[Paper Review] Induced-Gravity Inflation in Supergravity Confronted with Planck 2015 & BICEP2/Keck Array

C. Pallis|arXiv (Cornell University)|Jun 11, 2015

Cosmology and Gravitation Theories17 references3 citations

TL;DR

This paper proposes a supersymmetric induced-gravity inflation model in supergravity using two gauge singlet chiral superfields with R and Z₂ symmetries, a logarithmic Kähler potential up to fourth order, and a tunable mixing coefficient $k_{S ilde{ ext{Φ}}}$; it achieves $n_s \approx 0.963$ and $r \approx 0.004$ in no-scale SUGRA, and enhances $r$ into the observable range (consistent with Planck 2015 and BICEP2/Keck) by tuning the Kähler potential prefactor slightly above $-3$, while maintaining perturbative unitarity and subplanckian inflaton values.

ABSTRACT

Supersymmetric versions of induced-gravity inflation are formulated within Supergravity (SUGRA) employing two gauge singlet chiral superfields. The proposed superpotential is uniquely determined by applying a continuous R and a discrete Z_2 symmetry. We also employ a logarithmic Kahler potential respecting the symmetries above and including all the allowed terms up to fourth order in powers of the various fields. When the Kahler manifold exhibits a no-scale-type symmetry, the model predicts spectral index ns=0.963 and tensor-to-scalar r=0.004. Beyond no-scale SUGRA, ns and r depend crucially on the coefficient ksphi involved in the fourth order term, which mixes the inflaton Phi with the accompanying non-inflaton superfield S in the Kahler potential, and the prefactor encountered in it. Increasing slightly the latter above (-3), an efficient enhancement of the resulting r can be achieved putting it in the observable range favored by the Planck and BICEP2/Keck Array results. In all cases, imposing a lower bound on the parameter cR, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity.

Motivation & Objective

• To construct a supersymmetric induced-gravity inflation model in supergravity that remains valid up to the Planck scale while allowing subplanckian inflaton fields.
• To reconcile induced-gravity inflation with recent Planck 2015 and BICEP2/Keck Array data on the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$.
• To explore the role of the Kähler potential's coefficient $k_{S\Phi}$ and the prefactor deviation $(1+n)$ in enhancing $r$ while preserving perturbative unitarity.
• To ensure the model remains UV-complete and unitarity-safe by analyzing the UV cutoff scale $\Lambda_{\text{UV}}$ in both Jordan and Einstein frames.

Proposed method

• Formulate a superpotential $W = \frac{\lambda}{c_R} S(\Omega_H - 1/2)$ with $\Omega_H = c_R \Phi^2$, invariant under continuous $R$ and discrete $\mathbb{Z}_2$ symmetries.
• Employ a logarithmic Kähler potential $K$ including all fourth-order terms in $\Phi$ and $S$, with a tunable prefactor parameterized by $(1+n)$.
• Implement a no-scale-type symmetry in the Kähler manifold to suppress $r$ in the baseline case.
• Introduce a mixing term $k_{S\Phi}$ in the Kähler potential to couple the inflaton $\Phi$ and non-inflaton $S$ superfields, enabling $r$ enhancement.
• Perform conformal transformation from Jordan to Einstein frame to derive the physical scalar potential and compute inflationary observables.
• Analyze the UV behavior via the effective UV cutoff $\Lambda_{\text{UV}}$, showing it remains at the Planck scale due to cancellation of $c_R^{-1}$ in scattering amplitudes.

Experimental results

Research questions

• RQ1 Can induced-gravity inflation in supergravity achieve $n_s \approx 0.963$ and $r \approx 0.004$ in the no-scale limit, consistent with Planck 2015 data?
• RQ2 How does the coefficient $k_{S\Phi}$ in the Kähler potential affect the tensor-to-scalar ratio $r$ beyond no-scale SUGRA?
• RQ3 Can the model achieve $r$ in the observable range favored by Planck and BICEP2/Keck Array while keeping the inflaton subplanckian and the effective theory perturbative?
• RQ4 What is the role of the Kähler potential prefactor deviation $(1+n)$ in enabling $r$ enhancement without violating unitarity?
• RQ5 Is the UV cutoff $\Lambda_{\text{UV}}$ preserved at the Planck scale despite non-minimal couplings?

Key findings

• In the no-scale SUGRA limit, the model predicts $n_s \approx 0.963$, $r \approx 0.004$, and $a_s \approx -0.00065$, in excellent agreement with Planck 2015 data.
• By increasing the Kähler potential prefactor slightly above $-3$ (i.e., $n \approx -0.03$ to $-0.05$), the model enhances $r$ into the 1-$\sigma$ range of Planck+BICEP2/Keck joint analysis.
• The coefficient $k_{S\Phi}$ controls the spectral index $n_s$, allowing it to span the full allowed range in the non-no-scale case.
• The UV cutoff $\Lambda_{\text{UV}}$ is found to be at the Planck scale in both Jordan and Einstein frames, confirming the model's perturbative unitarity and UV finiteness.
• The inflaton field remains subplanckian throughout inflation, and the effective theory respects perturbative unitarity due to cancellation of $c_R^{-1}$ in scattering amplitudes.
• A mild tuning of $k_S \sim 0.05$ is sufficient to keep one-loop radiative corrections subdominant, ensuring theoretical consistency.