Cosmological test of an extended quintessence model

We investigate the cosmological observational test of the extended quintessence model, i. e. , a scalar-tensor gravity model with a scalar field potential serving as dark energy, by using the Planck 2018 cosmic microwave background (CMB) data, together with the baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider the model with a Brans-Dicke kinetic term () ;^; and a quadratic scalar potential V () =A+B (-₀) +C2 (-₀) ^2, which reduces to general relativity (GR) in the limit (), and the cosmological constant in the limit B=C=0. In such a model, the scalar field typically rolls down the potential and oscillates around the minimum of V (). We find that the model parameter estimate for the CMB+BAO+RSD data set is given by lg=-3. 6-₀. ₅₄^+0. 66 (68%) is defined in Eq. (3), corresponding to 3. 810^5<₀<9. 510^7 (68%) and lgC=4. 91. 4 (68%). However, the GR model can fit the data almost as good as this extended quintessence model and is favored by the Akaike information criterion. The variation of the gravitational constant since the epoch of Recombination is constrained to be 0. 97<Gₑ₄₂/G₀<1. 03 (1). In light of a recent report that the CMB data favor a closed universe, we consider the case with nonflat geometry in our fit and find that the mean value of ₊ shifts a little bit from -0. 049 to -0. 036, and the parameters in our model are not degenerate with ₊.