Inflation Model Based on Virasoro Squeezing

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 $\hat{I}¸$. 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.

38 pages, 5 figures. v2: Minor revisions. Several explanatory footnotes were added to clarify the assumptions and scope of the model, including the role of the squeezing transformation, treatment of quantum fluctuations, and the fixed background metric. v3: Appendix C added. v4: Updated explanations and revised figures