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We investigate the cosmological applications of a bi-scalar modified gravitythat exhibits partial conformal invariance, which could become full conformalinvariance in the absence of the usual Einstein-Hilbert term and introducingadditionally either the Weyl derivative or properly rescaled fields. Such atheory is constructed by considering the action of a non-minimallyconformally-coupled scalar field, and adding a second scalar allowing for anonminimal derivative coupling with the Einstein tensor and the energy-momentumtensor of the first field. At a cosmological framework we obtain an effectivedark-energy sector constituted from both scalars. In the absence of an explicitmatter sector we extract analytical solutions, which for some parameter regionscorrespond to an effective matter era and/or to an effective radiation era,thus the two scalars give rise to "mimetic dark matter" or to "dark radiation"respectively. In the case where an explicit matter sector is included we obtaina cosmological evolution in agreement with observations, that is a transitionfrom matter to dark energy era, with the onset of cosmic acceleration.Furthermore, for particular parameter regions, the effective dark-energyequation of state can transit to the phantom regime at late times. Thesebehaviours reveal the capabilities of the theory, since they arise purely fromthe novel, bi-scalar construction and the involved couplings between the twofields.

Bi-scalar modified gravity and cosmology with conformal invariance