New Field of Galileon Cosmology Shows Acceleration

October 2012

The biggest mystery in modern cosmology is to understand why the expansion rate of the universe is accelerating. The 2011 Nobel Prize in Physics was awarded for the discovery of the acceleration, which commenced in a cosmic jerk five billion years ago.

The standard explanation for the acceleration is that it’s due to a cosmological constant, as Einstein put it, or, in a modern interpretation, to dark energy. If correct, this idea means that the universe is filled with a component of energy. This is philosophically unsettling for theorists because it would then account for nearly three-quarters of the energy budget of the universe.

HandoutConcordance cosmology, with its baryonic matter, cold dark matter, and dark energy, gives a precision fit of the data to models, but in truth the theoretical underpinning can be regarded as quite poor. That’s because current theory is silent on the nature of dark matter, and it does not explain the origin of the early inflation or the later acceleration.

Physicists who demand beauty and elegance in their equations are perplexed that we apparently know so little about so much of the universe. It’s a puzzle so baffling that it calls into question the validity of general relativity (GR) over cosmological distances. GR has been tested to destruction in the laboratory and the solar system, and it has survived unscathed from every challenge for nearly a century. But now the dark-energy skeptics are exploring ways of modifying the action of gravity at large distances, in order to avoid the presence of dark energy.


It’s misleading to think that modifying gravity is a bright way to find solutions to dark problems. There are many ways of deviating from Einstein’s path, most of which lead nowhere because they fail to account for the observations, but there are exceptions. One of these alternative routes through the forest is scalar-tensor theory, which has been around for half a century. Einstein’s GR is a geometrical theory of space-time that uses a metric tensor field as its fundamental building block. In scalar-tensor theories, a scalar field is added and it is coupled to the tensor field. This leads to a whole new playground for theorists.

Galileon cosmology is now on a solid footing, just three years after being launched.

One type of scalar field, now named the “galileon,” is creating a buzz among theorists. It brings an extra degree of freedom to cosmological equations. Researchers are busy exploring the consequences, and papers on galileon cosmology are getting a lot of attention. That’s because the galileon scalar field permits models of the universe in which a cosmic jerk kicks in naturally, avoiding the need for a severe shock delivered by dark energy.

An analysis using Thomson Reuters Web of Knowledge allows an assessment of the impact being made by the galileon approach. No papers on galileon cosmology existed before 2009, when just five appeared. In 2010 the count leapt to 18, and then bounded to 48 in 2011. The number of citations to the 92 papers in the sample was 20 in 2009, 180 in 2010, and an impressive 925 in 2011. In 2012, the rising trend of papers published and citations earned has continued unabated.


The term apoptosis in literatureA selection of eight of the most highly cited papers on modifying gravity with the galileon (Table 1) gives glimpses of where the action is in this new field. Paper #1, the first to describe the galileon and the first to show that “self-accelerating” solutions exist, has earned 182 citations, which elevates it to the top of the citation rankings. In this hot paper Alberto Nicolis (Columbia University, New York), Riccardo Rattazzi (Institute of Theoretical Physics, Lausanne, Switzerland) and Enrico Trincherini (Scuola Normale Superiore, Pisa, Italy) give a technical account of how to generalize scalar theories so that their modifications to gravity do not apply “locally.” Local means “at less than cosmological distances,” where GR does not require modification in order to account for observations. This paper is now widely cited by researchers who are struggling to understand dark energy.

Paper #2 provides an important foundation to those new to the field. Nathan Chow and Justin Khoury (University of Pennsylvania, Philadelphia, and the Perimeter Institute, Waterloo, Ontario) make a study of the cosmology of a galileon field theory. Their analysis sets out a host of avenues for theorists to explore. The citation count of 73 in three years shows that the paper has been notable in building a strong following for galileon cosmology.

The self-accelerating universe is center stage in #3 by Fabio Silva and Kazuya Koyama (Institute of Cosmology & Gravitation, Portsmouth, UK). Their models inflate spontaneously at late times, when the universe is already billions of years old. But at early times and on small scales (for example, the solar system) they recover classical GR. Overall their models provide surprisingly rich phenomenology, which has probably stimulated the good following (69 citations) the paper enjoys.

Inflation of a different kind is the focus of #4 by Tsutomu Kobayashi (University of Tokyo), Masahide Yamaguchi (Tokyo Institute of Technology), and Jun’ichi Yokoyama (also of University of Tokyo). Inflation in the early universe is now a part of the standard cosmology, and a scalar field known as the inflaton drives it. This highly cited paper proposes a new class of models in which the inflaton is replaced by the galileon. It’s a move that may be testable in forthcoming gravitational wave experiments.


In order to account for the origin of structure in the universe, it is inescapable that perturbations are imprinted in the cosmos soon after the Big Bang. Two papers in the selection, #5 and #7, are concerned with the evolution of structure in galileon cosmology. Both conclude that this new cosmology does not pose problems for the emergence of large-scale structure.

In #6, Antonio De Felice and Shinji Tsujikawa (Department of Physics, Tokyo University of Science) examine a solution that leads to cosmic acceleration today. They point out that a future observational study may provide some signatures for the modification of gravity from GR.


Papers #6 and #8 touch on the confrontation of galileon theory with cosmological data. Observational cosmology is now precision science thanks the data from the Wilkinson Microwave Anisotropy Probe, which invites the question: Can galileon cosmology be tested?

The field equation of state examined in #6 has some peculiar behavior, which would open up the possibility of distinguishing galileon gravity from a cold dark matter model with a cosmological constant.

Paper #8 from Amna Ali (Centre of Theoretical Physics, New Delhi, India), Radouane Gannouji (IUCCA, Pune, India) and M. Sami (also of New Delhi) employs data from supernova cosmology, baryon acoustic oscillations, and the cosmic microwave background. They used these data to constrain the parameter space of their models.

The term apoptosis in literatureTo highlight centers of activity in this emergent field, Table 2 provides a listing of institutions that are particularly active in galileon cosmology, based on representation in our sampling of papers published since 2009. Heading the list is Tokyo University of Science.

Galileon cosmology is now on a solid footing, just three years after being launched. It is a credible field of enquiry, rich in intellectual puzzles as well as mathematical challenges. Its reach is global.

Dr. Simon Mitton is Vice-President of the Royal Astronomical Society and is based at the University of Cambridge, U.K.

cosmology, Galileon cosmology, dark energy, accelerating universe, Tokyo University of Science

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