Issue of the Beginning: Initial Conditions for Cosmological Perturbations

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

Quantum mechanics meets CMB physics

by Massimo Giovannini.


Since 1991 Massimo Giovannini has extensively researched, taught and written on high-energy physics, gravitation and cosmology. He wrote over 180 papers and various review articles. He is the author of a book entitled “A primer on the physics of Cosmic Microwave Background” published in 2008.

Which is the origin of the temperature and polarization anisotropies of the Cosmic Microwave Background? Classical or quantum? The temperature and the polarization anisotropies of the Cosmic Microwave Background (CMB) are customarily explained in terms of large-scale curvature inhomogeneities. Are curvature perturbations originally classical or are they inherently quantum mechanical, as speculated many years ago by Sakharov?

In the conventional view these questions are quickly dismissed since the quantum origin of large-scale curvature fluctuations is, according to some, an indisputable fact of nature. This is true if and when Continue reading

CQG+ Insight: The problem of perturbative charged massive scalar field in the Kerr-Newman-(anti) de Sitter black hole background

Written by Dr Georgios V Kraniotis, a theoretical physicist at the University of
Ioannina in the physics department.

Solving in closed form the Klein-Gordon-Fock equation on curved black hole spacetimes

Georgios Kraniotis

Dr Georgios V Kraniotis (University of Ioannina)

A new exciting era in the exploration of spacetime
The investigation of the interaction of a scalar particle with the gravitational field is of importance in the attempts to construct quantum theories on curved spacetime backgrounds. The general relativistic form that models such interaction is the so called Klein-Gordon-Fock (KGF) wave equation named after its three independent inventors. The discovery of a Higgs-like scalar particle at CERN in conjuction with the recent spectacular observation of gravitational waves (GW) from the binary black hole mergers GW150914 and GW151226 by LIGO collaboration, adds a further impetus for probing the interaction of scalar degrees of freedom with the strong gravitational field of a black hole.

Kerr black hole perturbations and the separation of the Dirac’s equations was a central theme in the investigations of Teukolsky and Chandrasekhar [1].

All the above motivated our research recently published in CQG on the scalar charged massive field perturbations for the most general four dimensional curved spacetime background of a rotating, charged black hole, in the presence of the cosmological constant \Lambda [2].

Where interesting physics meets profound mathematics
The KGF equation is the relativistic version of the Schrödinger equation and thus is one of the fundamental equations in physics.

In our recent CQG paper, we examined Continue reading

CQG+ Insight: Scalar-tensor cosmology: inflation and invariants

Written by Piret Kuusk, Mihkel Rünkla, Margus Saal, Ott Vilson, researchers from the Institute of Physics at the University of Tartu, Estonia.

The authors in front of the building of the Institute of Physics, University of Tartu, Estonia: doctoral students Mihkel Rünkla (far left), Ott Vilson (far right), senior researcher Margus Saal (center left), head of the Laboratory of Theoretical Physics Piret Kuusk (center right).

The authors in front of the building of the Institute of Physics, University of Tartu, Estonia: doctoral students Mihkel Rünkla (far left), Ott Vilson (far right), senior researcher Margus Saal (center left), head of the Laboratory of Theoretical Physics Piret Kuusk (center right).

Working in the field of cosmology one deals casually with modified gravity. Modifications can be small or large. Sometimes a small modification of the theory could cause a large effect. It is also possible that large modifications do not affect the predictions of the theory at all. The concept of cosmological inflation can probably illustrate both of these situations somehow. Adding a short period of inflation to the evolution of early universe seems as a small modification of the theory. This modification in turn has a large effect as it solves the horizon and flatness problems. In the simplest case inflation is driven by an additional scalar field with a suitable self-interaction potential. During inflation potential dominates over the kinetic term of the scalar field giving rise to a slow roll. Dealing with slow-roll inflation can illustrate the second aforementioned situation: slow-roll can be incorporated in different theoretical frameworks not affecting the universal predictions of slow-roll.

Although the predictions of slow-roll inflation are in some sense universal, the observational data can still invalidate some specific models. One can read sentences as “minimally coupled inflation is ruled out”, which invite us to consider Continue reading

Evolution of the Universe Through Soft Singularities

Vasilis Oikonomu

Dr Vasilis K. Oikonomou is a researcher in Tomsk State Pedagogical University and in the Laboratory for Theoretical Cosmology in Tomsk State University of Control Systems and Radioelectronics (TUSUR) in Tomsk Russia. His research interests are focused on inflationary and bouncing cosmology, modified gravity, supersymmetric quantum systems, mathematical physics and epistemic game theory.

Describing the correct Universe evolution is one of the challenges in modern theoretical cosmology. The vital features of a correct Universe evolution are the successful description of early and late-time acceleration and also the intermediate eras, the radiation and matter domination eras. With our recently published CQG paper entitled ‘’ Singular F(R) cosmology unifying early and late-time acceleration with matter and radiation domination era’’, the author and Prof. Sergei Odintsov provided an F(R) gravity description of all the evolution eras in an unified way.

The primordial curvature perturbations are so relevant today for current observations since these capture the information about the primordial Universe at the time inflation took place. During the Continue reading

Book Review: The Singular Universe and the Reality of Time


Julian Barbour is an independent theoretical physicist and Visiting Professor in Physics at the University of Oxford. He has specalized in the relational aspects of dynamics.

Review of “The Singular Universe and the Reality of Time” by Roberto Mangabeira Unger and Lee Smolin

The Singular Universe is effectively two separate books held together by some common ideas. Roberto Mangabeira Unger is a philosopher, social and legal theorist and politician who helped to bring about democracy in Brazil and has twice been appointed as its Minister of Strategic Affairs (in 2007 and 2015). According to Wikipedia (current entry), “his work begins from the premise that no natural social, political or economic arrangements underlie individual or social activity.” A similar spirit informs his approach to cosmology. Lee Smolin is of course well known as one of the creators of loop quantum gravity and as the author of several popular-science books. For brevity, I shall refer to the authors as RMU and LS. The book is over 500 pages in length. The first part, by RMU, is more than twice the length of LS’s and could have been shortened without loss of essential content. There is a final 20-page section detailing differences of view, which are substantial in some cases because RMU advocates a much greater break with the conventional approach to science than LS.

The two authors are agreed that a new ‘historical’ approach to cosmology is needed. For RMU, the mere fact that the universe has been shown to have a history is enough to indicate that the methods hitherto used to study the universe must be radically modified. LS argues for a new approach because of our failures to understand the history and properties of the universe as so far discovered. He points out that, Continue reading

Life-altered cosmologies

Jay Olson

Jay Olson (lecturer at Boise State University) seeks to minimize a convenient reserve of free energy.

A few assumptions regarding life and technology translate into new cosmological solutions.

For the universe as a whole, will the next several billion years be any different from the last several billion years? What kinds of things could make it different? Something like a phase transition or a big rip would definitely break up the monotony, but that kind of thing seems unlikely to happen any time soon. Barring that, we can expect cosmic acceleration to push a bit harder, galaxies to get a bit dimmer, black holes to get a bit fatter.  It’s mostly a boring, predictable, stable time for the cosmos.

Then again, there is something a little different happening now. It hardly seems worth mentioning. It takes a while for the universe to produce enough heavy elements to form earthlike planets. And then, judging by our Continue reading

The Universe is inhomogeneous. Does it matter?

Yes! The biggest problem in cosmology—the apparent acceleration of the expansion of the Universe and the nature of dark energy—has stimulated a debate about “backreaction”, namely the effect of inhomogeneities in matter and geometry on the average evolution of the Universe. Our recent paper aims to close a chapter of that debate, to encourage exciting new research in the future.

Although matter in the Universe was extremely uniform when the cosmic microwave background radiation formed, since then gravitational instability led to Continue reading

Book Review: On the topology and future stability of the universe, by Hans Ringström

Mihalis Dafermos

Mihalis Dafermos is Professor of Mathematics at Princeton University

This impressive new book is first and foremost an original and thought-provoking contribution to the study of cosmology in research monograph form, in the best tradition of the kind of deep mathematical work which has played a crucial role in the development of the subject. At the same time, the book doubles as a dependable introduction and  reference for several foundational results in the analysis of the Einstein equations and relativistic kinetic theory which are hard to find elsewhere but which form the basis of so much current (and hopefully, future!) work.

Both these roles are most welcome.

Let me first discuss what this Continue reading

Improved constraint on the primordial gravitational-wave density

Florent Robinet and Sophie Henrot-Versille

Sophie Henrot-Versillé and Florent Robinet are research associates at the Laboratoire de l’Accélérateur Linéaire d’Orsay

Many cosmological models predict the existence of a stochastic Gravitational-Wave (GW) background produced just after the universe was born. As gravitational waves do not interact with matter, their detection would give us a unique and pristine probe to study the very first instants of the Universe: when it was 50 orders of magnitude younger than its age at the epoch of the photon decoupling. Such a detection would be as important as the discovery of the Cosmological Microwave Background (CMB). CMB studies tell us what the universe looked like when it became optically thin (~300,000 years after the Big Bang). They help us to establish the standard ΛCDM model of cosmology and to understand the important role of inflation. Continue reading