Defocusing of Null Rays in Infinite Derivative Gravity

Abstract

Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any Ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any Ansatz to solve the full equations of motion.

8 pages plus references

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Cited by in corpus (17)

• Classical properties of non-local, ghost- and singularity-free gravity
• The spectrum of symmetric teleparallel gravity
• Consistent Higher Derivative Gravitational theories with stable de Sitter and Anti-de Sitter Backgrounds
• $R^2$ inflation to probe non-perturbative quantum gravity
• Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
• Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature
• Towards the Raychaudhuri Equation Beyond General Relativity
• Towards resolution of anisotropic cosmological singularity in infinite derivative gravity
• UV completion of the Starobinsky model, tensor-to-scalar ratio, and constraints on non-locality
• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
• Singularities in Spherically Symmetric Solutions with Limited Curvature Invariants
• Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity
• Conditions for defocusing around more general metrics in Infinite Derivative Gravity
• Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds
• Unruh-DeWitt Particle Detectors in Bouncing Cosmologies
• Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences