[Paper Review] Super-Hubble Supergravity Inflation

Anupam Mazumdar, S. Nadathur+1 more|arXiv (Cornell University)|May 2, 2011

Cosmology and Gravitation Theories3 citations

TL;DR

This paper demonstrates that cosmologically flat directions in the MSSM can remain stable against large super-Hubble supergravity corrections, enabling viable F-term inflation. It shows that an n=6 operator on a flat direction fits current CMB data for Hubble parameters between 10⁵ and 10⁸.⁵ GeV, resolving a key tension between slow-roll inflation and supergravity.

ABSTRACT

It is well known that large Hubble-induced supergravity corrections to the inflaton field can ruin the flatness of the potential, thus creating a tension between slow-roll inflation and supergravity. In this paper we show that it is possible to obtain a {\it cosmologically flat} direction, embedded within the MSSM (Minimal Supersymmetric Standard Model), in spite of very large super-Hubble corrections. As an illustration, we show that a flat direction which is lifted by an $n=6$ operator matches the current cosmic microwave background data for a wide range of the Hubble parameter, $10^{5} { m GeV}\lesssim H_{inf}\lesssim 10^{8.5}$ GeV. Our results are generic and can be applicable to any $F$-term inflationary models.

Motivation & Objective

• To resolve the tension between slow-roll inflation and supergravity corrections that typically ruin inflaton potential flatness.
• To identify conditions under which flat directions in the MSSM remain cosmologically flat despite large super-Hubble corrections.
• To demonstrate that F-term inflation models can remain viable when embedded in supergravity with large Hubble parameters.
• To show that a specific n=6 operator on a flat direction yields consistent predictions with current CMB observations.

Proposed method

• Analyzing the effective superpotential including higher-dimensional operators, particularly an n=6 operator, to model corrections from super-Hubble physics.
• Evaluating the scalar potential induced by F-terms in supergravity, focusing on the interplay between the F-term contribution and the super-Hubble corrections.
• Computing the effective potential along the flat direction, including both the F-term and the Hubble-induced corrections.
• Applying constraints from CMB data to determine the viable range of Hubble parameters for which the potential remains flat enough for slow-roll inflation.
• Using the MSSM framework to identify a flat direction that supports the required n=6 operator without breaking gauge invariance or renormalizability.
• Performing a parameter scan over Hubble scale and operator strength to identify regions consistent with observational bounds.

Experimental results

Research questions

• RQ1 Can flat directions in the MSSM remain stable against large super-Hubble supergravity corrections?
• RQ2 What is the maximum Hubble scale for which a flat potential can still support slow-roll inflation in F-term models?
• RQ3 How do higher-dimensional operators (e.g., n=6) affect the flatness of the inflaton potential in supergravity?
• RQ4 Can F-term inflation models remain viable when subjected to large Hubble-induced corrections?
• RQ5 What is the range of Hubble parameters for which the n=6 operator model matches current CMB data?

Key findings

• A flat direction in the MSSM with an n=6 operator remains cosmologically flat even under large super-Hubble supergravity corrections.
• The model yields a viable slow-roll inflationary potential for Hubble parameters in the range 10⁵ GeV ≤ H_inf ≤ 10⁸.⁵ GeV.
• The scalar potential remains sufficiently flat to support slow-roll inflation across the entire specified Hubble range.
• The model is consistent with current cosmic microwave background data, validating its phenomenological viability.
• The results are generic and extendable to other F-term inflationary models within supergravity.
• The n=6 operator effectively counteracts the destabilizing effects of super-Hubble corrections, preserving flatness.