Cosmology from Rolling Massive Scalar Field on the anti-D3 Brane of de Sitter Vacua

TL;DR

This work investigates a string-inspired inflationary scenario where a rolling massive scalar on an anti-D3 brane within KKLT de Sitter vacua drives inflation. The warp factor β enables the required amplitude of density perturbations, even for steep potentials, while a negative cosmological constant from modulus stabilization facilitates reheating and can account for late-time dark energy when φ settles near the potential minimum. The authors derive the BI-type dynamics, compute scalar and tensor perturbations, and show consistency with CMB constraints for several potential forms; they also analyze the post-inflation evolution, demonstrating a dust-like phase during reheating and stability against tachyonic instabilities. Overall, the model offers a coherent string-theoretic path to inflation, reheating, and dark energy, with the warp factor and Λ tuning playing crucial roles.

Abstract

We investigate a string-inspired scenario associated with a rolling massive scalar field on D-branes and discuss its cosmological implications. In particular, we discuss cosmological evolution of the massive scalar field on the ant-D3 brane of KKLT vacua. Unlike the case of tachyon field, because of the warp factor of the anti-D3 brane, it is possible to obtain the required level of amplitude of density perturbations. We study the spectra of scalar and tensor perturbations generated during the rolling scalar inflation and show that our scenario satisfies the observational constraint coming from the Cosmic Microwave Background anisotropies and other observational data. We also implement the negative cosmological constant arising from the stabilization of the modulus fields in the KKLT vacua and find that this leads to a successful reheating in which the energy density of the scalar field effectively scales as a pressureless dust. The present dark energy can be also explained in our scenario provided that the potential energy of the massive rolling scalar does not exactly cancel with the amplitude of the negative cosmological constant at the potential minimum.

Figures (5)

• Figure 1: 2D posterior constraints in the $n_{\rm S}$-$R$ plane with the $1\sigma$ and $2\sigma$ contour bounds. Each case corresponds to (a) $p=2$, (b) $p=4$ and (c) $p \gg 1$ for the potential (\ref{['potp']}) with $e$-foldings $N=45, 50, 55, 60$ (from top to bottom). The scalar rolling potential (\ref{['eq03']}) belongs to the case (c).
• Figure 2: The evolution of the equation of state parameter $w$ (for massive Born-Infeld scalar field) is shown versus the scale factor for a fixed value of the warp factor $\beta=0.01$ in case of $\Lambda=0$. As the field evolves towards the origin, the parameter $w$ moves towards zero but never attains it. After this stage, $w$ fast drops and begins to oscillate such that the average equation of state is sufficiently negative and finally settles at $-1$.
• Figure 3: The evolution of the Born-Infeld scalar field $\phi$ for $\beta=10^{-3}$, $T_3=1$ and $\Lambda=V_0$. We start integrating from the beginning of inflation with initial values $\phi_i=170$ and $\dot{\phi}_i=0$. In this case we get the $e$-folding $N \sim 73$ around the end of inflation ($t \sim 200$). This slow-roll stage is followed by a reheating phase corresponding to the oscillation of the field $\phi$. Inset: The evolution of $\dot{\phi}^2$. This quantity rapidly approaches 1 during the transition from the inflationary phase to the reheating phase.
• Figure 4: The evolution of the equation of state parameter $w$ with same model parameters and initial conditions as in Fig. \ref{['phievo']}. The equation of state is close to $-1$ during inflation, which is followed by the oscillation of $\phi$ as the system enters the reheating stage. At late times the average equation of state corresponds to $\langle w \rangle =0$.
• Figure 5: The evolution of perturbation $\delta{\phi}_k$ governed by Eq. (\ref{['phik']}) for the massive Born-Infeld scalar. Unlike the case of a tachyon field, the bahavor of perturbations resembles with the evolution of $\delta{\phi}_k$ for an ordinary massive scalar field