Empirical validation of general relativity I: solar system and astrophysical constraints

As we will see in the next three lectures, the nature of gravity is strongly constrained on a huge range of space-time scales and energies. If one wants to investigate modifications of our theory of gravity beyond general relativity, one must necessarily find a way to pass these fantastically sharp constraints.

For the purpose of our lectures, it can be useful to distinguish three different kind of constraints on gravity:

Local: in laboratory or in the solar system.
Astrophysical: using astrophysical probes in the Milky way or (more or less) nearby Galaxies.
Cosmological: considering cosmological evolution on the largest possible scales of space and time.

Three regimes :

weak fields: low energy tests of gravity.
strong fields: high density (compactness) tests.
extreme gravity: high compactness and high velocities.

See Yunes et al (2024) for a finer definition and discussion of these regimes.

The measurement of fundamental constants on various scales also provides a very powerful constraint on the nature of gravity, which we will leave for the next lecture. These measures are both local and astrophysical and in the weak and strong field regimes. Furthermore, we leave the discussion of cosmological constraints for their own dedicated lecture, such that this class focuses on local and astrophysical constraints.

Local validation of GR: lab and solar system

Some tests of the EEP. Left: tests of the WEP through measurement of $\eta$. Middle: tests of the LLI through measurement of $\delta$. Right: tests of LPI through measurements of $\tilde{\alpha}$. From Will 2014.

Tests of the weak equivalence principle

\[\eta = 2\frac{|\vec{a}_A - \vec{a}_B|}{|\vec{a}_A + \vec{a}_B|}\]

There are multiple ways to tests the EEP in the Solar system and beyond with a very high accuracy. The most competitive bound to date on $\eta$, is by far given by the MICROSCOPE experiment (Touboul et al (2022)). Using orbiting masses in free fall around the Earth inside a satellite experiment, the final results of the MICROSCOPE mission give a constraint on $\eta$ for a pair of titanium and platinum of

\[\begin{equation} \eta = (-1.5 \pm 2.7)\times 10^{-15}. \end{equation}\]

See also the review of Bergé et al 2023.

Tests of the LLI

Tests of the LPI

Eddington parameter

$\gamma$

Cassini spacecraft 2003 (Bertotti et al 2004)

Astrophysical validation of GR

Tests of the LPI: non-gravitational fundamental constants

Tests of the SEP: the gravitational constant

Gravitational waves: pulsar timing arrays

Pulsar “strong regime”

Gravitational waves: direct

Black holes and neutron star mergers “extreme regime”.

From space: greater horizon, other range of frequency.

EHT and black hole pictures

Völkel 2020