Revisiting oscillon formation in the Kachru-Kallosh-Linde-Trivedi scenario

Kachru-Kallosh-Linde-Trivedi (KKLT) scenario has succeeded in stabilizing the volume modulus and constructing metastable de Sitter (dS) vacua in type IIB string theory. We revisit to investigate the possibility of the oscillon (or I-ball) formation in the KKLT scenario when the volume modulus is initially displaced from the dS minimum. Special attention is paid to physically realistic initial conditions of the volume modulus, which was not taken in the literature. Using lattice simulations, we find that oscillons do not form unless the volume modulus is initially placed at very near the local maximum, which requires severe fine-tuning.

Figure 1

Potential of KKLT described by Eq. (8) in the case of $W_0=-{10}^{-5}$, $A=10$, $\kappa =2\pi$, and $D=3.17\times {10}^{-11}$. ${\varphi }_{\min }$ and ${\varphi }_{\max }$ are the field values at the minimum and the local maximum of the potential, respectively.

Figure 2

Floquet exponents of the KKLT model in units of the modulus mass for $W_0=-{10}^{-5}$, $A=10$, $\kappa =2\pi$, $m=2.38\times {10}^{-5}$ (left) and $W_0=-{10}^{-12}$, $A=10$, $\kappa =2\pi$, $m=1.8\times {10}^{-12}$ (right).

Figure 3

Evolution of the mean $⟨\varphi ⟩$ (left) and the variance $\sqrt{⟨\delta {\varphi }^2⟩}$ (right) when $W_0=-{10}^{-5}$, $A=10$ and $\kappa =2\pi$ as a function of the scale factor $a(t)$. The initial field values are taken to be ${\varphi }_{\text{initial}}=2.2$ (top) and ${\varphi }_{\text{initial}}=2.2105$ (bottom). The solid black line indicates the amplitude of the field at the inflection point of the potential.

Figure 4

Energy density distribution $\rho /⟨\rho ⟩$ in the two-dimensional lattice simulation for $W_0=-{10}^{-5}$, $A=10$, $\kappa =2\pi$, and ${\varphi }_{\text{initial}}=2.2105$. The top left, top right, bottom left, and bottom right panels correspond to the results at $a=24.5$, $a=27.4$, $a=32.6$, and $a=44.2$, respectively. The red regions indicate $\rho /⟨\rho ⟩\ge 10$.

Figure 5

Floquet exponents of the KKLT model in units of the modulus mass for $W_0=-{10}^{-5}$, $A=10$, $\kappa =2\pi$, $m=2.38\times {10}^{-5}$ (left) and $W_0=-{10}^{-12}$, $A=10$, $\kappa =2\pi$, $m=1.8\times {10}^{-12}$ (right) when self-gravity effect is added.