Can Solar System Orbits Constrain Cosmic Acceleration?

The Universe’s expansion is usually studied through observations across enormous distances. In “Constraining Cosmic Deceleration using the Solar System,” Paridhi Jain and colleagues ask whether orbital measurements closer to home could offer an independent test. Their work is an arXiv preprint; the supplied record lists no journal publication.

The central quantity is the present-day deceleration parameter, q₀. This dimensionless number describes whether cosmic expansion is speeding up or slowing down: negative values mean acceleration, while positive values mean deceleration. Despite its name, it can describe either behavior.

The study does not measure q₀ directly. Instead, it calculates how large a particular additional acceleration could be without exceeding orbital residuals or disrupting assumed distant Solar System dynamics. Translating those limits into q₀ requires a theoretical connection between cosmic expansion and local motion.

A proposed local imprint

The authors represent the extra radial acceleration as A = K₀r, where r is distance from the Sun and K₀ controls the effect’s strength and direction. They relate this coefficient to cosmology through K₀ = −q₀H₀², where H₀ is the present expansion rate. Their adopted H₀ is 67.4 kilometers per second per megaparsec.

This is called a Hooke-type term because its magnitude grows in proportion to distance, like an ideal spring’s restoring force. Unlike a spring, however, the proposed acceleration can point inward or outward, depending on its sign.

That correspondence is conditional. Gravitationally bound systems need not respond universally to cosmic expansion. Additional fields proposed in some gravity theories could also contribute forces, or have their effects suppressed locally through mechanisms called screening. Unless such contributions are negligible or separately modeled, an orbital constraint applies to an effective radial acceleration—not uniquely to q₀.

What planetary orbits allow

For Mars and Saturn, the analysis uses perihelion precession: the gradual rotation of an orbit’s closest approach to the Sun. Established gravitational effects already produce precession. A residual is the remaining allowance after those effects have been modeled.

The researchers translate published residual sensitivities into limits on K₀ and then q₀. Their representative estimates put the magnitude of q₀ below roughly 680 million for Saturn and 850 million for Mars. These are order-of-magnitude estimates based on existing results, not a new simultaneous fit of planetary observations with the extra acceleration included.

The authors also report Monte Carlo uncertainty propagation, a numerical method that repeatedly varies uncertain inputs to examine their influence on the result. Their reported 95% upper limits are approximately 1.60 billion for Saturn and 1.88 billion for Mars. These calculations retain the broad conclusion: planetary sensitivity is around one billion, vastly above cosmological estimates of order unity.

The paper also distinguishes a previously quoted Saturn constraint on how the acceleration coefficient changes with time from a constraint on its present value. Converting the former into q₀ alone requires an additional assumption about q₀’s evolution.

Farther away is not automatically better

Because the proposed acceleration grows with distance, distant bodies initially look attractive. But observations of objects such as Sedna cover only a small fraction of their extremely long orbits. Adjusting an ordinary fitted orbit can absorb much of a weak additional effect. The paper’s simple short-observation-arc estimate for Sedna gives a limit around 160 billion at an assumed positional residual of 0.1 arcsecond—worse than the planetary estimates.

The Oort cloud, the distant comet population considered in the study, offers a different approach. Rather than precisely tracking individual orbits, the authors require the additional acceleration to remain below solar gravity or an assumed characteristic Galactic tidal acceleration. Galactic tides are differences in the Milky Way’s gravitational pull across the region.

These comparisons produce nominal limits spanning roughly 100,000 to 100 million. They are not precision measurements: they depend on the cloud’s inferred extent, population history, stellar encounters and Galactic environment. The tidal comparison is a modeling criterion, not an independently isolated cosmological signal.

What could improve

The authors propose fitting K₀ directly within planetary ephemerides—models predicting planetary positions—so correlations with asteroid masses, the Sun’s shape and other parameters are handled together. Their illustrative future scenarios suggest improved Mars and Saturn analyses could reach limits around ten million to 100 million, with dedicated Uranus or Neptune tracking potentially reaching a few million.

Those projections depend on achieving assumed measurement precision. Even then, the approach would remain far from distinguishing cosmologically relevant q₀ values. Its supported contribution is a framework for testing possible local effects and exposing their assumptions, not evidence that planetary motion has detected cosmic acceleration.