The Fourth Gravity Test and Quintessence Matter Field

TL;DR

This paper investigates the impact of quintessence matter on the radar echo delay in a gravitational field, extending previous tests and using spacecraft data to constrain the quintessence field parameters.

Contribution

It calculates the fourth gravity test considering quintessence matter and constrains the field parameters using spacecraft observational data.

Findings

Quintessence matter affects the radar echo delay.

Field parameter  is constrained to ^{-9} from Viking data.

Field parameter  is constrained to ^{-18} from Cassini data.

Abstract

After the previous work on gravitational frequency shift, light deflection (arXiv:1003.5296) and perihelion advance (arXiv:0812.2332), we calculate carefully the fourth gravity test, i.e. radar echo delay in a central gravity field surrounded by static free quintessence matter, in this paper. Through the Lagrangian method, we find the influence of the quintessence matter on the time delay of null particle is presence by means of an additional integral term. When the quintessence field vanishes, it reduces to the usual Schwarzschild case naturally. Meanwhile, we also use the data of the Viking lander from the Mars and Cassini spacecraft to Saturn to constrain the quintessence field. For the Viking case, the field parameter $\alpha$ is under the order of $10^{-9}$. However, $\alpha$ is under $10^{-18}$ for the Cassini case.