Covariant gravity with Lagrange multiplier constraint

TL;DR

This paper reviews gravity models with Lagrange multiplier constraints, focusing on their symmetry breaking, specific $F(R)$ models, and potential for inflationary cosmology, highlighting their unique propagating modes and renormalization features.

Contribution

It introduces a covariant $F(R)$ gravity model with constraints, explores its properties, and discusses its implications for inflation and quantum consistency.

Findings

The model admits flat space solutions.

Only the graviton propagates, scalar and vector modes do not.

Preliminary cosmology suggests inflationary solutions.

Abstract

We review on the models of gravity with a constraint by the Lagrange multiplier field. The constraint breaks general covariance or Lorentz symmetry in the ultraviolet region. We report on the $F(R)$ gravity model with the constraint and the proposal of the covariant (power-counting) renormalized gravity model by using the constraint and scalar projectors. We will show that the model admits flat space solution, its gauge-fixing formulation is fully developed, and the only propagating mode is (higher derivative) graviton, while scalar and vector modes do not propagate. The preliminary study of FRW cosmology indicates to the possibility of inflationary universe solution is also given.