By Parampreet Singh, Louisiana State University, USA
A successful union of Einstein’s general relativity and quantum theory is one of the most fundamental problems of theoretical physics. Though a final theory of quantum gravity is not yet available, its lessons and techniques can already be used to understand quantization of various spacetimes. Of these, cosmological spacetimes are of special interest. They provide a simpler yet a non-trivial and a highly rich setting to explore detailed implications of quantum gravitational theories. Various conceptual and technical difficulties encountered in understanding quantum dynamics of spacetime in quantum gravity can be bypassed in such a setting. Further, valuable lessons can be learned for the quantization of more general spacetimes.
In the last decade, progress in loop quantum gravity has provided avenues which allow us to reliably answer various interesting questions about the quantum dynamics of spacetime in the cosmological setting. Quantum gravitational dynamics of cosmological spacetimes obtained using techniques of loop quantum gravity leads to a novel picture where singularities of Einstein’s theory of general relativity are overcome and a new window opens to test loop quantum gravity effects through astronomical observations.
The scope of the Focus Issue: Applications of loop quantum gravity to cosmology, published last year in CQG, is to provide a snapshot of some of the rigorous and novel results on this research frontier in the cosmological setting.
By Steven Carlip and Samuel Loomis
Imagine you are given a bucket of points and asked to assemble them into a spacetime. What kind of “glue” would you need?
In causal set theory, the only added ingredient is the set of causal relations, the knowledge of which points are to the past and future of which. In particular, suppose your points were taken at random from a real spacetime, at some typical length scale ℓ. Then on scales large compared to ℓ, the causal diamonds – the sets formed by intersecting the past of one point with the future of another – determine the topology; the causal relations determine the metric up to a scale factor; and the remaining scale factor is just a local volume, which can be obtained by counting points. As the slogan of Rafael Sorkin, the founder of the field, goes, “Order + Number = Geometry.”
Samuel Loomis and Steven Carlip with their causal set.
From quantum gravity to early universe cosmology using group field theory condensates
By Marco de Cesare, Daniele Oriti, Andreas Pithis, and Mairi Sakellariadou
“If you can look into the seeds of spacetime,
And say which grain will grow and which will not,
Speak then to me.”
– adapted quote from William Shakespeare’s, Macbeth
When we try to describe the earliest stages of the expansion of our Universe, the current picture of spacetime and its geometry as given by Einstein’s theory of General Relativity (GR) breaks down due to the extreme physical conditions faced at the Big Bang. More specifically, theorems by Hawking and Penrose imply that the cosmos emerged from a spacetime singularity. The existence of a cosmological singularity represents a main obstacle in obtaining a complete and consistent picture of cosmic evolution. However, there are reasons to believe that quantum gravitational effects taking place at the smallest scale could lead to a resolution of such singularities. This would have a huge impact for our understanding of gravity at a microscopic level, and for Cosmology of the very early Universe.
Marco de Cesare is a PhD student at King’s College London, working under the supervision of Mairi Sakellariadou on the cosmological consequences of quantum gravity.
Andreas Pithis is a PhD student at King’s College London, UK. He is a frequent visitor of the MPI for Gravitational Physics and held a visiting graduate fellowship at Perimeter Institute for Theoretical Physics, Canada.
Mairi Sakellariadou is a professor of theoretical physics at King’s College London and a member of the LIGO Scientific Collaboration. She is also Chair of the Gravitational Physics Division of the European Physical Society.
Daniele Oriti is a senior researcher and group leader at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam.
By Javier Olmedo, Sahil Saini and Parampreet Singh
Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.
Dr. Javier Olmedo is a postdoctoral researcher at Pennsylvania State University
Sahil Saini is a graduate student at Louisiana State University
Dr. Parampreet Singh is an associate professor at Louisiana Stare University
Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric. If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes. Continue reading
by Joseph Samuel.
Cricketing nations have a very good idea what a boundary is, it’s good for a cool four runs, without the bother of running! Corners are tense moments in a football (soccer to some) match when a well struck ball can curve into the goal. The crease is what a batsman lunges for when the wicket keeper ….. wait! this is not a sports column, but CQG+! Let’s back up and explain what our paper really is about.
In a path integral approach to quantum gravity, one has to divide up spacetime into pieces and focus on the action within each piece. In the elementary case of particle mechanics, this “skeletonisation” converts the action expressed as a Riemann integral into a discrete sum. A desirable property of the action is that it should be additive when we glue the pieces back together. This is achieved only when one properly takes into account the boundaries of the pieces. The boundaries can be spacelike, timelike or null. Much work has focused on the first two cases. The Einstein–Hilbert Action principle for spacetime regions with null boundaries has only recently attracted attention (look up the Arxiv for papers by E. Poisson et al and Parattu et al; references would not be consistent with the chatty, informal style of CQG+). These papers deal with the appropriate boundary terms that appear in all boundary signatures.
by J. Brian Pitts.
J. Brian Pitts is a Senior Research Associate, Faculty of Philosophy, University of Cambridge.
Observables and the Problem of Time
Mixing gravity and quantum mechanics is hard. Many approaches start with a classical theory and apply the magic of quantization, so it is important to have the classical theory sorted out well first. But the “problem of time” in Hamiltonian General Relativity looms: change seems missing in the canonical formulation.
Are Hamiltonian and Lagrangian forms of a theory equivalent? It’s not so obvious for Maxwell’s electromagnetism or Einstein’s GR, for which the Legendre transformation from the Lagrangian to the Hamiltonian doesn’t exist. It was necessary to reinvent the Hamiltonian formalism: constrained Hamiltonian dynamics. Rosenfeld’s 1930 work was forgotten until after Dirac and (independently) Bergmann’s Syracuse group had reinvented the subject by 1950. Recently a commentary and translation were published by Salisbury and Sundermeyer.
As canonical quantum gravity grew in the 1950s, it seemed less crucial for Continue reading
by Abhay Ashtekar and Brajesh Gupt.
Abhay Ashtekar holds the Eberly Chair in Physics and the Director of the Institute for Gravitation and the Cosmos at the Pennsylvania State University. Currently, he is a Visiting Professor at the CNRS Centre de Physique Théorique at Aix-Marseille Université.
Although our universe has an interesting and intricate large-scale structure now, observations show that it was extraordinarily simple at the surface of last scattering. From a theoretical perspective, this simplicity is surprising. Is there a principle to weed out the plethora of initial conditions which would have led to a much more complicated behavior also at early times?
In the late 1970s Penrose proposed such a principle through his Weyl curvature hypothesis (WCH) [1,2]: in spite of the strong curvature singularity, Big Bang is very special in that the Weyl curvature vanishes there. This hypothesis is attractive especially because it is purely geometric and completely general; it is not tied to a specific early universe scenario such as inflation.
However, the WCH is tied to general relativity and its Big Bang where classical physics comes to an abrupt halt. It is generally believed that quantum gravity effects would intervene and resolve the big bang singularity. The question then is Continue reading
One of the authors, Ian Jubb, discussing a pair of trousers with his colleagues at Imperial College London. Ian Jubb is currently the PhD student of Fay Dowker in the Theoretical Physics group at Imperial College London.
by Ian Jubb and Michel Buck.
Did you know that Quantum Gravity literally sets pants on fire?
Your pants are not just a nifty garment, they are also a perfect example of a space undergoing a process known as topology change. Take a space that initially consists of two separate circles. If they were to meet and merge into a single circle, the topology of the space would have changed. The trousers allow us to visualise each stage of this process, with cross sections higher up the trouser leg corresponding to later times in the process (if we hold the trousers upside-down, we get the reverse process, corresponding to a single circle splitting into two circles). Instead of viewing this process as the space changing in time, Einstein would tell us to view the trousers in their entirety, as one whole spacetime — the trousers spacetime.
But why should we care about spaces that can ‘split’ and ’attach’ like this? It turns out that there are good reasons to believe that Continue reading
by Parampreet Singh.
Parampreet Singh with a young student who often asks him the most difficult and so far unanswerable questions on the resolution of singularities. Dr Parampreet Singh is Associate Professor at Department of Physics and Astronomy at Louisiana State University.
Einstein’s theory of classical general relativity breaks down when spacetime curvature
becomes extremely large near the singularities. To answer the fundamental questions
about the origin of our Universe or what happens at the central singularity of the black holes thus lies beyond the validity of Einstein’s theory. Our research deals with discovering the framework which guarantees resolution of singularities.
It has been long expected that quantum gravitational effects tame the classical singularities leading to insights on the above questions. A final theory of quantum gravity is not yet there but the underlying techniques can be used to understand whether quantum gravitational effects resolve cosmological and black hole singularities. Our goal is Continue reading
by Yasaman K. Yazdi and Niayesh Afshordi.
Thought experiments highlight the edge of our understanding of our theories. Sometimes, however, we can get so caught up in heated debates about the solution to a thought experiment, that we may forget that we are talking about physical objects, and that an actual experiment or observation may give the answer. In this Insight we discuss a proposed solution to the black hole information puzzle, and a possible observational signal that might confirm it.
The black hole information puzzle and a potential solution
The black hole information loss problem is a decades old problem that highlights the tensions between some of the pillars of modern theoretical physics. It has evolved from being Continue reading