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Non-Minimal Dilaton Inflation from the Effective Gluodynamics

Pirzada, Imtiaz Khan, Mussawair Khan, Tianjun Li, Ali Muhammad

Abstract

We study single-field inflation in which the inflaton is identified with the lightest scalar (dilaton) excitation of a confining gauge theory. The inflaton potential is not postulated: it follows from the pure effective Gluodynamics Lagrangian tightly constrained by the trace anomaly and the associated infinite tower of Ward identities, yielding a Coleman--Weinberg form with a logarithmic term fixed by nonperturbative condensates. After coupling to gravity via a non-minimal interaction $ξ\,\varphi^2 R$, the Einstein-frame potential develops a plateau consistent with current CMB observables. In the large-$ξ$ limit the model approaches the standard plateau attractor, while the Migdal--Shifman(MS) logarithmic structure induces a controlled, testable deformation governed by $A/λ$ across the CMB window. We quantify the resulting shifts in $(n_s,r)$ and the running analytically and confirm them with numerical scans over $(ξ,λ,A,μ)$, making the departure from the attractor both microphysically motivated and observationally predictive.

Non-Minimal Dilaton Inflation from the Effective Gluodynamics

Abstract

We study single-field inflation in which the inflaton is identified with the lightest scalar (dilaton) excitation of a confining gauge theory. The inflaton potential is not postulated: it follows from the pure effective Gluodynamics Lagrangian tightly constrained by the trace anomaly and the associated infinite tower of Ward identities, yielding a Coleman--Weinberg form with a logarithmic term fixed by nonperturbative condensates. After coupling to gravity via a non-minimal interaction , the Einstein-frame potential develops a plateau consistent with current CMB observables. In the large- limit the model approaches the standard plateau attractor, while the Migdal--Shifman(MS) logarithmic structure induces a controlled, testable deformation governed by across the CMB window. We quantify the resulting shifts in and the running analytically and confirm them with numerical scans over , making the departure from the attractor both microphysically motivated and observationally predictive.
Paper Structure (10 sections, 58 equations, 6 figures, 1 table)

This paper contains 10 sections, 58 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Migdal--Shifman gluodynamics and anomaly-matching scalar EFT
  3. Nonminimal coupling and field dynamics
  4. Inflationary dynamics and observables
  5. Numerical Scan
  6. Observational status and numerical interpretation
  7. Discussion on EFT control
  8. Single-field validity of the gluodynamics EFT.
  9. Reheating.
  10. Conclusions

Figures (6)

  • Figure 1: MS potential in $X$. $V(X)/|e_{\rm vac}|=(X-1)e^X$Migdal:1982.
  • Figure 2: Einstein-frame potential $U(\phi)$ and plateau deformation. The nonminimal coupling produces an asymptotic plateau at large field, while the MS anomaly term induces a mild logarithmic deformation consistent with Eq. \ref{['eq:UlargeExact']}Callan:1970Bezrukov:2008Kallosh:2014.
  • Figure 3: Numerical predictions in the $(n_s,r)$ plane. The scan evaluates $n_s$ and $r$ using Eqs. \ref{['eq:epsExact']}--\ref{['eq:ObsExact']}. The attractor curve emerges at large $\xi$ when Eq. \ref{['eq:deformSmall']} holds Bezrukov:2008Kallosh:2014.
  • Figure 4: Heatmap of $n_s$ over parameter space. Scan in $(\log_{10}\xi, A/\lambda)$ illustrating the approach to the attractor at large $\xi$ and controlled departures as $A/\lambda$ increases.
  • Figure 5: Heatmap of $\log_{10} r$ over parameter space. The tensor amplitude decreases toward the plateau regime, consistent with the scaling $r\simeq 12/N^2$ in the attractor domain Kallosh:2014.
  • ...and 1 more figures