Oxford University Mathematics Professor John Lennox and MIT Physics Professor Alan Guth. 

John Lennox is Professor of Mathematics at the University of Oxford, Fellow in Mathematics and the Philosophy of Science, and Pastoral Advisor at Green Templeton College, Oxford. Lennox also teaches for the Oxford Strategic Leadership Programme at the Executive Education Centre, Said Business School, Oxford University.

Alan Guth is Victor F. Weisskopf Professor of Physics and a Margaret MacVicar Faculty Fellow at MIT. Guth is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Guth has won many awards and medals, including most recently the 2009 Isaac Newton Medal, awarded by the British Institute of Physics.

Introductory thoughts on the issues:

Stephen Hawking: Our universe and its laws appear to have a design that both is tailor-made to support us and, if we are to exist, leaves little room for alteration. That is not easily explained and raises the natural question of why it is that way…. The discovery relatively recently of the extreme fine-tuning of so many of the laws of nature could lead at least some of us back to the old idea that this grand design is the work of some grand designer…. That is not the answer of modern science…our universe seems to be one of many, each with different laws.

competing for your attention as an explanation for the origin of our universe. 

...because there is a law such as gravity, the Universe can and will create itself from nothing.

Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.

John Lennox: The idea of a theory or physical laws bringing the universe into existence strikes me as a serious misunderstanding of the nature of such laws—or am I missing something? Scientists expect to develop theories involving mathematical laws that describe natural phenomena, and have done so with spectacular success. However, the laws that we find cannot themselves even cause anything, let alone create it.

Thus we arrive at the multiverse. I am tempted to add that belief in God seems an infinitely more rational option if the alternative is to believe that every other universe that can possibly exist does exist, including one in which Richard Dawkins is the Archbishop of Canterbury, Christopher Hitchens the Pope, and Billy Graham has just been voted atheist of the year!

His call for us to choose between physics and God is as manifestly absurd as demanding that we choose either the laws of physics or aeronautical engineer Sir Frank Whittle in order to explain the jet engine. Both explanations are necessary: they do not conflict, but complement one another. 

When Newton discovered his law of gravitation he did not say, “Now I have gravity, I don’t need God.” What he did was to write Principia Mathematica, the most famous book in the history of science, expressing the hope that it would “persuade the thinking man” to believe in God.

Alan Guth: While there is no consensus, many physicists including me believe that there is meaningful evidence that the big bang that gave rise to the visible universe was not a unique event. Instead it seems likely that we live in a multiverse, in which a huge or perhaps infinite number of big bangs have occurred or will occur, widely separated in space and time. Each big bang would give rise to a "pocket universe," and our visible universe would be a small part of one pocket universe.

In the multiverse picture the underlying laws of physics are assumed to be the same everywhere. Nonetheless, we believe that these laws of physics allow a huge number of different types of vacuum --- different types of empty space --- and pocket universes filled with all types of vacuum would be produced. The type of vacuum would determine what kinds of particles could exist in each pocket universe, and how they would interact.

Most pocket universes would presumably be devoid of life, but life would form in those rare pocket universes where the particle interactions have just the right properties to make life possible.  The universes that contain life would then look like they were tailored for the existence of life, giving the illusion of intelligent design without the need for any intelligent intervention.