[Paper Review] Extending Starobinsky inflationary model in gravity and supergravity

S.V. Ketov, Maxim Khlopov|arXiv (Cornell University)|Sep 24, 2018

Cosmology and Gravitation Theories22 references3 citations

TL;DR

This paper proposes a minimal $χ=1$ supergravity model embedding the Starobinsky inflation in a massive vector multiplet, avoiding the $η$-problem and enabling spontaneous SUSY breaking via a Polonyi superfield. It achieves a viable CMB spectrum, generates gravitino dark matter through Schwinger production and Polonyi decay, and allows for primordial black hole formation under specific scalar potential deformations, unifying inflation, dark matter, dark energy, and SUSY breaking in a single framework.

ABSTRACT

We review some recent trends in the inflationary model building, the supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the Primordial Black Holes (PBHs) production in supergravity. The Starobinsky inflation can be embedded into supergravity when the inflaton belongs to the massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge symmetry. The SUSY and R-symmetry can be also spontaneously broken after inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos are super heavy and can be copiously produced during inflation via the Schwinger mechanism sourced by the Universe expansion. The overproduction and instability problems can be avoided, and the positive cosmological constant (dark energy) can also be introduced. The observed abundance of the Cold Dark Matter (CDM) composed of gravitinos can be achieved in our supergravity model too, thus providing the unifying framework for inflation, supersymmetry breaking, dark energy and dark matter genesis. Our supergravity approach may also lead to a formation of primordial non-linear structures like stellar-mass-type black holes, and may include the SUSY GUTs inspired by heterotic string compactifications, unifying particle physics with quantum gravity.

Motivation & Objective

• To embed the Starobinsky $R^2$ inflation model into $χ=1$ supergravity using a massive vector multiplet, avoiding the $η$-problem associated with chiral multiplet inflatons.
• To achieve spontaneous supersymmetry breaking after inflation via the Polonyi mechanism, enabling a de-Sitter vacuum and positive cosmological constant.
• To resolve the gravitino overproduction and Big Bang Nucleosynthesis (BBN) problems by ensuring super-heavy gravitinos and Polonyi particles.
• To generate the observed cold dark matter abundance via Schwinger-type production during inflation and subsequent Polonyi decay.
• To explore the possibility of primordial black hole (PBH) formation, particularly stellar-mass type, through scalar potential instabilities in the inflationary dynamics.

Proposed method

• Embed the Starobinsky model in $χ=1$ supergravity using a massive vector multiplet, where the inflaton is part of a $D$-term potential, avoiding $F$-term stabilization issues.
• Introduce a Polonyi chiral superfield with a linear superpotential to trigger spontaneous SUSY breaking and generate a positive cosmological constant post-inflation.
• Use the Schwinger mechanism during inflation to produce super-heavy gravitinos and Polonyi particles, with decay of Polonyi particles contributing to gravitino abundance.
• Construct a deformed scalar potential $V/V_0 = (1 + \xi - e^{-\alpha\phi} - \xi e^{-\beta\phi^2})^2$ with a near-inflection point to enable large curvature fluctuations and PBH formation.
• Ensure the model remains consistent with CMB observables by tuning parameters $\alpha$, $\beta$, and $\xi$ to reproduce $n_s \approx 0.965$ and $r \ll 0.1$.
• Analyze the phase transition dynamics and bubble nucleation from a false vacuum to a true vacuum to source PBH formation via first-order phase transitions.

Experimental results

Research questions

• RQ1 Can the Starobinsky inflationary model be consistently embedded in $χ=1$ supergravity using a massive vector multiplet instead of a chiral multiplet?
• RQ2 How can spontaneous supersymmetry breaking and a positive cosmological constant be achieved after inflation in a supergravity framework without violating BBN constraints?
• RQ3 What is the origin of the observed cold dark matter abundance in this model, and can it be explained by Schwinger production and Polonyi decay?
• RQ4 Under what conditions can primordial black holes of stellar-mass scale be produced in this supergravity model?
• RQ5 Can the scalar potential deformation support both viable CMB observables and large curvature fluctuations necessary for PBH formation?

Key findings

• The model successfully embeds the Starobinsky $R^2$ inflation in $χ=1$ supergravity using a massive vector multiplet, avoiding the $η$-problem and stabilizing the inflaton via a $D$-term potential.
• The inclusion of a Polonyi superfield with a linear superpotential leads to spontaneous SUSY breaking and a de-Sitter vacuum, consistent with a positive cosmological constant.
• Gravitino dark matter abundance is achieved through a combination of Schwinger production during inflation and decay of super-heavy Polonyi particles, with the correct relic density for $m_{3/2} \sim 10^6$ GeV.
• A deformed scalar potential $V/V_0 = (1 + \xi - e^{-\alpha\phi} - \xi e^{-\beta\phi^2})^2$ with $\alpha = \sqrt{2/3}$, $\beta \geq 0$, and $\xi \geq 0$ allows for a near-inflection point, enabling large curvature fluctuations and PBH production.
• The model predicts the possibility of stellar-mass primordial black holes formed via first-order phase transitions from a false vacuum, with potential gravitational wave signatures detectable by LIGO/Virgo.
• The framework is consistent with CMB observations, BBN constraints, and provides a unified scenario for inflation, dark energy, dark matter, and SUSY breaking, with testable predictions in high-energy neutrino and gravitational wave experiments.