. Overall, the paper demonstrates that relaxing the time-independence of the cosmological constant opens new avenues for string-based cosmologies and identifies the key technical hurdles toward phenomenologically viable late-time acceleration.

Abstract

We study slow-roll accelerating cosmologies arising from geometric compactifications of type IIA string theory on $T^{6}/(\mathbb{Z}_{2}\,\times\,\mathbb{Z}_{2})$. With the aid of a genetic algorithm, we are able to find quasi-de Sitter backgrounds with both slow-roll parameters of order $0.1$. Furthermore, we study their evolution by numerically solving the corresponding time-dependent equations of motion, and we show that they actually display a few e-folds of accelerated expansion. Finally, we comment on their perturbative reliability.

Figures (3)

• Figure 1: The second time-derivative of the scale factor $\ddot{a}(t)$ as a function of time for all the different solutions ordered by rows (Sol. $1$ and $2$ in the first row, Sol. $3$ and $4$ in the second one). As one can see in all cases, such acceleration turns out to be positive around the time of maximal acceleration (not located at $t=0$).
• Figure 2: The logarithm of the inverse Hubble scale $\log \frac{1}{H}$ (dashed blue) versus the logarithm of the KK radius $\log \rho^{1/2} \equiv \log \sqrt[6]{\textrm{Im}(U_{1})\textrm{Im}(U_{2})\textrm{Im}(U_{3})}$ (magenta). The different solutions are listed as in figure 1. Phenomenologically one would like to achieve separation between these two scales through $\frac{1}{H}\gg\rho^{1/2}$. Please note that all the quantities are given in Planck units.
• Figure 3: The above images illustrate the profile of the potential of solution $3$ in table \ref{['table:eps_eta']} in the time-dependent two-dimensional field subspace given by the direction of rolling $\phi_{\epsilon}^{I}$ as defined in \ref{['rolling_dir']} and the eigenstate of the mass matrix corresponding to the lowest eigenvalue that remains. The three top images represent the potential during the early times of the acceleration phase; $t=-3.04,\ -3,\ -2.8$, respectively. The three lower images depict the potential at later times; the origin $t=0$, at maximum acceleration $t=0.58$, and at the end of the acceleration phase $t = 27.1$, respectively.