Lanczos equation on light-like hypersurfaces in a cosmologically viable class of kinetic gravity braiding theories

TL;DR

This paper derives generalized junction conditions, including a Lanczos equation, for null hypersurfaces in a specific class of scalar-tensor gravity theories compatible with gravitational wave constraints and cosmological evolution.

Contribution

It introduces a generalized Lanczos equation and scalar junction conditions for light-like hypersurfaces in kinetic gravity braiding models with second order dynamics.

Findings

Derived a 2+1 decomposed form of the Lanczos equation for null hypersurfaces.

Established scalar junction conditions relating distributional sources to curvature jumps.

Identified constraints on models compatible with gravitational wave and cosmological data.

Abstract

We discuss junction conditions across null hypersurfaces in a class of scalar-tensor gravity theories with i) second order dynamics, ii) obeying the recent constraints imposed by gravitational wave propagation, and iii) allowing for a cosmologically viable evolution. These requirements select kinetic gravity braiding models with linear kinetic term dependence and scalar field-dependent coupling to curvature. We explore a pseudo-orthonormal tetrad and its allowed gauge fixing, with one null vector standing as the normal, the other being transversal to the hypersurface. We derive a generalization of the Lanczos equation in a 2+1 decomposed form, relating the energy density, current and isotropic pressure of a distributional source to the jumps in the transverse curvature and transverse derivative of the scalar. Additionally we discuss a scalar junction condition and its implications for the distributional source.