Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms

TL;DR

This paper explores how invariants of algebraic forms relate to the curvature of Kahler manifolds in supergravity, providing insights into early universe phenomena like inflation and baryogenesis, with potential model-independent constraints.

Contribution

It establishes a connection between algebraic invariants and curvature order parameters in supergravity, offering a new approach to analyze early universe cosmology.

Findings

Curvature of Kahler manifolds can be linked to invariants of algebraic forms.

Invariants like Aronhold invariants relate to moduli space properties.

Constraints on baryogenesis derived from curvature relations.

Abstract

The presence of light scalars can have profound effects on early universe cosmology, influencing its thermal history as well as paradigms like inflation and baryogenesis. Effective supergravity provides a framework to make quantifiable, model-independent studies of these effects. The Riemanian curvature of the Kahler manifold spanned by scalars belonging to chiral superfields, evaluated along supersymmetry breaking directions, provides an order parameter (in the sense that it must necessarily take certain values) for phenomena as diverse as slow roll modular inflation, non-thermal cosmological histories, and the viability of Affleck-Dine baryogenesis. Within certain classes of UV completions, the order parameter for theories with $n$ scalar moduli is conjectured to be related to invariants of $n$-ary cubic forms (for example, for models with three moduli, the order parameter is given by the ring of invariants spanned by the Aronhold invariants). Within these completions, and under the caveats spelled out, this may provide an avenue to obtain necessary conditions for the above phenomena that are in principle calculable given nothing but the intersection numbers of a Calabi-Yau compactification geometry. As an additional result, abstract relations between holomorphic sectional and bisectional curvatures are utilized to constrain Affleck-Dine baryogenesis on a wide class of Kahler geometries.