A Multiverse from Nothing
The Hartle-Hawking Process, Inflation, and the Shape of Our Universe
The universe’s origin has always been a topic of profound mystery and fascination and it’s not even clear yet whether the universe had a beginning or not. One fascinating possibility is described by the Hartle-Hawking process, also known as Hawking’s ‘no-boundary’ proposal, which suggests that the universe can emerge spontaneously from ‘nothing’. Of course, ‘nothing’ here isn’t our usual conception of emptiness. As proposed by Stephen Hawking and James Hartle (and independently by Alexander Vilenkin) in the ’80s, ‘nothing’ in this context refers to a quantum state where neither space nor time exist, but the laws of quantum mechanics do.
At the quantum level, particles can pop in and out of existence in a seemingly random fashion. Imagine a vast, silent forest where, every so often, a seed spontaneously sprouts, growing rapidly into a tree. While many of these trees might not last long, some find the right conditions to thrive and grow, becoming a permanent part of the landscape. In this analogy, the universe is like one of those trees that found the right conditions to expand and evolve.
The Hartle-Hawking proposal offers a profound perspective on the universe’s origin. Instead of envisioning the birth of the universe as a distinct ‘starting point’ or ‘moment in time’, this theory suggests that time itself might not have had a traditional beginning. Imagine a book where instead of starting on the first page, you’re already in the middle of a chapter. There’s no clear beginning; the story just is. Similarly, according to this proposal, the universe didn’t ‘start’ in the conventional sense. It exists in a state that transcends our usual understanding of time and beginnings.
In our day-to-day experience, time holds a unique position. It’s distinct from the three spatial dimensions we’re familiar with: length, width, and height. One way to understand this distinction is through the concept of entropy, which always increases with time, giving us a clear sense of past, present, and future. This forward march of time makes it special in what physicists call the ‘Minkowski signature’, from the name of the mathematician who first studied these types of mathematical spaces.
However, when physicists delve into the mysteries of the universe’s origins, they sometimes employ a mathematical technique called ‘Wick rotation’. This method transforms time so that it’s no longer this unique, forward-marching dimension. Instead, using a trick involving imaginary numbers, it becomes equivalent to the other spatial dimensions, just like length, width, and height. In this ‘Euclidean space’, time loses its special status and blends seamlessly with space. It’s as if we’re looking at a world where every direction, including time, can be navigated just like moving left or right, up or down. This approach simplifies the mathematics of the Hartle-Hawking process and provides insights into how the universe can emerge from ‘nothing’.
The concept of Euclidean space challenges our everyday understanding of cause and effect, where every event has a preceding cause. In the realm of the Hartle-Hawking proposal, the universe simply exists without needing a cause or a starting point in the traditional sense.
Now, while the Hartle-Hawking proposal addresses the nature of the universe’s origin, the theory of inflation provides insights into its early evolution. If the universe exists without a traditional beginning, as posited by Hartle and Hawking, then its early (or better, what we now consider to be the ‘early’ stage of the universe’s history) state would be crucial in determining its subsequent evolution. This is where inflation comes into play.
Inflation is the widely accepted theory that, at some point early on (according to the current estimates, roughly 14 billion years ago), the universe underwent an extremely rapid expansion. Think of it as a sudden and intense growth spurt. This rapid expansion smoothed out any initial irregularities, leading to the relatively uniform cosmos we observe today on large scales. If the universe emerged in a state that aligns with the Hartle-Hawking proposal, then the subsequent inflationary phase would be a natural progression, shaping the universe into the vast expanse we observe today.
Now, if the Hartle-Hawking proposal is correct, then the universe that emerges from ‘nothing’ would be what is called a de Sitter (dS) universe. This universe is characterized by an accelerated expansion, aligning perfectly with the inflationary scenario.
At the heart of the idea of a dS universe is the concept of cosmological constant, a value that plays a crucial role in determining the universe’s fate. This is directly related to the energy density of the vacuum of space. A positive cosmological constant leads to a dS universe, causing it to expand at an accelerating rate. Alternatively, a negative value would result in an Anti de Sitter (AdS) universe, which after expanding for a while, contracts back and collapses into a big crunch. If the constant is zero, we get a Minkowski universe, which neither undergoes an accelerated expansion nor contracts. Understanding this constant is vital, not just for grasping the universe’s shape but also for deeper questions about its origins and ultimate fate.
The Hartle-Hawking process, combined with the theory of inflation, paints a comprehensive picture of our universe’s origins and early evolution. It suggests that our vast cosmos might have originated from a tiny, quantum-sized blip and then rapidly expanded, much like a tree sprouting from a spontaneous seed in our vast forest analogy and then experiencing a growth spurt.
String Theory’s Landscape and the Evolution from a Single Universe to a Multiverse
If our universe began as a dS space as dictated by the Hartle-Hawking proposal, emerging spontaneously from ‘nothing’, it set the stage for a fascinating cosmic evolution. The rapid expansion characteristic of a dS universe aligns with the concept of eternal inflation. This is the idea that, once inflation starts, certain regions of the universe will continue to expand at an accelerated rate indefinitely, giving rise to diverse ‘bubble universes’ within the larger inflating space.
Here, string theory plays a pivotal role. String theory is a theoretical framework where the fundamental entities are not point-like particles but one-dimensional strings. These strings can vibrate at different frequencies, and different vibrations correspond to different particles. Crucially, string theory predicts a vast array of possible states or ‘vacua’ for the universe, often referred to as the string landscape. An important observation is that different vacua correspond to different laws of physics, i.e. a different value for the mass of the electron or a different value of the cosmological constant.
Each of the bubble universes, emerging from eternal inflation, can represent different points in this landscape, having distinct properties or vacua. First introduced by Sidney Coleman and Frank De Luccia, vacuum transitions describe the mechanisms that enable the universe to transition from one state or vacuum to another within the vast array of possibilities presented by the string theory landscape. In essence, if we begin with a dS universe, as suggested by the Hartle-Hawking process, various regions of this universe can undergo transitions, forming ‘bubble universes’ with varying cosmological constants, be they positive, negative, or zero.
One of the most interesting features of this multiverse of bubble universes, each representing a different point in the string landscape, is that it naturally provides a way to solve the cosmological constant problem. The cosmological constant, determining the universe’s expansion rate, has an observed value that is positive (hence we currently live in a dS universe) but puzzlingly small. However, the multiverse offers a potential solution. If there are countless universes, each with its own value of the cosmological constant, then it’s conceivable that we inhabit one of the rare universes where this constant allows for the formation of galaxies, stars, and life. This perspective is supported by the anthropic principle, which suggests that the properties of our universe are as they are because if they were any different, we wouldn’t be here to observe them.
For the string multiverse to effectively address the cosmological constant problem, it’s essential that a mechanism exists to explore every possible vacuum within the string landscape. In other words, for every possible value of the cosmological constant allowed by the string landscape, there should be a corresponding bubble universe that adopts that specific value. This highlights the significance of vacuum transitions, as they allow the shift from one vacuum state to another.
In summary, the universe’s journey from a spontaneous emergence to its place within a vast multiverse is intricately linked with the predictions of string theory. The dance of eternal inflation, vacuum transitions, and the anthropic principle, all set against the backdrop of string theory’s landscape, paints a comprehensive picture of our universe’s origins and its place in the cosmos.
Rethinking the Dynamics of the Landscape: From Forbidden Transitions to New Possibilities
In the vast landscape of possible universes predicted by string theory, understanding the transitions between different states or vacua is crucial. These transitions dictate how the universe might evolve over time and navigate through the myriad possibilities within the landscape.
Historically, based on previous calculations, there was a significant limitation: transitions from AdS universes to dS universes were considered forbidden. In this picture, AdS universes acted as ‘sinks’ within the landscape. Once a universe found itself in an AdS state, it was trapped there, unable to ‘up-tunnel’ to a dS universe like our own. This constraint had profound implications for the dynamics of the landscape, limiting the possible evolutionary paths a universe could take.
In recent research I conducted with Sebastian Cespedes (Imperial College London), Senarath de Alwis (Colorado University), and Fernando Quevedo (University of Cambridge), we’ve built upon the foundational work of Willy Fischler, Daniel Morgan, and Joe Polchinski to reevaluate a long-standing assumption in cosmology. Our findings indicate that prior conclusions, which deemed ‘up-tunnelling’ transitions from AdS to dS impossible, were influenced by a specific assumption related to the Wick rotation discussed earlier. By employing the techniques introduced by Fischler, Morgan, and Polchinski, we sidestepped this mathematical constraint. Our refined calculations suggest that transitions from AdS to dS universes are indeed possible. This discovery is pivotal. It reshapes our understanding, suggesting that AdS universes aren’t cul-de-sacs in the cosmic landscape but can evolve and transform into dS universes.
The implications of this discovery are vast. By allowing AdS to dS transitions, a wealth of new possibilities opens up for the dynamics of the landscape. Universes can navigate through the landscape in more diverse ways, potentially leading to a richer tapestry of cosmic scenarios and evolutionary paths. This breakthrough not only reshapes our understanding of the landscape’s dynamics but also offers fresh insights into the universe’s potential origins, evolution, and fate.
