# Inflation, bifurcations of nonlinear curvature Lagrangians and dark energy

## TL;DR

This paper explores a unified framework linking dark matter, dark energy, and inflation through bifurcations in nonlinear curvature Lagrangians, suggesting multiple Einsteinian domains and implications for cosmological phenomena.

## Contribution

It introduces a novel analysis of scalar dark matter, inflaton, and modified gravity equivalence, revealing bifurcations and multiple Einsteinian solutions in the effective Lagrangian.

## Key findings

- Bifurcation of effective Lagrangian into multiple Einsteinian spaces.
- Presence of a swallow tail catastrophe indicating coexistence of domains.
- Implications for understanding dark matter, dark energy, and inflation as interconnected phenomena.

## Abstract

A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.