Most astronomy textbooks describe the Big Bang as the fiery beginning of everything, when the whole known universe started to expand from a tiny point of fantastically high temperature and density. But in 2010 the scientists Roger Penrose and V.G.Gurzadyan created quite a stir when they published a paper entitled “Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity.”
The WMAP data in question is data from the Wilkinson Microwave Anisotropy Probe, a satellite which has analyzed the cosmic background radiation. The cosmic background radiation is the faint microwave afterglow of the Big Bang, and its discovery in the 1960's was one of the two main pieces of evidence for the Big Bang theory, the other being the expansion of the universe. The discovery of the cosmic background radiation by Arno Penzias and Robert Wilson led to them winning the Nobel Prize in physics. The cosmic background radiation bathes the Earth from all directions of the sky in a highly uniform temperature of 3.2 degrees Kelvin.
What Penrose and Gurzadyan claimed to have detected are concentric circles in the cosmic background radiation, which they have claimed may support Penrose's highly speculative and idiosyncratic theory of a cyclical universe, called CCC, which stands for conformal cyclic cosmology. This theory does not seem to be supported by any cosmologists other than Penrose and Gurzadyan themselves, despite the claim in their paper.
The WMAP data for the cosmic background radiation is shown below, and no matter how you magnify this image, you will not be able to see any circles with your eyes. Penrose and Gurzadyan used statistical techniques that led them to see circles where the naked eye does not detect them. Their circles are “circles you may see if you tweak the data in our special way” kind of circles.
The paper by Penrose and Gurzadyan attracted attention in the popular press, and it led to a few headlines back in 2010 saying that scientists may have detected traces of something from before the Big Bang. Other very careless headline writers used the paper by Penrose and Gurzadyan to justify headlines about hints of a cyclical universe or hints of a universe existing before our universe. But this uproar was a gigantic case of a false alarm, a classic case of runaway hype. No one has detected any evidence of all of anything occurring before the Big Bang, nor have they detected anything supporting the idea of a cyclical universe.
Other scientists tried to replicate the findings of Penrose and Gurzadyan, and ended up debunking their findings. There was this scientific paper by Wehus and Eriksen which examined the same data, and found no evidence of anomalies other than what would be produced by chance. Then there was this scientific paper by Moss, Scott, and Zibin which also debunked the findings of Penrose and Gurzadyan. Then there was this scientific paper by Hajian which also found that the alleged circles are not anomalous.
The link here gives a Nature article on the controversy, which is entitled “No evidence of time Before Big Bang: Latest research deflates the idea that the Universe cycles for eternity.”
Apparently there may be some way to statistically torture the WMAP data to get something weakly resembling concentric circles, but it is nothing different from what one would be expected to get from a random data set. It's a little like the fact that hundreds of digits deep into a printout of the digits of pi (the ratio between the circumference and diameter of a circle) we find 7777 followed about 80 digits later by another 7777. But nonrandom as it may seem, this type of thing is exactly what one might expect to find in a set of random digits of the same length.
If we did find evidence of circles in the cosmic background radiation, which were hard to explain by chance, it would not be evidence of some cosmic cycle existing before the Big Bang. It would merely be another unexplained mystery about the Big Bang. We already have lots of those, such as the mystery of what caused the Big Bang. In fact, it can be said rather firmly that there is nothing we could detect in the cosmic background radiation that would be evidence of a previous cycle of a cyclical universe. If there had been any activity or previous cycle before the Big Bang, all trace of it would have been entirely wiped out by the unimaginable heat and density of the Big Bang, far more certainly than a 100 megaton H-bomb would wipe out any trace of a building if that building is at ground zero. This point has been made by numerous scientists such as Robert Jastrow, who pointed out that even if there had been some history of the universe before the Big Bang, it would have been entirely wiped out by the Big Bang.
We have not one particle of evidence of any natural events or processes or history existing prior to the Big Bang. And it is extremely unlikely that we ever will have any such evidence. Like it or not, the Big Bang is a locked door. We are forever barred from tracing back any history of our universe prior to this event.
As for the notion of a cyclical universe, it is on life-support ever since the discovery that the expansion of the universe is accelerating. The one cyclical theory of the universe which seemed halfway plausible was the theory of an oscillating universe. This theory held that the current expansion of the universe would slow down because of gravitational contraction, and that the universe's expansion would be followed by an equally lengthy period of contraction, ending in a “big crunch” in which the universe became incredibly dense and hot as it was at the time of the Big Bang. The theory of an oscillating universe held that there were an infinite number of cycles consisting of a Big Bang, a period of expansion, a period of contraction, and a Big Crunch. However, the theory was ruled out when scientists discovered in the 1990's that the universe's expansion is accelerating, meaning the universe will continue expanding forever, never to contract down to a hot and dense state. No other cyclical theory of the universe has gained wide acceptance. Like it or not, the finding that the universe is accelerating suggests with almost final certainty that our universe has only one cycle, consisting of a Big Bang followed by endless expansion.