## The cosmological constant

## and the creation of the universe.

BY THANU PADMANABHAN

There are two tantalizing mysteries about our universe, one dealing with its final fate and the other with its beginning, that have intrigued cosmologists for decades. The community has always believed these to be independent problems—but what if they are not?

The first problem has to do with the existence of something called “dark energy,” which is today accelerating the expansion of the universe and will determine its final fate. Theorists tell us that the effects of dark energy can be explained by introducing a term into Einstein’s equations of gravity called the cosmological constant. But, for this explanation to work, the cosmological constant must have a very specific—and tiny—value. In natural units, the cosmological constant is given by 1 divided by a number made of 1 followed by 123 zeros! Explaining this value is considered one of the greatest challenges faced by theoretical physics today.

The second problem relates to another crucial number that shapes our universe, and is related to the formation of structures like galaxies and groups of galaxies. We know that the early universe, while being very smooth, also contained tiny fluctuations in density that acted as seeds for all the cosmic structures we see today. These fluctuations must have a specific magnitude and shape to be consistent with present-day observations. Understanding how these tiny fluctuations were created during the earliest stages in the evolution of the universe, and explaining their magnitude and shape, is an equally fascinating mystery in cosmology.

In the conventional approaches to cosmology, these two numbers—the numerical value of the cosmological constant and the magnitude of initial perturbations—are considered unrelated. After all, one deals with the earliest phase of the universe, and the other with a very late phase, separated in cosmic time by about 14 billion years. What’s more, standard cosmology does not offer any explanation for these two numbers from fundamental principles. The conventional models of the universe are totally silent about the numerical value of the cosmological constant, or predict a totally inappropriate value. As regards the magnitude of the initial perturbations, the most popular approach is to obtain it from a class of models that describe inflation, which is a period of rapid growth in the early phase of the universe. The trouble with inflationary models is that they can be designed to produce virtually any desired result, and hence totally lack predictive power.

Why, after decades of work, have theorists still not merged gravity and quantum theory?

My recent work, done in collaboration with my daughter, Hamsa Padmanabhan, and Tomalla Fellow at ETH Zurich, Switzerland, connects both these numbers to cosmogenesis—the creation of the universe—and explains their precise numerical values. Our paper, published recently in *Physics Letters B*, demonstrates that the very existence of the cosmological constant, as well as its tiny value, can be understood as a direct consequence of the information content of cosmic spacetime.1 As a bonus, the analysis also leads to the correct value for the size and shape of the small fluctuations in the early universe.

The remarkable confluence of these fundamental constants has important implications for our understanding of the universe. In particular, it rewrites our understanding of the Big Bang, and removes the need for any period of inflation in the early phase of the universe.

The Big Bang is probably the most famous feature of standard cosmology. But it is also an undesirable one. That’s because the classical model of the universe, described by Einstein’s equations, breaks down in the conditions of the Big Bang, which include an infinite density and temperature, or what physicists call a singularity.

But what if there were no singularity? Since the 1960s, physicists have been working on describing the universe without a Big Bang by attempting to unify gravitational theory and quantum theory into something called quantum gravity. Physicists John Wheeler and Bryce deWitt were the first to apply these ideas to a hypothetical pre-geometric phase of the universe, in which notions of space and time have not yet-emerged from some as-yet unknown structure. This heralded the study of quantum cosmology, in which physicists attempted to describe the dynamics of simple toy models of the universe in a quantum language. Needless to say, several different, but related, ideas for the description of the pre-geometric phase mushroomed over the decades. The unifying theme of these models is that the classical universe arises, without any singularity, through a transition from a pre-geometric phase to one in which spacetime is described by Einstein’s equations. The main difficulty in constructing such a description is that we do not have a complete theory of quantum gravity, which would allow us to model the pre-geometric phase in detail.

The key new ingredient we have introduced, which helps to bypass this technical difficulty, is the concept of cosmic information. The idea that information should play a key role in the description of physics has gained considerable support in recent times. This notion arises in several contexts when one attempts to combine the principles of quantum theory and gravity like, for example, in the study of quantum black holes. There is also the intriguing notion of holography in some of these models, which suggests that the information content in a bulk region can be related to the information content on its boundary. But, unfortunately, the mathematical description of the information turns out to be different in different contexts, and we still have not found a unifying principle applicable in all cases. Therefore, in order to apply the notion of information to the whole universe, we have to first come up with a definition for it that is physically appropriate.

The definition of cosmic information that we used can be best illustrated with an analogy. When a piece of ice melts to form water, a transition from solid to liquid phase takes place. The actual dynamics of the phase transition can be very complex but the total number of atoms in the ice will be the same as the total number of atoms in water. This number represents the number of degrees of freedom in the system, which does not change during the phase transition. Similarly, the phase transition that led to the birth of the universe can be described by a number that links the degrees of freedom in the pre-geometric phase with those of the classical spacetime. Using this number, which we call “CosmIn,” we can connect the two phases of the universe, bypassing the complications of a complete quantum gravity model.

Spacetime should be thought of as made of microscopic degrees of freedom, just as matter is made of atoms.

CosmIn, being a physical observable number, must be finite. In fact we expect all physical quantities to be finite in the absence of singularities. In addition, we have been able to demonstrate that CosmIn will be finite only if the universe undergoes an accelerated phase of expansion at late times, exactly as we observe today. This connection not only suggests a fundamental reason for the existence of the cosmological constant, but also a means of calculating its numerical value—if we know the value of CosmIn.

The value of CosmIn in the pre-geometric or quantum gravitational phase of the universe can be determined using results repeatedly suggested by several models of quantum gravity. It turns out that the total information transferred from the quantum gravitational phase to the classical phase must be equal to a simple number: 4π, just the area of a sphere of unit radius. This is equivalent to one unit of information per unit surface area of a sphere of unit radius. Using this fact, we can relate the numerical value of the cosmological constant to the energy scale at which the universe made a transition from the quantum gravitational phase to the classical phase.

This transition energy scale, in turn, can be related to the second enigmatic feature of our universe: the magnitude of the tiny quantum fluctuations in the early universe that grew to form the galaxies and galaxy clusters that we see today. The popular procedure for calculating the size of these fluctuations is to use inflationary models of the universe, which describe the early universe as going through an enormous and rapid increase in size. But inflationary models come in all shapes and sizes and can be designed to produce any value whatsoever for this amplitude. It’s also worth nothing that the shape of the primordial fluctuations was originally obtained by Edward Robert Harrison in 1970 (and independently by Yakov B. Zeldovich) and is called the Harrison-Zeldovich spectrum. What many people fail to appreciate or emphasize is that Harrison derived his result more than a decade before inflationary models were invented!

Our model allows us to relate both the numbers—the numerical value of the cosmological constant and the size of the primordial fluctuations—to the energy scale at which the pre-geometric universe went through a phase transition and became the classical universe we all live in. Lo and behold, when we choose the appropriate energy scale, we obtain the correct observed value for both these quantities. This, in turn, leads to an algebraic relation between the cosmological constant, the amplitude of the primordial fluctuations and the value of the CosmIn. We can turn this relation around, using the observed values of the cosmological parameters, and test whether the CosmIn is indeed 4π. The theory passes the test with flying colors; we find that CosmIn, determined from observations, is equal to 4π to an accuracy of one part in 1,000.

It is incredible that a complex combination of cosmological parameters—considered unrelated to each other—should have such a simple value. The conventional approach must consider this result as a random numerical coincidence. We, on the other hand, believe it is telling us something deep and beautiful about our universe.

We believe ours is the first effort to link the numerical value of the cosmological constant to the size of the fluctuations in the early universe, and the first to obtain both these numbers from a model which has no adjustable parameters and relates them to the energy scale at which the classical universe came into being.

All of these ideas rest within the broader framework of quantum gravity, a theory that physicists still do not have even after nearly five decades of work. One of the strengths of our model is that it does not require the details of quantum gravity to be worked out. But it does provide two significant hints regarding the nature of quantum gravity and the structure of spacetime. First, it strongly suggests that spacetime should be thought of as made of microscopic degrees of freedom, just as matter is made of atoms. Second, it suggests that the correct theory of the origin of the universe is very likely to involve a phase transition from a pre-geometric phase to the classical phase.

These hints could also answer a key question: Why, after decades of work, have theorists still not merged gravity and quantum theory? We believe this can be best illustrated with another analogy. We know that fluid mechanics can be described as a self-consistent physical theory, expressed with a set of equations. If we take these equations as fundamental and apply the principles of quantum theory to them, we can discover interesting new phenomena, like, for example, the notion of phonons (discrete quanta of vibration) and their interactions. However, we can never get to the quantum structure of matter with such an approach.

We believe it is telling us something deep and beautiful about our nature.

There is evidence to suggest that the equations describing gravity are similar to the equations of fluid mechanics in this way. In other words, reinterpreting equations describing gravity by using the principles of quantum theory is analogous to applying quantum principles to the equations of fluid mechanics. We will not discover the quantum nature of spacetime this way—which, we believe, is the reason decades of effort to quantize Einstein’s theory have led to resounding failures.

What is required instead is to re-examine the nature of gravity and learn what it tells us about the microscopic structure of spacetime. Such an approach is precisely what the physicist Ludwig Boltzmann used to understand that thermal phenomena require that matter be made of discrete degrees of freedom (in other words, atoms). Boltzmann essentially said that, if something can be hot, it must contain microscopic degrees of freedom.

Spacetime, too, can possess temperature and thus can appear to be hot to certain observers. This idea came up first through the work of Jacob Bekenstein and Stephen Hawking in the specific context of black holes. Very soon afterward, in the mid-70s, work by Bill Unruh and Paul Davies showed that this is a very general feature of spacetime. If you combine Boltzmann’s paradigm with the fact that spacetime—like normal matter—can be hot, you are led to the conclusion that spacetime must possess internal degrees of freedom, like the atoms in matter. Theoretical evidence supporting this conclusion has emerged in recent years.2 This observation holds the key to understanding the micro-structure of spacetime and quickly leads to three remarkable results.

First, the evolution of a region of spacetime can be described in terms of the degrees of freedom (or, equivalently, the information content) that resides in the bulk and boundary of that region. Second, gravity becomes immune to changes in the zero level of energy. In Einstein’s theory, gravity responds to the absolute amount of energy, making the cosmological constant virtually impossible to calculate. This is not the case in a paradigm based on information content. Third, the information approach suggests that we should not think of cosmic evolution as described by a specific solution to Einstein’s equations. Instead, those equations arise in a suitable limit from a more exact set of equations describing the quantum degrees of freedom of the spacetime.3

The information approach, validated by our CosmIn model, gives us a vivid new picture of the universe as being analogous to a large chunk of ice containing a point source of heat. The heat source melts the ice around it, creating a region of water, which in turn expands, reaching local thermodynamic equilibrium. At large scales, close to the boundary of the phases, the molecules have not yet reached equilibrium, since the chunk of ice is being heated up from the inside. Incredibly enough this is similar to how our universe behaves. The region with water is analogous to the observed universe (described by Einstein’s theory). It is surrounded by a pre-geometric phase (analogous to ice) that is described by—as yet unknown—laws of quantum gravity. The notion of a Big Bang is completely eliminated, and replaced by a transition from one phase to another at the boundary. And the need for an inflationary period in the universe’s early history is also eliminated.

The entire framework is simple and elegant because it is described by a single parameter: the energy scale of the early-universe phase transition from pre-geometry to Einsteinian geometry. This is unlike standard inflationary models, which contain scores of parameters and lack any predictive power. Our model does not use any untested physics. The *only* postulate we make is that the information content of the universe should be equal to 4π, the area of a unit sphere.

The work opens up three new avenues of research: First, it invites us to explore the physics of the pre-geometric phase in different quantum gravitational models. Second, it opens the opportunity to explore the specific notion of cosmic information used in this work and attempt to relate it to other, similar ideas of information used in other contexts. Third, it reinforces the notion that spacetime is made of more elementary degrees of freedom—just as matter is made of atoms—and challenges us to study different phases of spacetime just as we explore different phases of matter in condensed matter physics.

*Thanu Padmanabhan is a distinguished professor at the Inter-University Centre for Astronomy and Astrophysics, in India. He can be contacted at This email address is being protected from spambots. You need JavaScript enabled to view it..*

**References**

1. Padmanabhan, T. & Padmanabhan, H. Cosmic information, the cosmological constant and the amplitude of primordial perturbations. *Physics Letters B* **773**, 81-85 (2017).

2. Padmanabhan, T. The atoms of spacetime and the cosmological constant. *Journal of Physics: Conference Series* **880**, 012008 (2017).

3. Padmanabhan, T. Do We Really Understand the Cosmos? *Comptes Rendus Physique* **18**, 275-291 (2017).

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