[Paper Review] Interplanetary Measures Can Not Bound the Cosmological Constant

E. L. Wright|arXiv (Cornell University)|May 21, 1998

Astronomy and Astrophysical Research1 references3 citations

TL;DR

This paper demonstrates that planetary orbital precession due to a cosmological constant is far too small to be measured, rendering interplanetary observations ineffective for constraining the cosmological constant. Using Mercury's orbit as a test case, Wright calculates a precession effect of approximately 10^{-23}, which is many orders of magnitude below current measurement sensitivity, thus invalidating claims that such measurements could bound Λ.

ABSTRACT

The effect of a cosmological constant on the precession of the line of apsides is O(Λc^2 r^3/GM) which is 3(H_\circ P)^2/8π^2 \approx 10^{-23} for a vacuum-dominated Universe with Hubble constant H_\circ = 65 km/sec/Mpc and for the orbital period P = 88 days of Mercury. This is unmeasurably small, so planetary perturbations cannot be used to limit the cosmological constant, contrary to the suggestion by Cardona & Tejeiro (1998).

Motivation & Objective

• To evaluate whether planetary orbital precession can be used to bound the cosmological constant Λ.
• To assess the feasibility of using interplanetary measurements, such as Mercury's orbital precession, to detect or constrain Λ.
• To challenge the claim by Cardona & Tejeiro (1998) that planetary perturbations could limit the value of the cosmological constant.
• To quantify the magnitude of the cosmological constant's effect on orbital precession in a vacuum-dominated universe.

Proposed method

• The paper derives the precession rate of the line of apsides due to a cosmological constant using general relativistic perturbation theory.
• It applies the formula O(Λc²r³/GM) to estimate the precession effect for Mercury's orbit.
• The calculation uses standard cosmological parameters: Hubble constant H₀ = 65 km/s/Mpc and orbital period P = 88 days.
• The result is expressed as 3(H₀P)²/8π² to quantify the expected precession in a Λ-dominated universe.
• The derived value is compared to current observational sensitivity limits to assess measurability.
• The analysis concludes that the effect is many orders of magnitude too small to be detected with existing technology.

Experimental results

Research questions

• RQ1 Can planetary orbital precession due to the cosmological constant be measured with current interplanetary tracking techniques?
• RQ2 What is the expected magnitude of the cosmological constant's effect on Mercury's orbital precession?
• RQ3 Is the precession induced by Λ large enough to provide a meaningful bound on its value through planetary observations?
• RQ4 Does the claim by Cardona & Tejeiro (1998) that planetary perturbations can constrain Λ hold under quantitative scrutiny?
• RQ5 How does the predicted precession compare to the sensitivity limits of modern astrometric and radiometric tracking systems?

Key findings

• The cosmological constant induces a precession of the line of apsides on the order of 10^{-23} for Mercury's orbit.
• This value is derived as 3(H₀P)²/8π², with H₀ = 65 km/s/Mpc and P = 88 days.
• The precession effect is far too small to be detected with current observational technology.
• The paper concludes that interplanetary measurements cannot be used to bound the cosmological constant.
• The claim by Cardona & Tejeiro (1998) that such measurements could constrain Λ is therefore invalid.
• The result underscores the fundamental inaccessibility of Λ through solar system-scale dynamical measurements.