We briefly review an important shortcoming—unearthed in previous works—of the standard version of the inflationary model for the emergence of the seeds of cosmic structure. We consider here some consequences emerging from a proposal inspired on ideas of Penrose and Diósi [R. Penrose, The Emperor’s New Mind. Concerning Computers, Minds and Laws of Physics (1989).][R. Penrose, in Physics meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, edited by C. Callendar and N. Huggett (2001), pp. 290-+.][L. Diósi, Phys. Lett. A 120, 377 (1987).PYLAAG0375-960110.1016/0375-9601(87)90681-5][L. Diósi, Phys. Rev. A 40, 1165 (1989).PLRAAN0556-279110.1103/PhysRevA.40.1165] about a quantum-gravity induced reduction of the wave function, which has been put forward to address the shortcomings, arguing that its effect on the inflaton field is what can lead to the emergence of the seeds of cosmic structure [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity 23, 2317 (2006).CQGRDG0264-938110.1088/0264-9381/23/7/008]. The proposal leads to a deviation of the primordial spectrum from the scale-invariant Harrison-Zel’dovich one, and consequently, to a different CMB power spectrum. We perform statistical analyses to test two quantum collapse schemes with recent data from the CMB, including the 7-yr release of WMAP and the matter power spectrum measured using LRGs by the Sloan Digital Sky Survey. Results from the statistical analyses indicate that several collapse models are compatible with CMB and LRG data, and establish constraints on the free parameters of the models. The data put no restriction on the timescale for the collapse of the scalar field modes.