The message is that physics has an „outward bound” of scientific inquiry in the field of cosmology. I present it in the historical development. Physics and astronomy, developing since the seventeenth century, inherited from the early Greek philosophers the conception that the Universe as a whole is invariable. In nineteenth century this conception in conjunction with the conception of eternity of the Universe gave rise to contradictions with other laws of physics indicating that cosmology is not a branch of physics (...) since the notion of the Universe is not a physical one. Cosmology returned to physics as its important branch due to the advent of general relativity theory and the discovery of the cosmic microwave background radiation. Modern cosmology generates fundamental problems creating real limits to inquiries in physics viewed as an empirical science. The very notion of the Universe shows that the scientific method reaches there limits of its applicability. Does „to exist” mean „to be observed by someone”? Should the definition of the Universe be based on a current physical theory, e.g. on Einstein’s general relativity, giving rise to a kind of mathematical instability? Is the fashionable concept of the „multiverse” a physical one or is a purely metaphysical notion in a scientific disguise? If the Universe is unique, is it meaningful to describe it in the framework of physics, which by its method always assumes that the number of objects it describes, is unlimited? Apart from these permanent philosophical problems there are concrete urgent problems generated by cosmology: the nature of dark matter and dark energy. These two species of „substance” appear only in cosmology and do not fit the laboratory physics; contrary to the three centuries long tradition of modern science, now cosmology inspires physics in a troublesome way. A separate class of limits to physics is generated by the theorem in general relativity that the Universe emerged from an initial curvature singularity of the spacetime. At the singularity the whole scientific inquiry breaks down. Cosmology of the very early Universe suggests that in its evolution two specific epochs took place, that of quantum gravity and an inflationary epoch. The underlying them two physical theories are incomplete and seem to be inherently untestable. Furthermore, the experimentally verifiable physics cannot explain the origin of the initial conditions determining properties of the Universe which emerged from the singularity. (shrink)