Research

(Note that this page is still under construction.)

The members of the Centre currently work on the following three broad areas of research:

• String theory
• Classical and quantum gravity
• Cosmology
• Gravitational waves

In the context of string theory, ..... In the context of classical and quantum gravity, the group has been investigating the physics of black holes and possible quantum gravitational corrections to standard results in quantum field theory. In cosmology, members of the group have been working towards understanding the physics of the early universe and exploring alternatives to the standard paradigms. We have also been comparing models of the early universe with the cosmological data. In the context of gravitational waves, the group has gathered considerable expertise on gravitational waves emitted by coalescing compact binaries observed by gravitational wave detectors such as advanced LIGO. Moreover, members of the group have been developing efficient codes to arrive at constraints on parameters describing theories of gravitation and cosmology using the advanced LIGO data.

A proposal for a Centre for Strings, Gravitation and Cosmology:

• PART A: PROJECT DESCRIPTION

1. Introduction

• The century of gravitation

Amongst the four forces of nature (viz. gravitation, electromagnetism, weak and strong), while gravitation and electromagnetism have a long range, the weak and the strong forces operate over considerably shorter distances. The theoretical frameworks used to describe these interactions prominently involve the three fundamental constants of nature: Newton’s gravitational constant G, the speed of light c and Planck’s constant ~ (in this context, see figure 1). Due to their long range, the influences of gravitation and electromagnetism have been known — through phenomena such as falling apples, rubbed combs lifting pieces of paper or magnets attracting each other — for more than two millennia. However, they were described by concrete mathematical theories only in the seventeenth and the nineteenth centuries. In the early part of the twentieth century, the realization that Maxwell’s theory of electromagnetism is inconsistent with the laws of Galilean and Newtonian dynamics led to the formulation of special relativity by Einstein. The next natural step was to reconsider the non-relativistic law of Newtonian gravitation and arrive at a relativistic formulation of the gravitational force. This effort led to insights far beyond a simple relativistic extension of the law of the gravitational force. It brought to the fore the notion of spacetime as a dynamical entity, with gravitation emerging as a manifestation of spacetime geometry rather than as a force. The first and simplest description of this manifestation is the theory of general relativity, which was conceived single-handedly by Einstein a decade after he had formulated special relativity.



The fact that gravitation and electromagnetism operate over a long range implies that there exist domains where these theories can be described classically. While it was the results from a variety of experiments that led to the development of the theory of electromagnetism, as we mentioned, the general theory of relativity was proposed primarily due to the motivation to bring gravitation within the ambit of relativity. But another major development of the twentieth century, viz. the formulation of quantum mechanics, clearly established that nature is fundamentally quantum mechanical. Nowhere is this more evident than in the characterization of the weak and the strong forces — descriptions which must be inherently quantum since these forces operate over small scales where the quantum effects dominate. Therefore, for a complete characterization of the physical interactions, one must also describe electro-magnetism and gravitation in a quantum framework. As a first step in the process, a quantum theory of electromagnetism was constructed and the lessons learnt from these exercises were applied to understand the weak and the strong forces. These efforts have since led to a unified quantum field theory of the weak and the electromagnetic forces. Though there exist aspects of the strong force that remain to be understood satisfactorily, it would be fair to say that we have a reasonable working knowledge of the strong force. These developments took place during the the latter half of the twentieth century.

As we mentioned, it is the classical relativistic theory of gravitation that is expected to play a pivotal role at the largest scales comparable to the size of the universe. At the smallest lengths — much smaller than those over which the weak and the strong forces operate — it is the quantum theory of gravitation that is expected to become important (see the regions highlighted in figure 1). However, despite half a century of effort, the approaches that have helped us understand the quantum nature of the electro-magnetic, weak and strong forces, have not proved adequate to allow us to construct a viable quantum theory of gravitation. In such a situation, there have been two approaches adopted in the literature which we can broadly refer to as the top-down and the bottom-up approaches. Without a doubt, string theory constitutes the most popular bottom-up approach. It attempts to construct a fundamental description of all interactions in terms of the dynamics of extended objects called strings. In the top-down approach, one essentially attempts to reconstruct an effective description of spacetime, guided by some very generic results that arise when one combines the basic principles of general relativity and quantum field theory. Such an approach is independent of any specific framework of a quantum theory of gravitation, and it is expected to serve as a bridge between any such framework and the large scale, classical description of spacetime. One can then explore observational and experimental implications of such an effective description. With the recent discovery of gravitational waves from merging binary black holes, the classical theory of gravitation is being probed to increasingly higher precision and greater strengths. It is also being simultaneously tested on the largest scales through observations of the distribution of matter in the universe. With improved observational techniques, it is expected that we would be able to probe the very early universe through the imprints of primary as well as secondary gravitational waves. It is hoped that these observations will provide us with some clues to the quantum nature of gravitation. With a plethora of experimental results and theoretical formulations that led to a comprehensive understanding of these results, twentieth century can clearly be labeled as the century of the weak and the strong forces. One fondly hopes that the twenty-first century will see the successful development of a quantum theory of gravitation and be referred to as the century of gravitation.

• Exploring physics of the large and the small

The key theme of our proposed Centre for Strings, Gravitation and Cosmology will be to explore the fundamental laws of physics from largest scales in the universe down to the smallest of scales dominated by quantum gravity, with the aim of deriving the imprints and possible relics of a quantum spacetime that can be tested using various upcoming observational missions in cosmology and gravitational wave physics.

The members of the centre include Prof. Suresh Govindarajan (SG), Dr. Dawood Kothawala (DK), Dr. Chandra Kant Mishra (CM), Dr. Ayan Mukhopadhyay (AM) and Prof. L. Sriramkumar (LS). With expertise available on a variety of closely related topics, during the course of the next few years, we intend to investigate in detail a range of interrelated issues in classical and quantum gravity as well as cosmology. The work involved will be largely theoretical in nature supplemented by extensive nu- merical computations. Therefore, the group primarily requires financial support to maintain a regular stream of visitors and conduct an active program of schools and workshops on these topics which can aid in developing quality expertise in these areas of research.

2. State of scientific knowledge

In this section, we shall briefly outline the state of scientific knowledge and the challenges that remain in the topics that we intend to investigate.

• Probing extreme gravity and states of matter using GWs:

Since the first detection [1] the two LIGO detectors [2] have reported over 60 gravitational wave (GW) candidates and have been joined by the European detector Virgo [3] and the KAGRA (the Japanese detector) [4] forming a global network of GW detectors. While observation of gravitational waves from compact binary mergers have provided first probes into late stages of compact binary dynamics (in addition to the first direct proof that BHs exist in nature and can form a binary system) the true power of gravitational waves lie in answering questions which couldn’t possibly be answered with the use of other astronomical messengers such as light. (Probes into neutron star interiors or into the earliest epochs of the history of our universe are examples.) Moreover, there is a whole spectrum of gravitational wave sources (from compact binary mergers involving BHs ranging from sub-solar masses to millions of solar masses to signals from isolated neutron stars to supernovae to cosmological and astrophysical background of GWs). (In this context, see, for instance, the left panel of Fig. 2.)

Modelling and data analysis efforts prior to the first direct detection of GWs focused primarily on observing first such signals and hence on the simplest configurations such as mergers of binary black holes. While the simplest among possible sources, it took over three decades for signal waveforms to mature to the accuracy needed for detecting these waves. Since, the accuracy of these models would also determine the scope of investigations following the first detections [5, 6], various efforts that took place (while impressive in delivering completely new science) need to be revisited in the light of models that will eventually incorporate missing physics [7]. While existing GW detectors (such as the two LIGO detectors) undergo planned upgrades reaching their respective design sensitivities in coming years (see (right panel) Fig. 2 for the observation plans for ground based detector network), groups across conti- nents are making accelerated efforts towards constructing models by including missing physical effects. Work plan presented below outlines set of ideas ideas that would be developed and implemented over the next five years. These efforts are in line with the global modelling efforts and development of data-analysis tools by various groups across the globe.

• Physics of the early universe, constraints from cosmological data and scope:

The inflationary scenario is the leading paradigm for the generation of perturbations in the early universe. The physics of inflation involves high energies, much beyond what can conceivably be probed by particle accelerators. The inflationary epoch is usually driven with the aid of one or more scalar fields that are regularly encountered in high energy physics and string theory. Over the last two decades, increasingly precise observations of the anisotropies in the cosmic microwave background (CMB), coupled with the vast influx of data on the distribution of large scale structure, has led to stringent limits on the physics of the early universe. For instance, the most recent CMB data from Planck constrains the primordial scalar spectral index$(n\_S\; )$ and the tensor-to-scalar ratio (r) to be nS = 0.9649 0.0042 and r < 0.056, respectively [8]. In fact, the observations by Planck have also led to relatively strong bounds on primordial non-Gaussianities, limiting the values of the non-Gaussianity parameters often introduced to characerterise the primordial bispectrum to be: f local = —0.9 ± 5.1, f equil = —26 ± 47 and f ortho = —38 ± 24 [9]. However, as scalar fields are abundant in high energy physics, despite these strong bounds, a variety of inflationary models continue to remain consistent with the data. This is primarily due to the fact that the above-mentioned constraints from the CMB cover only a limited range of wave lengths over large scales or, equivalently, a small part of the inflationary potential, leaving considerable freedom on small scales. It has now been recognized that finer details of the inflationary mechanism as well as signatures on smaller scales need to be examined simultaneously in order to arrive at a limited set of viable models of inflation. In particular, it has been realized that the presence of additional fields need to be systematically accounted for before we can converge on a unique class of inflationary models. On the theoretical side, the challenge remains to embed the inflationary scenario in an ultra-violet complete quantum gravitational framework such as string theory, an issue often referred to as the swampland conjecture [10, 11, 12, 13, 14]. In this proposal, we intend to examine a variety of issues related to the inflationary scenario with the aim identifying and evaluating all possible observables simultaneously. We believe that the development of such a finer and comprehensive approach will help us arrive at the strongest possible constraints on the primordial physics.

• Gravity as a universal regulator:

Despite their spectacular successGeneral Relativity (GR) and Quantum field theory (QFT) have divergences which can not satisfactorily be addressed within their respective paradigms. It is believed that a complete framework of quantum gravity will resolve these divergences. Indeed, one of most generic implications of principle of equivalence (GR) and the uncertainty principle (QFT) is the existence of a lower bound to measurement of spacetime intervals, believed to be of the order of Planck length `0 = (G~/c3)1/2 = 10—33 cm. It has been suggested that such a length scale can act as a universal regulator for divergences in QFT and GR , with various attempts to quantify this idea at the level of effective field theory. Most such models introduce “new physics” at high energies by violating one or more of the basic principles of QFT - Lorentz invariance, locality and unitarity. This severely constrains such models. In particular, violation of Lorentz invariance is severely constrained by known observational bounds. It seems worthwhile, therefore, to study models of QFT which can incorporate the effects of gravity without violating local Lorentz invariance. The most probable assump- tion one can question, then, is that of locality [15]. Implications of such a non-locality can potentially be described in terms of `0 dependent modifications of spacetime geometry itself. Indeed, the role of quantum fluctuations in studying the small scale structure of spacetime has recently acquired interest due to its implications for the Cosmological Constant puzzle. There is also the tantalising possibility that causal structure of spacetime might be drastically altered at small scales, resulting in ultra-locality due to closing up of light cones - a phenomenon known as asymptotic silence, as well as the possibility of a euclidean regime [16, 17] in the spirit of the proposal by Hawking and Hawking & Hartle. We intend to develop a program that addresses these phenomenon by building up a framework for describing space- time geometry itself using non-local observables that inherently endow it with a fundamental length scale and hence, by a characteristic non-locality that can lead to observable effects at all scales.

• Quantum black holes: Entropy and gravitational waves:

If we measure the success of string theory as a fundamental theory of quantum gravity by the usual gold standards, then the first consistency test would be if it can reproduce the entropy of a (micro)canonical ensemble, i.e. whether it has the right degrees of freedom to account for the microstates of a black hole which is indeed a blackbody with a precise temperature and entropy in semi-classical gravity. On this frontier string theory has passed with flying colours exactly reproducing the Bekenstein-Hawking entropy of supersymmetric extremal black holes [18, 19]. At the turn of the century, more spectacular successes have been achieved by reproducing even the finite volume corrections which can be computed both macroscopically and microscopically, and these independent computations match remarkably [20, 21, 22, 23, 24, 25, 26, 27]. These developments continue to be at the center of the field helping us to test and unravel the degrees of freedom of consistent quantum gravity and also in discovering new symmetries by using powerful new methods to count them such as the mock modular forms which appeared first in Ramanujan’s notebook more than a century ago.

Despite such spectacular progress elucidating the consistency of the string theory framework, some very deep questions remain unanswered: (i) what accounts for the universality of the Bekenstein Hawk- ing entropy from microscopics (is it the analogue of an ideal gas type approximation)? (ii) can we define a simple framework (an analogue of kinetic theory) that can describe the interiors of black holes? Any development related to the second question should be able resolve the various information paradoxes encountered whenever we combine quantum and gravity together in the context of black holes [28]. The sharpest of these is the AMPS paradox which uses the subadditivity of entanglement entropy to argue that the standard assumptions particularly the validity of semi-classical approximation at the horizon of a supermassive black hole and the local equivalence principle cannot be compatible with each other [29, 30, 28]. Recently a breakthrough has been achieved in the computation of the entanglement entropy of Hawking radiation using gauge/gravity duality which reproduces the Page curve that must follow from unitarity of this process [31, 32, 33]. This still does not explain how the information of the interior is encoded in the Hawking evaporation. Needless to say, quantum black holes remain at the forefront of research is string theory.