In the article "The Big Bang Didn't Need God to Start Universe, Researchers Say" from SPACE.COM, it refers to a conference called SETICon 2 during a discussion titled "Did the Big Bang Require a Divine Spark?" on June 23, 2012. It briefly summarizes the contention that the findings of the Standard Big Bang Model often referred to by theists arguing for the existence of a creator and comments made by panelists at the conference in reference to research done on quantum fluctuations and loop quantum gravity models.
It’s referring to two primary scientific studies that are represented in many different papers, the Standard Big Bang Model and Loop Quantum Gravity. Without going into too much detail, the summary of the studies is around the evidence of the universe being in a constant state of expansion and cosmic microwave background radiation, suggesting the universe was in a state of infinite density and violently expanded. This is the Big Bang. This standard model as many verified predictions and has a beginning of spacetime at T=0.
Hypotheses of quantum fluctuations have been proposed by Tyron in 1973 published in Nature, and others like Stenger in 1989, suggesting that fluctuations in the quantum vacuum predicted by quantum mechanics can explain the change resulting in a state of “nothingness” to the Big Bang. The article briefly summarizes quotes about quantum mechanics;
… quantum mechanics, which describes action on a subatomic scale, random fluctuations can produce matter and energy out of nothingness. And this can lead to very big things indeed, researchers say.
What the article gets right is explaining that the studies show quantum mechanics can have “random fluctuations” and “..can lead to very big things indeed” referring to the Big Bang. These physicists implying that quantum physics can indeed possibly explain this change in the state leading to the Big Bang. The reference to random fluctuations is called the Heisenberg Uncertainty Principle.
There are, however, many misleading summaries. In the same sentence it also says, “..can produce matter and energy out of nothingness”. This use of language is very imprecise and can potentially be factually inaccurate with improper assumptions.
First is this use of the word “nothingness”. When this is used by scientists, it does not mean the same thing the average person means by “nothing”. We tend to mean a universal negation of “not anything”. Scientists are referring to the quantum vacuum, which is a real physical state of energy governed by physical laws.
The second is the use of the phrase “..produce matter and energy”. Scientists are not suggesting the first law of thermodynamics is false. They are referring to this state of energy changing from the quantum vacuum. When they quote scientists about their opinion on the need of a Divine Creator, this is not a result of scientific objectivity or proper scientific method to come to this conclusion. Instead this is those scientists’ opinion based on the scientific research and their metaphysical beliefs.
For this very reason, there are no peer reviewed papers published in Scientific journals defending a hypothesis that "There is no Divine Creator". You are far more likely to find something similar in a philosophy journal such as American Philosophical Quarterly or Analytic Philosophy.