⚛️ general relativity

A New Paradigm for Testing Gravity: Theory-Independent Constraints Using Data From All Astrophysical and Cosmological Scales

This paper introduces a unified framework called Parametrized Post-Newtonian Cosmology (PPNC) that combines Solar System, astrophysical, and cosmological observations to provide theory-agnostic constraints on deviations from General Relativity, finding that average deviations across cosmic history are less than approximately 10%.

Original authors: Daniel B Thomas, Theodore Anton, Timothy Clifton

Published 2026-07-01

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Daniel B Thomas, Theodore Anton, Timothy Clifton

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out the rules of a giant, cosmic game of billiards. For over a century, physicists have been testing the rules of gravity (specifically Einstein's General Relativity) by watching how balls move in different parts of the universe.

The problem is that scientists have been playing these tests in very different "rooms."

Room 1 (Solar System): They watch how planets orbit the Sun and how light bends around the Sun. They use tools like the Cassini probe and Mars tracking.
Room 2 (The Deep Universe): They look at the "baby picture" of the universe (the Cosmic Microwave Background) and how galaxies are spaced out (Baryon Acoustic Oscillations).

Historically, the rules written for Room 1 didn't easily translate to Room 2. It was like trying to compare a recipe for baking a cake with a recipe for building a bridge; they both use math, but the specific numbers and contexts were so different that you couldn't easily see if they were describing the same underlying reality.

The New Approach: A Universal Translator
This paper introduces a new framework called PPNC (Parametrized Post-Newtonian Cosmology). Think of PPNC as a "universal translator" or a single, unified rulebook that works in both rooms simultaneously.

Instead of creating a new theory for every new experiment, the authors use a single set of adjustable knobs (parameters) to describe how gravity might deviate from Einstein's predictions. They ask: "If gravity is slightly different than Einstein said, how would that change the orbit of Mars and the pattern of the ancient universe light?"

How They Tested It
The team combined data from four very different sources into one giant puzzle:

The Cassini Probe: A spacecraft that measured how radio waves bent around the Sun.
Mars Ephemeris: Precise tracking of where Mars is and how fast it moves.
The Cosmic Microwave Background (CMB): The afterglow of the Big Bang.
Baryon Acoustic Oscillations (BAO): The "frozen sound waves" from the early universe that dictate how far apart galaxies are today.

The Results: Gravity is Holding Up
When they turned all the knobs and looked at the combined data, here is what they found:

Gravity is mostly Einstein: The "knobs" they adjusted to describe gravity came out very close to the values Einstein predicted. Specifically, the average deviation from Einstein's theory over the entire history of the universe is less than 10%.
The "Twin" Effect: They found that two specific gravity parameters (let's call them "Alpha" and "Gamma") are tightly linked. No matter how you look at the universe, from the early days to today, these two numbers stay within 1% of each other.
The "Local" Illusion: Because Alpha and Gamma are so close together, if you were an alien living in the universe at any point in time and tested gravity locally, you would conclude that Einstein's theory is perfect. You might just think the "strength" of gravity (Newton's constant) is slightly different, but the rules would look exactly right.

Why This Matters
The authors argue that this is a "paradigm shift." Before, you had to trust that the rules found in our Solar System applied to the edge of the universe, or vice versa. Now, they have proven you can test them together.

They found that while the universe allows for some wiggle room in how gravity behaves over time, the data from our Solar System (Mars and Cassini) and the deep universe (CMB and BAO) actually help each other. The Solar System data acts like a tight clamp, preventing the "wiggle room" from getting too wild, while the deep universe data fills in the gaps of time.

In a Nutshell
This paper doesn't discover a new force of gravity. Instead, it builds a better measuring tape. It shows that when we measure gravity using everything we know—from the neighborhood of Mars to the edge of the observable universe—Einstein's theory still holds up remarkably well, with any possible errors being less than 10%. It also proves that we can finally compare "local" gravity tests with "cosmic" gravity tests using the same language.

Technical Summary: Parametrized Post-Newtonian Cosmology (PPNC)

Problem Statement
Testing General Relativity (GR) is a central objective of modern physics, yet current constraints are typically context-specific, relying on distinct theoretical frameworks for Solar System, astrophysical, and cosmological scales. This fragmentation prevents the direct comparison and combination of results across disciplines, hindering a unified understanding of deviations from Einstein's theory. While model-agnostic approaches exist for cosmology (often based on perturbation theory), they lack a direct link to the Parametrized Post-Newtonian (PPN) parameters used in Solar System tests. Consequently, there is no single framework capable of constraining deviations from GR using a unified set of parameters across all astrophysical and cosmological scales.

Methodology
The authors introduce "Parametrized Post-Newtonian Cosmology" (PPNC), a framework extending the standard PPN formalism to include cosmological background expansion and the evolution of inhomogeneities.

Theoretical Construction: The cosmological metric is constructed as a patchwork of $\sim 100$ Mpc regions, each described by the PPN test metric. In a spatially flat universe dominated by matter and dark energy, the dynamical equations for the background and inhomogeneities are modified to include time-dependent PPN parameters, $\alpha(a)$ and $\gamma(a)$ .
Parameterization: The PPN parameters are treated as functions of the scale factor $a$ , modeled via a simple power law: $X(a) = A(a_1/a)^n + B$ . The framework defines gravitational coupling functions ( $\mu, G, \eta$ ) in terms of these parameters on both large (cosmological horizon) and small ( $\sim 100$ Mpc) scales.
Data Integration: The study combines four distinct datasets to constrain the parameters:
1. Cosmic Microwave Background (CMB): Planck 2018 data release.
2. Baryon Acoustic Oscillations (BAO): Data from 6dFGS, SDSS, BOSS, eBOSS, and Lyman- $\alpha$ surveys.
3. Solar System Data (SSD): Constraints from the Cassini probe and Mars ephemeris data, implemented as Gaussian priors on $\dot{\alpha}$ and $\gamma$ at the present epoch ( $a=1$ ).
Implementation: The analysis utilizes a modified version of the Boltzmann code CLASS, interfaced with the MontePython MCMC sampler. The study varies standard cosmological parameters alongside the PPNC parameters ( $\bar{\alpha}, \bar{\gamma}, \gamma(a=1), n$ ), where $\bar{X}$ represents the average value of a parameter over cosmic history.

Key Results
The combined analysis yields theory-agnostic constraints on deviations from GR over the history of the Universe:

Average Deviations: The average deviations from GR are constrained to be less than $\sim 10\%$ . At the 68% confidence level, the mean values are $\bar{\alpha} = 0.97^{+0.06}_{-0.07}$ and $\bar{\gamma} = 0.97^{+0.05}_{-0.05}$ (where GR corresponds to unity).
Parameter Degeneracy: A strong mutual degeneracy exists between $\bar{\alpha}$ and $\bar{\gamma}$ . The difference between these parameters is constrained to be within 1% for all of cosmic history. This implies that while the effective Newton's constant ( $G$ ) may vary, local tests of gravity at any cosmic time would remain compatible with GR.
Time Evolution Constraints: The inclusion of Solar System data tightens constraints on the time evolution of the parameters. The rate of change at the present epoch is constrained to $\dot{\alpha} = \dot{\gamma} = 0.4^{+0.6}_{-0.8} \times 10^{-13} \text{ yr}^{-1}$ (68% CL), representing a more than twofold improvement over Mars ephemeris constraints on $\dot{\alpha}$ alone and providing the first constraint on $\dot{\gamma}$ .
Data Synergy:
- BAO vs. SSD: BAO data improves constraints on $H_0$ and $\omega_c$ , effectively breaking degeneracies that allow large deviations from GR to be compensated by adjusting cosmological parameters. SSD primarily constrains the present-day values and time derivatives.
- Power Law Index ( $n$ ): The inclusion of BAO data restricts the allowed range of the power-law index $n$ , preventing the compensation of large deviations via $H_0$ adjustments. However, a three-way degeneracy between $n$ , $\omega_c$ , and $\bar{\gamma}$ remains when only CMB and BAO are used, which is resolved by adding Solar System data.

Significance and Claims
The paper claims to present the first study to directly combine Solar System and cosmological data to constrain a single, coherent set of theory-agnostic gravity parameters. The PPNC framework is described as a "paradigm shift" in precision tests of gravity, offering a holistic approach that unifies constraints from the Solar System, astrophysical environments, and the early Universe.

The authors assert that this approach is particularly valuable for upcoming missions (e.g., LSST, Euclid, SKA, LISA, DESI) that seek to constrain the same underlying gravitational interaction across different scales. By demonstrating that average deviations are small and that $\bar{\alpha}$ and $\bar{\gamma}$ are tightly coupled, the results suggest that GR remains a robust description of gravity, even when allowing for a cosmologically varying Newton's constant. The framework is presented as a tool to optimize constraints on modifications to Einstein's theory by leveraging the full breadth of temporal and spatial scales available in modern observational cosmology.

Technical Summary: Parametrized Post-Newtonian Cosmology (PPNC)

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