String-Inspired Infinite-Derivative Theories of Gravity: A Brief Overview

Abstract

In String Theory there often appears a rather interesting class of higher derivative theories containing an infinite set of derivatives in the form of an exponential. These theories may provide a way to tame ultraviolet divergences without introducing ghost-like states. In this invited article we provide a brief overview on the progress that has been made over the last decade to construct such infinite derivative theories of gravity which may be able to address the singularity problems in gravity. In the process we will also be able to present some general results that applies to covariant torsion-free metric theories of gravity.

arXiv comment22 pages. Accepted review article in "New trends in theory of gravity," Mod. Phys. Lett. A, v2: very minor changes

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• Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity
• Higher-order modified Starobinsky inflation
• Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom
• Pre-inflationary primordial perturbations
• Determination of Angle of Light Deflection in Higher-Derivative Gravity Theories
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Wave propagation and shock formation in the most general scalar-tensor theories
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Hawking radiation in Non local field theories
• Doubly special relativity as a non-local quantum field theory
• Discrete heat kernel, UV modified Green's function, and higher derivative theories
• Non-local quantum field theory from doubly special relativity
• Quasinormal Modes and Shadows of Black Holes in Infinite Derivative Theory of Gravity
• Quantum fluctuation of stress tensor in a higher-derivative scalar field theory around a cosmic string
• The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term
• Calculations in induced gravity from higher-derivative field theories