[Paper Review] New massless and massive infinite derivative gravity in three dimensions and perturbations around Minkowski and in (A)dS

Anupam Mazumdar, Georg Stettinger|arXiv (Cornell University)|Nov 2, 2018

Cosmology and Gravitation Theories5 citations

TL;DR

This paper proposes a new class of massless and massive infinite derivative gravity theories in three spacetime dimensions, using a quadratic curvature action with infinitely many covariant derivatives. By employing an entire function in the propagator, it resolves point-like singularities via Gaussian smearing in the UV while recovering general relativity in the IR, and embeds massive gravity as an infrared limit. The theory maintains parity invariance and torsion-freeness, with unitarity preserved in (A)dS backgrounds through perturbative analysis.

ABSTRACT

In this paper we will consider the most general quadratic curvature action with infinitely many covariant derivatives of massless gravity in 3 space time dimensions. The action is parity invariant and torsion free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened by a Gaussian distribution, while in the infrared the theory reduces to general relativity. We will also show how to embed new massive gravity in ghost free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the perturbative unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter space times in 3 spacetime dimensions by perturbing the geometries.

Motivation & Objective

• To develop a parity-invariant, torsion-free infinite derivative gravity theory in 3D spacetime with the same off-shell degrees of freedom as general relativity.
• To resolve point-like curvature singularities in the ultraviolet using a Gaussian-like smearing via an entire function in the propagator.
• To show that the theory reduces to general relativity in the infrared limit.
• To embed massive gravity as an infrared limit within the ghost-free infinite derivative framework on a Minkowski background.
• To derive and analyze perturbative unitarity conditions for infinite derivative gravity in de Sitter and Anti-de Sitter spacetimes in three dimensions.

Proposed method

• Formulate a general quadratic curvature action with infinitely many covariant derivatives in 3D spacetime, ensuring parity invariance and torsion-freeness.
• Construct the propagator using an entire function, specifically an exponential of a polynomial, to achieve UV smearing of singularities.
• Analyze the theory's behavior in the ultraviolet and infrared regimes to confirm singularity resolution and recovery of general relativity.
• Demonstrate that massive gravity can be embedded as a low-energy limit in the Minkowski background by tuning the propagator parameters.
• Perturb the geometry around Minkowski, de Sitter, and Anti-de Sitter backgrounds to derive unitarity conditions for the infinite derivative theory.
• Use perturbative methods to assess the unitarity of the theory in (A)dS spacetimes, ensuring absence of ghost states.

Experimental results

Research questions

• RQ1 How can a consistent infinite derivative gravity theory be constructed in three spacetime dimensions that preserves parity and avoids torsion?
• RQ2 Can the point-like curvature singularity in 3D gravity be resolved through an entire function in the propagator, leading to a Gaussian-like smearing of the curvature?
• RQ3 Does the proposed theory reduce to general relativity in the infrared limit while maintaining the same number of degrees of freedom as Einstein-Hilbert gravity?
• RQ4 Can massive gravity be embedded as an infrared limit of the ghost-free infinite derivative gravity framework in Minkowski spacetime?
• RQ5 What are the perturbative unitarity conditions for infinite derivative gravity in three-dimensional de Sitter and Anti-de Sitter spacetimes?

Key findings

• The theory features a propagator constructed from an entire function, which smears point-like curvature singularities into Gaussian distributions in the ultraviolet regime.
• In the infrared limit, the theory reduces to general relativity, recovering the standard Einstein-Hilbert dynamics.
• Massive gravity emerges as a low-energy limit of the infinite derivative theory in Minkowski spacetime, consistent with ghost-free conditions.
• The theory maintains unitarity in de Sitter and Anti-de Sitter spacetimes when perturbations are analyzed around these backgrounds.
• Perturbative analysis confirms that the infinite derivative gravity model avoids ghost states in (A)dS backgrounds, ensuring stability and consistency.