[Paper Review] Observable Gravitational Waves From Higgs Inflation in SUGRA

C. Pallis|arXiv (Cornell University)|Oct 12, 2017

Cosmology and Gravitation Theories7 references3 citations

TL;DR

This paper proposes a supersymmetric Higgs inflation model in Supergravity (SUGRA) with a shift-symmetric Kähler potential slightly broken by a parameter $ r_{ ext{±}} = c_+ / c_- $, enabling observable primordial gravitational waves. It achieves excellent agreement with Planck and Bicep2/Keck Array data, predicting tensor-to-scalar ratio $ r \gtrsim 0.0019 $, while maintaining subplanckian inflaton values and perturbative unitarity up to the Planck scale.

ABSTRACT

We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its supersymmetric value. Employing quadratic Kaehler potentials with a prominent shift-symmetric part proportional to c- and a tiny violation, proportional to c+, included in a logarithm we show that the inflationary observables provide an excellent match to the recent Planck and Bicep2/Keck Array results setting, e.g., 0.012<=c+/c-<1/N where -N<0 is the prefactor of the logarithm. Moreover, we analyze several possible stabilization mechanisms for the non-inflaton accompanying superfield using just quadratic terms. In all cases, inflation can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.

Motivation & Objective

• To construct viable Higgs inflation models in SUGRA that reproduce current CMB observations, particularly the tensor-to-scalar ratio $ r $.
• To stabilize the non-inflaton superfield using only quadratic terms in the Kähler potential, ensuring theoretical consistency.
• To achieve subplanckian inflaton field values while preserving perturbative unitarity up to the Planck scale.
• To identify parameter ranges for $ c_+ / c_- $ and $ n $ that yield observable gravitational waves consistent with Planck and Bicep2/Keck Array data.

Proposed method

• Uses a superpotential $ W = \lambda S(\bar{\Phi}\Phi - M^2/4) $ to induce spontaneous $ U(1)_{B-L} $ breaking and stabilize the vacuum at $ |\Phi| = |\bar{\Phi}| = M/2 $.
• Constructs Kähler potentials $ K_1, K_2, K_3 $ with a dominant shift-symmetric part $ c_- F_- $ and a small breaking term $ c_+ F_+ $, parameterized by $ r_{\pm} = c_+ / c_- $.
• Implements stabilization of the singlet superfield $ S $ via quadratic terms in $ K $, including exponential and logarithmic forms $ F_{iS} $, ensuring minimal field dependence.
• Derives the effective inflationary potential and kinetic term in the Einstein frame, expanding around $ \phi \ll 1 $ to analyze small-field behavior and unitarity.
• Computes inflationary observables $ n_s $, $ r $, and $ \Delta_{\star} $ using the number of e-foldings $ \widehat{N}_\star \simeq 58 $, and fits to Planck and Bicep2/Keck Array data.
• Analyzes perturbative unitarity by expanding the kinetic and potential terms in powers of $ \widehat{\phi} $, showing safety up to $ m_P $ when $ r_{\pm} \leq 1/N $.

Experimental results

Research questions

• RQ1 Can Higgs inflation in SUGRA produce observable gravitational waves while maintaining subplanckian inflaton values and perturbative unitarity?
• RQ2 What is the role of the $ r_{\pm} = c_+ / c_- $ parameter in shaping the inflationary observables and fitting CMB data?
• RQ3 How do different stabilization mechanisms for the non-inflaton superfield affect the viability and predictions of the model?
• RQ4 Can the model achieve a good fit to Planck and Bicep2/Keck Array data across the full range of $ n_s $ and $ r $, particularly in the $ r \gtrsim 0.0019 $ window?
• RQ5 What are the bounds on $ r_{\pm} $, $ n $, and $ \lambda / c_- $ that ensure consistency with observational constraints and unitarity?

Key findings

• The model achieves excellent agreement with Planck and Bicep2/Keck Array data, with $ 0.012 \lesssim c_+ / c_- \lesssim 1/N $, where $ N $ is the prefactor of the logarithmic term.
• For $ n_s = 0.968 $ and $ \widehat{N}_\star \simeq 58 $, the tensor-to-scalar ratio is predicted as $ 0.4 \lesssim r / 0.01 \lesssim 7 $, implying $ r \gtrsim 0.0019 $, making it testable by upcoming experiments.
• The model supports hilltop inflation for $ 0 < n \leq 0.0215 $, with $ \Delta_{\rm max\star} \gtrsim 0.4 $, indicating a mild tuning requirement.
• The parameter $ a_s $ is confined to $ -(5-6) \cdot 10^{-4} $, ensuring consistency with $ \Lambda $CDM + $ r $ fitting to observational data.
• Perturbative unitarity is preserved up to the Planck scale, as shown by the small-field expansion where $ r_{\pm} \leq 1/N $, ensuring no Landau poles from higher-order terms.
• The allowed region in the $ n $–$ r_{\pm} $ plane is fully covered by varying $ n $ and $ r_{\pm} $, with $ -1.21 \lesssim n / 0.1 \lesssim 0.215 $, $ 0.12 \lesssim r_{\pm} / 0.1 \lesssim 5 $, and $ 10^5 \lambda / c_- \lesssim 2.6 $.