Inflation Model Based on Virasoro Squeezing

TL;DR

This work develops a novel inflation scenario in which a complex scalar field undergoes Virasoro-squeezed conformal transformations, producing plateau-like potentials without explicit gravitational coupling and aligning with CMB constraints. The framework hinges on holomorphic Virasoro transformations, with the transformed potential $V_{\chi}^{(m,n)}(\chi)$ displaying a plateau that naturally enables slow-roll inflation; the plateau height is fixed by the boundary value via the maximum modulus theorem. Analytically tractable in the special case $n=-2$ (recovering the $t$-model/Starobinsky potential at leading order) and numerically explored for general $n$, the model yields $n_{s}$ and $r$ in agreement with Planck data across multiple branches and parameter choices. The approach provides a flexible, gravity-decoupled route to viable inflationary phenomenology and suggests avenues for connections to higher-dimensional or brane-inspired dynamics, as well as future tests with upcoming cosmological observations.

Abstract

We propose a novel mechanism for realizing slow-roll inflation that is fully consistent with observational data, based on conformal transformations acting exclusively on a complex scalar field -- without coupling to the gravitational sector. These transformations generically produce a plateau in the inflaton potential, as guaranteed by the maximum modulus theorem, thereby naturally satisfying the slow-roll conditions. Our framework utilizes squeezing operations generated by the Virasoro algebra without central extension, as developed in our earlier work. The resulting inflationary potentials depend on the Virasoro mode $n$, the power $m$ of the original potential, and the squeezing parameter $θ$. We present approximate analytical expressions at leading order for the special case $n=-2$, and perform numerical analyses for both $n=-2$ and other values of $n$. These reveal parameter regimes in which the predicted cosmological observables $(n_{s},r)$ align remarkably well with current CMB measurements.

Figures (7)

• Figure 3.1: Potential $V(\chi)$ for $n=-2,m=2,\theta=1$. The horizontal axis represents the inflaton field $\chi$, and the vertical axis shows the potential $V(\chi)$. The vertical dashed lines indicate the beginning and end points of the slow-roll inflation phase.
• Figure 3.2: $(n_{s},r)$ parametric plot with $\theta=0\sim100$, $n=-2,m=2,N_{e}=50,55,60$. The gray shaded region indicates the range allowed by current observational constraints.
• Figure 3.3: $(n_{s},r)$ parametric plot with $\theta=0\sim100$, $n=-2,m=\text{2,\ 4,\ 8},N_{e}=60$. The gray shaded region indicates the range allowed by current observational constraints.
• Figure 4.1: Parametric plots of the spectral index $n_{s}$ and tensor-to-scalar ratio $r$ for various $(n,\ m)$ in Branch 1. The solid circles indicate parameter sets that satisfy observational constraints, while crosses correspond to values outside the allowed region.
• Figure 4.2: Same as Figure \ref{['fig:Branch1Graph']}, but for Branch 2.

Theorems & Definitions (2)

• Proposition
• Corollary