Think about it this way: Previously, we thought that our universe was like a spherical balloon. In the new picture, it's like a balloon producing balloons, producing balloons. This is a big fractal. The Greeks were thinking about our universe as an ideal sphere, because this was the best image they had at their disposal. The 20th-century idea is a fractal, the beauty of a fractal. How many different types of these elements of fractals are there, which are irreducible to each other? The number will be exponentially large; in the simplest models, it is about 10 to the degree 10, to the degree 10, to the degree 7. It actually may be much more than that, even though nobody can see all of these universes at once.

ANDREI LINDE, a Russian-American theoretical physicist and professor of physics at Stanford University, is the father of "eternal chaotic inflation," one of the varieties of the inflationary multiverse theory, which proposes that the universe may consist of many universes with different properties. He is an inaugural winner of the $3 million Fundamental Physics Prize, awarded by the Milner Foundation. In 2002, he was awarded the Dirac Medal, along with Alan Guth of MIT and Paul Steinhardt of Princeton University. Andrei Linde's Edge Bio Page

I seem to be saying two things that contradict each other. On the one hand, we trust scientific knowledge, on the other hand, we are always ready to modify in-depth part of our conceptual structure about the world. But there is no contradiction, because the idea of a contradiction comes from what I see as the deepest misunderstanding about science: the idea that science is about certainty.                    

Introduction
by Lee Smolin 

Carlo Rovelli is a leading contributor to quantum gravity, who is also made influential proposals regarding the foundation of quantum mechanics and the nature of time. Shortly after receiving his Ph.D he did work which made him regarded as one of the three founders of the approach to quantum gravity called loop quantum gravity-the other two being Abhay Ashtekar and Lee Smolin. Over the last 25 years he has made numerous contributions to the field, the most important of which developed the spacetime approach to quantum gravity called spin foam models.These have culminated over the last five years in a series of discoveries which give strong evidence that loop quantum gravity provides a consistent and and plausible quantum theory of gravity.  

Rovelli's textbook, Quantum Gravity has been the main introduction to the field since its publication in 2004, and his research group in Marseille has been a major center for incubating and developing new talent in the field in Europe.Carlo Rovelli's approach to the foundations of quantum mechanics is called relational quantum theory, he also, with the mathematician Alain Connes, proposed a mechanism by which time could emerge from a timeless world called the thermal time hypothesis.

– Lee Smolin

CARLO ROVELLI is a theoretical physicist, working on quantum gravity and on foundations of spacetime physics. He is professor of physics at the University of the Mediterranean in Marseille, France and member of the Intitut Universitaire de France. He is the author of The First Scientist: Anaximander and His Legacy; and Quantum Gravity.

Carlo Rovelli's Edge Bio Page
Lee Smolin's Edge Bio Page

Andrei Linde had some ideas, Alan Guth had some ideas, Alex Vilenkin had some ideas.  I thought I was coming in with this radically new idea that we shouldn't think of the universe as existing on this global scale that no one observer can actually see, that it's actually important to think about what can happen in the causally connected region to one observer, what can you do in any experiment that doesn't actually conflict with the laws of physics, and require superluminal propagation, that we have to ask questions in a way that conform to the laws of physics if we want to get sensible answers.

Introduction 

by Leonard Susskind

The parable of the blind men and elephant is a perfect metaphor for the universe and for the physicists who try to grasp its larger shape: each man feels a part of the elephant and tries to visualize its overall essence: "It's a wall"; "It's a rope"; "a tree": they almost come to blows. The universe, even more than the elephant, is too big for any one perspective, and most of us are busy squabbling about some small part.

Fortunately, now and then someone comes along who is brave enough, bold enough, and with clear enough vision, to have a chance of seeing the bigger picture. Raphael Bousso is one of those few.

— Leonard Susskind

RAPHAEL BOUSSO, Professor of Physics at the University of California, Berkeley, is recognized for discovering the general relation between the curved geometry of space-time and its information content, known as the "covariant entropy bound." This allowed for a precise and general formulation of the holographic principle, which is believed to underlie the unification of quantum theory and Einstein's theory of gravity. Bousso is also one of the discoverers of the landscape of string theory, which explains the small but non-vanishing value of the cosmological constant (or "dark energy"). His work has led to a novel view of cosmology, the multiverse of string theory. 

Raphael Bousso's Edge Bio page

LEONARD SUSSKIND, Felix Bloch Professor in theoretical physics at Stanford University, whose contributions to physics include the discovery of string theory. His most recent book is The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics.

Leonard Susskind's Edge Bio page

 Infinity can violate our human intuition, which is based on finite systems, and create perplexing philosophical problems.

ANTHONY AGUIRRE holds a BS (1995) in mathematics and physics from Brown University and a PhD (2000) in astronomy from Harvard University. He is an associate professor of physics at the University of California, Santa Cruz, where he studies a variety of topics in theoretical cosmology, including the early universe and inflation, gravity physics, first stars, the intergalactic medium, galaxy formation, and black holes.

_{Excerpted from Future Science: Essays From The Cutting Edge, Edited by Max Brockman (Vintage Books, 2011)}

[ANTHONY AGUIRRE:] The question of whether the world is finite or infinite has bedeviled us for a long time. It was a classic question in ancient Indian     philosophy. Aristotle cogently argued that while infinity made sense in the “potential,” the world could not “actually” be infinite. Giordano Bruno declared the world infinite and was burned at the stake. Galileo, more circumspect, had his clever alter ego, Salviati, completely befuddle Simplicio with how paradoxical and slippery infinity is. And Immanuel Kant really threw down the gauntlet, arguing that both an infinite and a finite world were logically impossible: an infinite universe would take an infinite time to be “synthesized” and thus could never at any one time be said to be infinite—but a finite universe must somehow be embedded in a seemingly meaningless “emptiness” that is not part of the universe. Because finite and infinite spaces alike tax our conception of space, and because we, as finite creatures, clearly cannot measure or directly observe an infinite system, it might appear that the question could most conveniently be consigned to the dustheap of purely philosophical inquiries that hard-nosed scientists can safely ignore.

Yet Albert Einstein’s theories of space and time radically reformulated the questions of finite and infinite spaces and times, and the ensuing development of cosmology has brought infinity into the domain of testable physical science. For example, a uniform space can be curved like a sphere—and comprise a universe that is finite in volume without having any “edge” or empty space outside it. Even more impressive are the tricks that relativity can play concerning infinite spaces, which have come to occupy a central place in contemporary cosmology. To tell this story, I will contend in the following four sections of this essay that: