Scalar-tensor gravity with scalar-matter direct coupling and its cosmological probe

Making use of the SNIa data set, Nesseris and Perivolaropoulos [Phys. Rev. D 73, 103511 (2006)] have found the gravitation constant to evolve in accordance with scalar-tensor gravity. On the other hand, Majerotto et al. [arXiv:astro-ph/0410543] and Guo et al. [Phys. Rev. D 76, 023508 (2007)] have found a definite signature of dark energy-dark matter coupling in Einstein tensor gravity background. However, the results of the above works are quite contradictory, so we cannot be sure which of these results should be accepted because both models use different background gravitation. We construct a more inclusive model with scalar-background space-time and scalar-matter couplings. Making use of SNIa(Union) and baryon acoustic oscillation data sets, we made likelihood analyses; the results show that the background gravitation has the tensor characteristics within a confidence level of 68% and the scalar-matter coupling has a rather large positive value delta = +/- 1.01. As Guo et al. showed, however, inclusion of the cosmic microwave background (CMB) data set in the likelihood analysis significantly reduces the allowed region of the coupling compared to the case without CMB data. Therefore, the value of scalar-matter coupling in this paper could have been estimated too large and the inclusion of CMB data in the next work is expected to yield a more realistic result.