The detection of a wide range of substructures such as rings, cavities, and spirals has become a common outcome of high spatial resolution imaging of protoplanetary disks, both in the near-infrared scattered light and in the thermal millimetre continuum emission. The most frequent interpretation of their origin is the presence of planetary-mass companions perturbing the gas and dust distribution in the disk (perturbers), but so far the only bona fide detection has been the two giant planets carving the disk around PDS 70. Here, we present a sample of 15 protoplanetary disks showing substructures in SPHERE scattered-light images and a homogeneous derivation of planet detection limits in these systems. To obtain mass limits we rely on different post-formation luminosity models based on distinct formation conditions, which are critical in the first million years of evolution. We also estimate the mass of these perturbers through a Hill radius prescription and a comparison to ALMA data. Assuming that one single planet carves each substructure in scattered light, we find that more massive perturbers are needed to create gaps within cavities than rings, and that we might be close to a detection in the cavities of RX J1604.3-2130A, RX J1615.3-3255, Sz Cha, HD 135344B, and HD 34282. We reach typical mass limits in these cavities of 3–10 MJup. For planets in the gaps between rings, we find that the detection limits of SPHERE high-contrast imaging are about an order of magnitude away in mass, and that the gaps of PDS 66 and HD 97048 seem to be the most promising structures for planet searches. The proposed presence of massive planets causing spiral features in HD 135344B and HD 36112 are also within SPHERE’s reach assuming hot-start models. These results suggest that the current detection limits are able to detect hot-start planets in cavities, under the assumption that they are formed by a single perturber located at the centre of the cavity. More realistic planet mass constraints would help to clarify whether this is actually the case, which might indicate that perturbers are not the only way of creating substructures.

Few statements in cosmology can be made without assuming a cosmological model within which to interpret data. Statements about cosmic acceleration are no exception to this rule, and the inferred positive volume acceleration of our Universe often quoted in the literature is valid in the context of the standard Friedmann-Lemaître-Robertson-Walker (FLRW) class of space-times.Using the Joint Light-curve Analysis (JLA) catalogue of type Ia supernovae (SNIa), we examine the fit of a class of exact scaling solutions with dynamical spatial curvature formulated in the framework of a scalar averaging scheme for relativistic inhomogeneous space-times. In these models, global volume acceleration may emerge as a result of the non-local variance between expansion rates of clusters and voids, the latter gaining volume dominance in the late-epoch Universe.We find best-fit parameters for a scaling model of backreaction that are reasonably consistent with previously found constraints from SNIa, CMB, and baryon acoustic oscillations data. The quality of fit of the scaling solutions is indistinguishable from that of the ΛCDM model and the timescape cosmology from an Akaike Information Criterion (AIC) perspective. This indicates that a broad class of models can account for the z 1 expansion history.