Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

TL;DR

This paper develops a higher derivative gravity theory with Lagrange multipliers and scalar projectors, showing it admits inflationary solutions with only the graviton propagating, despite higher derivatives.

Contribution

It introduces a novel formulation of higher derivative gravity with constraints and scalar projectors, analyzing its gauge-fixed form and Lorentz symmetry breaking effects.

Findings

Only the graviton propagates as a mode.

The first Friedmann equation remains first order despite higher derivatives.

The theory admits inflationary universe solutions.

Abstract

We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.