So to conclude, in this session we have seen how for centuries cosmology was regarded as a branch of philosophy rather than a science. In the 18th century the Kant-Leplace Nebular hypothesis was one of the very first attempts at a scientific explanation of the origin of our universe. Cosmology faces three distinct methodological problems as a science. First, whether our current laws apply to the origin of our universe. Second, the uniqueness of its subject of study, and third, the unobservability of large portions of our universe. But although we can't see all of the universe, we've seen enough of it by now to know it is very uniform in its large scale properties. This is possible because of the general red shifting of galaxies, first measured by Slipher, from about 1913. And via Hubble's law, those red shifts increase with distance, so we're able to make three dimensional maps of the universe in this way. But theory played an important part in the establishment of the expanding universe. In 1917, Einstein had introduced into his theory of gravity the idea of the cosmological constant; something that today we call dark energy equivalent to the density of empty space, and, how this can produce an accelerating expansion. Very quickly De Sitter, produced the first expanding model of the universe in which Hubble's law was predicted. And in fact many astronomers, try to find this prediction. But the full understanding of the expanding universe, came only in 1922, with a Soviet cosmologist Friedmann. He solved Einstein's equations in their general form containing both dark energy, ordinary matter and radiation. The conclusion he reached was an astonishing one, that such expanding universes couldn't have lived forever, they must have emerged from a finite time in the past from a state of infinite density, what we call a singularity, or today the Big Bang. But as we know today, the matter in the universe is predominantly dark, so we have dark matter and dark energy. Two very similar sounding names, but they're very different in practice. The dark energy is uniformly distributed throughout space, and it causes expansion of the universe to accelerate. But dark matter, in contrast, can clump under gravity, and it makes the structures in the universe around us, indeed of which we're part. In the next lectures, we'll be talking about these topic in more detail. We believe in the general correctness of Friedmann's ideas about an expanding universe because they can be observed. The early universe was a very small place. Small means dense, and therefore, extremely hot. At these temperatures, ordinary matter can't exist. Only when the universe is expanded and cooled, can protons and electrons come together, and make ordinary atoms. From this time onwards, radiation can travel freely, so we can actually look back to this time, the formation of the first atoms. And the radiation coming from this time is visible to us, this is cosmic microwave background. So since about the 1960s, we've had a very successful picture for the evolution of the universe that allows us to understand what happened during the last, say, 10 billion years or so. But it leaves many open unanswered questions. That the universe began with the Big Bang, what happened beforehand? Why did the universe start expanding? And most particularly, why when it expanded, did it contain small fluctuations in density, that subsequently collapsed into the astronomical structures that we now inhabit? Possible ways of overcoming the problem with laws of nature are either by assuming a different philosophical view of what laws of nature are or by hypothesizing that rules of nature change over time and evolve with our universe. Despite there being only one object under study, our universe, cosmology is amenable to Popper's method of falsification. For example the discovery of cosmic microwave background falsified the hypothesis of the steady state universe. The restriction of observability to the past light-cone of events means that there may well be many observationally indistinguishable spacetimes, and an inductive inference from the available data to the natural spacetime we live in, is unwarranted. In the next lecture, we'll discuss in more detail the nature of dark matter and dark energy. Particularly in the context of the broader philosophical debate about the rationality of theory choice, and the challenge posed by what philosophers of science call the problem of the underdetermination of theory by evidence. We go back to Thomas Kuhn's view and explore its implication for the rationality of theory choice, and we also look at some rival cosmological theories that don't resort to dark matter and dark energy. So we very much look forward to seeing you all in the next class. Thank you.