[論文レビュー] Earthquakes as probing tools for gravity theories

Aleksander Kozak, Aneta Wojnar|arXiv (Cornell University)|Aug 3, 2023

Geophysics and Gravity Measurements被引用数 8

ひとこと要約

The paper proposes a method to constrain gravity model parameters using Earth's seismic data, mass, and moment of inertia, yielding 2-sigma bounds on Palatini f(R) gravity, EiBI gravity, and DHOST theories.

ABSTRACT

We propose a novel method for testing gravity models using seismic data from Earth. By imposing observational constraints on Earth's moment of inertia and mass, we rigorously limit the gravitational models' parameters within a $2σ$ accuracy. Our method constrains the parameters governing additional terms to the General Relativity Lagrangian to the following ranges: $-2 imes10^9\lesssimβ\lesssim 10^9 ext{m}^2$ for Palatini $f(R)$ gravity, $-8 imes10^9\lesssimε\lesssim 4 imes 10^9 ext{m}^2$ for Eddington-inspired Born-Infeld gravity, and $-10^{-3}\lesssimΥ\lesssim10^{-3}$ for Degenerate Higher-Order Scalar-Tensor theories. We also discuss potential avenues to enhance the proposed method, aiming to impose even tighter constraints on gravity models.

研究の動機と目的

• Motivate testing of modified gravity theories using terrestrial data rather than cosmological observations.
• Develop a framework connecting seismic Earth models to constraints on gravity theory parameters.
• Quantify how Earth’s mass and polar moment of inertia constrain corrections to the Poisson equation in specific gravity models.
• Assess robustness and limitations of the method and outline extensions for tighter bounds.

提案手法

• Start from modified Poisson equation with a density-dependent correction term alpha(r, rho) for spherical symmetry.
• Apply non-relativistic hydrostatic equilibrium and mass equations under the spherical Earth model.
• Use PREM-like density profiles and Birch’s law to relate pressure, density, and seismic parameter Phi_s.
• Compute Earth’s mass and polar moment of inertia for varying theory parameters beta (Palatini f(R)) and Upsilon (DHOST).
• Compare computed M and I to observed values with a 2-sigma tolerance to derive parameter bounds.
• Explore how uncertainties in Earth’s density parameters affect constraints.

Figure 1: [color online] The density profile of the Earth according to the Preliminary Reference Earth Model (PREM) prem ; Kozak:2023axy , which assumes Newtonian gravity. The velocity plots are derived from observational data without incorporating any gravitational theory. The primary waves refer t

実験結果

リサーチクエスチョン

• RQ1 Can seismic Earth models constrain additional gravity terms in the Poisson equation beyond GR?
• RQ2 What are the 2-sigma bounds on beta for Palatini f(R) gravity, epsilon for EiBI gravity, and Upsilon for DHOST theories from Earth’s mass and I?
• RQ3 How do uncertainties in Earth’s interior parameters influence the gravity-model constraints?

主な発見

• Palatini f(R) gravity yields -2×10^9 ≤ beta ≤ 10^9 m^2 at 2-sigma.
• EiBI gravity yields -8×10^9 ≤ epsilon ≤ 4×10^9 m^2 at 2-sigma.
• DHOST theories yield -1×10^-3 ≤ Upsilon ≤ 1×10^-3 at 2-sigma.
• Earth’s mass and polar moment of inertia constraints can be satisfied within PREM-like density choices.
• Reducing uncertainty in Earth’s mantle density could further tighten gravity-model bounds.

(a)