Search for light curve modulations among Kepler candidates: Three very low-mass transiting companionsAuthors:Lillo-Box et alAbstract:Context.Light curve modulations in the sample of Kepler planet candidates allows the disentangling of the nature of the transiting object by photometrically measuring its mass. This is possible by detecting the effects of the gravitational pull of the companion (ellipsoidal modulations) and in some cases, the photometric imprints of the Doppler effect when observing in a broad band (Doppler beaming).Aims.We aim to photometrically unveil the nature of some transiting objects showing clear light curve modulations in the phase-folded Kepler light curve.Methods.We selected a subsample among the large crop of Kepler objects of interest (KOIs) based on their chances to show detectable light curve modulations, i.e., close (a< 12 R⋆) and large (in terms of radius, according to their transit signal) candidates. We modeled their phase-folded light curves with consistent equations for the three effects, namely, reflection, ellipsoidal and beaming (known as REB modulations).Results.We provide detailed general equations for the fit of the REB modulations for the case of eccentric orbits. These equations are accurate to the photometric precisions achievable by current and forthcoming instruments and space missions. By using this mathematical apparatus, we find three close-in very low-mass companions (two of them in the brown dwarf mass domain) orbiting main-sequence stars (KOI-554, KOI-1074, and KOI-3728), and reject the planetary nature of the transiting objects (thus classifying them as false positives). In contrast, the detection of the REB modulations and transit/eclipse signal allows the measurement of their mass and radius that can provide important constraints for modeling their interiors since just a few cases of low-mass eclipsing binaries are known. Additionally, these new systems can help to constrain the similarities in the formation process of the more massive and close-in planets (hot Jupiters), brown dwarfs, and very low-mass companions.