Post-Newtonian parametersγandβof scalar-tensor gravity with a general potential

Abstract

We calculate the PPN parameters γ and β for scalar-tensor gravity with a generic coupling function ω and scalar potential V in the Jordan conformal frame in the case of a static spherically symmetric source. Since the potential generally introduces a radial dependence to the effective gravitational constant as well as to γ and β, we discuss the issue of defining these PPN parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of γ and β and thus draw restrictions on the form of the functions ω and V around their asymptotic background values.

Parametrizations in scalar-tensor theories of gravity and the limit of general relativity

“…However, we saw that despite the transformation becoming singular the general relativity limit in terms of the field equations and PPN parameters, namely the first cases discussed above, does also occur in the corresponding JF BEPS value φ = 0 and EF canonical parametrization value ϕ = 0. It is interesting that in the JF BDBW parametrization this GR limit is realized by satisfying the condition (20), while in the JF BEPS and EF canonical parametrizations it comes from the conditions (18), (19). This confirms the discussion in Secs.…”

“…Among the particular forms of STG the condition (20) can be only realized in JF BDBW parametrization where it translates into 1 ω | Ψ⋆ = 0. In the JF BEPS and nonminimal, and EF canonical parametrizations the function B is fixed to a constant value which precludes (20).…”

“…Hereby we restrict our attention to the cases where A ′ and α ′ are not singular at the same value of scalar field Φ, and therefore to achieve a GR-like behaviour we do not consider this possibility. Furthermore, for the sake of mathematical simplicity we also leave aside the rather fine-tuned theories where the conditions (18), (19) and (20) are realized together, or where both the numerator and denominator of the RHS term of (17) vanish simultaneously thus requiring a much more thorough analysis. Now, given the rather different conditions (18), (19) and (20), one is entitled to ask whether there is any connection between them.…”

“…if some Φ in a certain frame and parametrization satisfies it, then the correspondingΦ in another frame and parametrization will also satisfy it. Although, it is completely feasible that Φ • obeying (18), (19) may get translated intoΦ ⋆ obeying (20).…”

“…Note that the twin condition (19) is automatically satisfied due to the PPN ansatz. The second option would be given by (20), with α ′ , α ′′ not infinite, and B ′ B 3 = 0. Comparing the latter with the discussion in the previous section we may note that the condition on B ′ to achieve the GR limit is marginally less strict in PPN than the one obtained from the equations of motion, i.e.…”