In recent years, observational techniques at cosmological distances have been sufficiently improved that cosmology has become an empirical science, rather than a field for unchecked speculation. There remains the fact that its object, the whole universe, exists only once; hence, we are unable to separate “general” features from particular aspects of “our” universe. This might not be a serious drawback if we were justified in the belief that presently accepted laws of nature remain valid on the cosmological scale. In the (...) author's opinion, however, there are grounds for doubting that belief. The three arguments presented are (1) the possibility that apparent constants of nature may, during cosmological times, turn out to vary (Dirac conjecture); (2) the effective breakdown of the principle of relativity caused by the effects of the cosmological environment on local experiments; and (3) the fact that present theory leads to field singularities at the early stages of the expanding universe, which might be a signal that currently accepted theoretical concepts are inadequate for an understanding of highly condensed matter. (shrink)