Causal Modifications of Gravity and Their Observational Bounds

TL;DR

This paper investigates causal scalar field models with non-canonical kinetic terms as modifications to gravity, analyzing their observational bounds from astrophysical systems while avoiding superluminality and acausality issues.

Contribution

It introduces subluminal, causal scalar field models with nonlinear kinetic terms and derives observational constraints from binary pulsars, neutron stars, and merger events.

Findings

Constraints from binary pulsar precession

Bounds from neutron star hydrostatic equilibrium

Limits on scalar radiation during mergers

Abstract

Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most existing studies of such scalars invoke models that exhibit some kind of "screening" at short distances to hide the force from solar system tests. However, as is well known, such modifications also exhibit superluminality, which can be interpreted as a form of acausality. In this work we explore explicitly subluminal and causal scalar field models. In particular, we study a conformally coupled scalar $\phi$, with a small coupling to matter to obey solar system bounds, and a non-canonical kinetic term $K(X)$ ($X=(\partial\phi)^2/2$) that obeys all subluminality constraints and is hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As opposed to screening (and superluminality), this new force becomes more and more important in the regime of high densities (and subluminality). We then turn to the densest environments to put bounds on this new interaction. We compute constraints from precession in binary systems such as Hulse-Taylor, we compute corrections to neutron star hydrostatic equilibrium, and we compute power in radiation, both tensor mode corrections and the new scalar mode, which can be important during mergers.