---
title: "Can the same expansion come with different gravity?"
description: "Yes. Distances fix how fast the universe expanded, but not how hard gravity pulls; growth of structure and lensing tell the two apart."
canonical_url: "https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/same-expansion-different-gravity/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/dark-energy-or-modified-gravity/same-expansion-different-gravity/"
last_modified: "2026-11-12"
---

[Dark energy or modified gravity](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/)

# Can the same expansion come with different gravity?

Sandbox Physics · 2026-11-12

Yes. Measuring how fast the universe has expanded does not tell you how strongly gravity pulls matter together. Two universes can stretch at exactly the same rate while one builds galaxy clusters faster than the other. Astronomers tell them apart by measuring three things together: distances, the growth of structure, and the bending of light.

## A ruler, a clock and a puzzle

Look at a distant galaxy and you see it as it was when its light left. The light has been stretched on the way. That stretch is the redshift, and it says how much the universe has expanded since then. If you also know how far away the galaxy is, you learn how fast the expansion went over that stretch of history.

Exploding white dwarfs, called type Ia supernovae, give one kind of distance: they all reach nearly the same peak brightness, so a fainter one is farther. A second kind comes from a pattern frozen into the distribution of galaxies. Sound waves in the young universe left a preferred separation of about 150 megaparsecs between galaxies. Seen across the sky at different redshifts, that fixed ruler looks smaller the farther away it is.

These measurements showed in 1998 that the expansion is speeding up. The simplest explanation is a cosmological constant, a fixed energy of empty space. Later data from the Dark Energy Spectroscopic Instrument (DESI) hint that the push may change over time. With its second data release in 2025, DESI combined its galaxy ruler with the cosmic microwave background and supernovae and found a preference for evolving dark energy at 2.8 to 4.2 standard deviations, depending on which supernova sample is used. [DESI DR2 BAO results, 2025, §VII.1](https://arxiv.org/html/2503.14738v3)

## Why distances cannot settle it

Every one of those distances depends only on the expansion rate at each moment. A changing dark energy changes that rate. So could a modified law of gravity, because gravity also decides how matter and space push back on the expansion. Given only a history of the expansion rate, many theories can be tuned to reproduce it exactly.

The question in the title is therefore not a trick. It is the reason modern surveys measure more than distances. The Particle Data Group review of dark energy puts the strategy plainly: measure the expansion history, predict how structure should grow if Einstein's gravity is right, and check the prediction against the growth you observe. [Weinberg and White, PDG Review of Particle Physics 2025, §28.2.2](https://pdg.lbl.gov/2025/reviews/rpp2025-rev-dark-energy.pdf)

## Growth and lensing feel gravity directly

Matter in the universe started almost perfectly smooth. Slightly denser regions pulled in more matter and grew into the cosmic web of filaments and clusters. How fast they grew depends on two things: how fast space was stretching, which works against the collapse, and how hard gravity pulls.

Surveys measure that growth through the motions of galaxies. Galaxies falling into a cluster add a little velocity along our line of sight, which squashes the cluster when its position is worked out from redshift. The size of that squashing measures the growth rate. A survey reports it as $f\sigma_8$, roughly the speed of infall times the clumpiness of matter.

Gravity also bends light. Mass in the foreground slightly distorts the shapes of background galaxies; this is weak gravitational lensing. In Einstein's theory, the same mass gives a fixed amount of bending and a fixed amount of pull on slow matter. In many modified theories the two can differ. Light might be bent less while matter falls in faster.

## How the test works

Start from the measured distances and work out the expansion history. Feed that history into Einstein's equations and predict how fast clusters should have grown and how strongly they should lens. If the observed growth and lensing agree, an evolving dark energy with ordinary gravity is enough. If they disagree in a particular way, gravity itself is the suspect.

Two numbers summarize the outcome. One is the extra pull on matter compared with Einstein's value, written $\mu$. The other is the extra bending of light, written $\Sigma$. Both equal one in general relativity. DESI applied this test to its first year of data, combined with the microwave background, Dark Energy Survey lensing and supernovae, and found both consistent with one: for a cosmological-constant expansion, the present-day deviations were $0.05\pm0.22$ for the pull on matter and $0.008\pm0.045$ for the bending of light. [Ishak et al. 2024, DESI 2024 modified gravity, §3](https://arxiv.org/abs/2411.12026v3)

## A surprising twist: crossing minus one

The DESI hint has an odd feature. Dark energy's pressure, divided by its energy density, is a number $w$. A cosmological constant has w exactly minus one. The DESI fits prefer w a little above minus one today and below minus one before redshift about 0.4. In the simplest theories, a single smooth field cannot cross that line without its fluctuations becoming unstable: small ripples would grow without limit. Vikman showed this in 2005. [Vikman 2005](https://arxiv.org/abs/astro-ph/0407107)

A scalar field that couples to gravity in a particular way, called braiding, can cross the line safely. [Deffayet, Pujolàs, Sawicki and Vikman 2010](https://arxiv.org/abs/1008.0048) So if the crossing is real, it already hints at modified gravity. That is one reason the DESI collaboration fitted modified gravity on the evolving background and reported a preference for nonzero braiding, while noting that systematic effects in the data could also produce it.

## Where it stands

No measurement so far demands modified gravity. Growth and lensing agree with Einstein's theory within their current precision, and the significance of the dark-energy hint depends on which data are combined. What has changed is that surveys now have the precision to run the test seriously. Euclid, the Rubin Observatory and later DESI releases will measure growth and lensing over the same redshifts where the expansion seems to change.

The next chapters build the test step by step: first the distances, then the growth and lensing, then the conditions a modified theory must meet to be stable.

## Sources

1. [DESI DR2 BAO results, 2025, §VII.1](https://arxiv.org/html/2503.14738v3)
2. [Weinberg and White, PDG Review of Particle Physics 2025, §28.2.2](https://pdg.lbl.gov/2025/reviews/rpp2025-rev-dark-energy.pdf)
3. [Ishak et al. 2024, DESI 2024 modified gravity, §3](https://arxiv.org/abs/2411.12026v3)
4. [Vikman 2005](https://arxiv.org/abs/astro-ph/0407107)
5. [Deffayet, Pujolàs, Sawicki and Vikman 2010](https://arxiv.org/abs/1008.0048)

Choose Same expansion, stronger pull and compare the distance and growth charts. [Open the Lab](https://sandboxphysics.com/labs/dark-energy-modified-gravity/)

## Keep reading

Dark energy or modified gravity · Reading path

### Distances, growth, lensing and stability

1. [You are here **Can the same expansion come with different gravity?**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/same-expansion-different-gravity/)
2. [Article **How distances record the expansion**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/how-distances-record-expansion/)
3. [Article **How growth and lensing feel gravity**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/how-growth-and-lensing-feel-gravity/)
4. [Article **Modified gravity in four functions, and when it is stable**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/modified-gravity-in-four-functions-and-stability/)
5. [Article **Recompute the expansion and growth grid**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/recompute-a-background-growth-grid/)
6. [Article **Reading the DESI 2024 modified-gravity paper**](https://sandboxphysics.com/stories/dark-energy-or-modified-gravity/reading-desi-2024-modified-gravity/)