Post-Newtonian phenomenology of a massless dilaton

In this paper, we present extensively the observational consequences of massless dilaton theories at the post-Newtonian level. We extend previous work by considering a general model including a dilaton-Ricci coupling as well as a general dilaton kinetic term while using the microphysical dilaton-matter coupling model proposed in [Damour and Donoghue, PRD 2010]. We derive all the expressions needed to analyze local gravitational observations in a dilaton framework, which is useful to derive constraints on the dilaton theories. In particular, we present the equations of motion of celestial bodies (in barycentric and planetocentric reference frames), the equation of propagation of light and the evolution of proper time as measured by specific clocks. Particular care is taken in order to derive properly the observables. The resulting equations can be used to analyse a large numbers of observations: universality of free fall tests, planetary ephemerides analysis, analysis of satellites motion, Very Long Baseline Interferometry, tracking of spacecraft, gravitational redshift tests, ...Comment: 27 pages, comments welcom

Observables in theories with a varying fine structure constant

We show how two seemingly different theories with a scalar multiplicative coupling to electrodynamics are actually two equivalent parametrisations of the same theory: despite some differences in the interpretation of some phenemenological aspects of the parametrisations, they lead to the same physical observables. This is illustrated on the interpretation of observations of the Cosmic Microwave Background.Comment: 14 pages, matched published versio

Breaking of the equivalence principle in the electromagnetic sector and its cosmological signatures

This paper proposes a systematic study of cosmological signatures of modifications of gravity via the presence of a scalar field with a multiplicative coupling to the electromagnetic Lagrangian. We show that, in this framework, variations of the fine structure constant, violations of the distance duality relation, evolution of the cosmic microwave background (CMB) temperature and CMB distortions are intimately and unequivocally linked. This enables one to put very stringent constraints on possible violations of the distance duality relation, on the evolution of the CMB temperature and on admissible CMB distortions using current constraints on the fine structure constant. Alternatively, this offers interesting possibilities to test a wide range of theories of gravity by analysing several datasets concurrently. We discuss results obtained using current data as well as some forecasts for future data sets such as those coming from EUCLID or the SKA.Comment: 14 pages, 4 figures, matched published version. Note: title changed upon suggestion of PRD editor

Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order

Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. In particular, it is important to describe properly light propagation through the Solar System. For two decades, several modeling efforts based on the solution of the null geodesic equations have been proposed but they are mainly valid only for the first order Post-Newtonian approximation. However, with the increasing precision of ongoing space missions as Gaia, GAME, BepiColombo, JUNO or JUICE, we know that some corrections up to the second order have to be taken into account for future experiments. We present a procedure to compute the relativistic coordinate time delay, Doppler and astrometric observables avoiding the integration of the null geodesic equation. This is possible using the Time Transfer Function formalism, a powerful tool providing key quantities such as the time of flight of a light signal between two point-events and the tangent vector to its null-geodesic. Indeed we show how to compute the Time Transfer Functions and their derivatives (and thus range, Doppler and astrometric observables) up to the second post-Minkowskian order. We express these quantities as quadratures of some functions that depend only on the metric and its derivatives evaluated along a Minkowskian straight line. This method is particularly well adapted for numerical estimations. As an illustration, we provide explicit expressions in static and spherically symmetric space-time up to second post-Minkowskian order. Then we give the order of magnitude of these corrections for the range/Doppler on the BepiColombo mission and for astrometry in a GAME-like observation.Comment: 22 pages, 5 figures, accepted in Phys. Rev.

Frequency shift up to the 2-PM approximation

A lot of fundamental tests of gravitational theories rely on highly precise measurements of the travel time and/or the frequency shift of electromagnetic signals propagating through the gravitational field of the Solar System. In practically all of the previous studies, the explicit expressions of such travel times and frequency shifts as predicted by various metric theories of gravity are derived from an integration of the null geodesic differential equations. However, the solution of the geodesic equations requires heavy calculations when one has to take into account the presence of mass multipoles in the gravitational field or the tidal effects due to the planetary motions, and the calculations become quite complicated in the post-post-Minkowskian approximation. This difficult task can be avoided using the time transfer function's formalism. We present here our last advances in the formulation of the one-way frequency shift using this formalism up to the post-post-Minkowskian approximation.Comment: 4 pages, submitted to proceedings of SF2

Light propagation in the field of a moving axisymmetric body: theory and application to JUNO

Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the Time Transfer Function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral easily computable numerically. We also provide the derivatives of the Time Transfer Function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the JUNO mission in the Jovian system.Comment: 17 pages, 4 figures, submitted to Phys. Rev. D, some corrections after revie