[Paper Review] Superconformal approach to Higgs inflation from new K\"ahler potential

Sayantan Choudhury, Trina Chakraborty+1 more|arXiv (Cornell University)|May 5, 2013

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a new class of Higgs inflation models using a superconformal approach in supergravity by modifying the K"ahler potential. By introducing a superconformal symmetry breaking parameter $\chi$, it classifies models into three categories, with minimal coupling at $\chi = \pm\frac{2}{3}$, and studies their inflationary predictions, successfully confronting them with WMAP9 and complementary data, while identifying allowed ranges for non-minimal couplings and Yukawa-type interactions.

ABSTRACT

We introduce a new class of models of Higgs inflation using the superconformal approach to supergravity by modifying the K\ahler geometry. Using such a mechanism, we construct a phenomenological functional form of a new K\ahler potential. From this we construct various types of models which are characterized by a superconformal symmetry breaking parameter $\chi$, and depending on the numerical values of $\chi$ we classify all of the proposed models into three categories. Models with minimal coupling are identified by $\chi=\pm\frac{2}{3}$ branch which are made up of shift symmetry preserving flat directions. We also propose various other models by introducing a non-minimal coupling of the inflaton field to gravity described by $\chi eq\frac{2}{3}$ branch. We employ all these proposed models to study the inflationary paradigm by estimating the major cosmological observables and confront them with recent observational data from WMAP9 and other complementary data sets. We also mention an allowed range of non-minimal couplings and the {\it Yukawa} type of couplings appearing in the proposed models used for cosmological parameter estimation.

Motivation & Objective

• To develop a new class of Higgs inflation models using the superconformal approach in supergravity.
• To explore the role of a modified K"ahler potential in generating viable inflationary dynamics.
• To classify models based on the superconformal symmetry breaking parameter $\chi$ and identify distinct classes, including minimal and non-minimal coupling scenarios.
• To estimate cosmological observables and confront model predictions with observational data from WMAP9 and complementary datasets.
• To determine allowed ranges for non-minimal couplings and Yukawa-type couplings in the proposed models.

Proposed method

• A phenomenological functional form of a new K"ahler potential is constructed to modify the K"ahler geometry in superconformal supergravity.
• The superconformal symmetry breaking parameter $\chi$ is introduced as a key control parameter to classify the resulting models into three distinct categories.
• Models with $\chi = \pm\frac{2}{3}$ are identified as those with minimal coupling and shift symmetry preserving flat directions.
• Non-minimal coupling to gravity is introduced for $\chi \neq \frac{2}{3}$, enabling broader model construction.
• Inflationary observables such as the scalar spectral index and tensor-to-scalar ratio are computed from the constructed models.
• Model predictions are confronted with observational data from WMAP9 and complementary datasets to constrain parameters and validate consistency.

Experimental results

Research questions

• RQ1 How does modifying the K"ahler potential in the superconformal approach affect the realization of Higgs inflation?
• RQ2 What are the distinct classes of Higgs inflation models that emerge from different values of the superconformal symmetry breaking parameter $\chi$?
• RQ3 Can models with $\chi = \pm\frac{2}{3}$ support flat directions consistent with shift symmetry and viable inflation?
• RQ4 How do non-minimal couplings to gravity, introduced via $\chi \neq \frac{2}{3}$, affect the inflationary dynamics and observables?
• RQ5 What are the allowed ranges for non-minimal couplings and Yukawa-type couplings that are consistent with current observational constraints?

Key findings

• The proposed models are classified into three categories based on the value of the superconformal symmetry breaking parameter $\chi$.
• Models with $\chi = \pm\frac{2}{3}$ correspond to minimal coupling and feature shift symmetry preserving flat directions.
• Non-minimal coupling to gravity is realized through $\chi \neq \frac{2}{3}$, enabling a broader class of inflationary models.
• The cosmological observables derived from the models are consistent with recent WMAP9 and complementary data sets.
• An allowed range for non-minimal couplings is identified, ensuring compatibility with observational constraints.
• Yukawa-type couplings in the models are constrained to ranges compatible with cosmological parameter estimation from current data.