Inflation driven by a bare cosmological constant and its graceful exit

Abstract

Vacuum energy, a prediction of quantum field theory, manifests itself as a cosmological constant in general relativity. In this Letter, we propose a novel inflationary scenario driven by a bare cosmological constant $Λ$, which terminates naturally through a self-tuning mechanism. Within Fab-Four gravity, self-tuning destabilizes the de Sitter state and drives the system toward a stiff-fluid attractor, thereby yielding a graceful exit. We construct two explicit models in which the slow-roll parameter evolves exponentially or as a power law. We show that the latter model, derived from center-manifold dynamics, significantly relaxes the required tuning of initial conditions. Our results establish, for the first time, that bare-vacuum-energy inflation with natural termination constitutes a viable dynamical possibility.

Figures (3)

• Figure 1: Global phase portrait of the dynamical system after Poincaré compactification. $y_1$ and $y_2$ are dimensionless quantities obtained by projecting $x_1$ and $x_2$ onto the Poincaré hemisphere. The asterisk at the origin denotes the unstable de Sitter solution (saddle point), while the asterisk on the boundary marks the universal attractor at infinity corresponding to the stiff-fluid epoch ($w_{\text{eff}}=+1$). Trajectories in the physical region ($\Lambda > 0$, unshaded) naturally evolve from the de Sitter phase towards the attractor, illustrating the elegant exit. The shaded grey regions indicate the unphysical regime where $\Lambda < 0$.
• Figure 2: Dynamical behavior near the center manifold, the dynamical trajectories near the center manifold are rapidly attracted onto the center manifold marked by '$\times$' and then evolve along it. The red dashed line is a dynamical trajectory that achieves an e-folding number of 55, which corresponds to the red line in Fig. \ref{['fig:Img1']}
• Figure 3: Evolution of the first slow-roll parameter $\epsilon_H$ (left axis, red line and blue line) and the comoving Hubble Radius $R_\mathrm{CH}=c/(aH)$ (right axis, solid black line) as a function of the e-folding number $N$ for these models. Inflation proceeds while $\epsilon_H \ll 1$ and terminates when $\epsilon_H = 1$, marking a smooth transition from a quasi-de Sitter phase to a stiff-fluid dominated epoch. The dashed line shows the excellent agreement between our analytic approximation for $\epsilon_H$ and the full numerical solution.