## Research overview

My main fields of interest are field theory, general relativity and theoretical cosmology. My research has been interdisciplinary; it has centered on aspects of black-hole physics, cosmological inflation, cosmological perturbation theory, modified gravity models, quantum gravity phenomenology and semi-classical gravity. I am interested in both building and testing new theoretical extensions to standard models.

Over the last few years, I have been interested in the following areas:

- Entanglement signatures of quantum phase transistions
- Alternate models of cosmological inflation
- Higher order cosmological perturbations
- Using cosmic microwave background as a tool to probe new physics near the scale of inflation
- Quantum entanglement as the source of black-hole entropy

### Current interests

__Entanglement signatures of quantum phase transitions__Top

Quantum Phase transitions occur when the zero-temperature quantum fluctuations in a quantum many body system cause a transition from one type of ground state to another. Such phase transistions are induced by the change of a (coupling) parameter that enhances a quantum fluctuations. At the critical point long-range (non-local)correlations are developed. In many body quantum system, entanglement (by definition) is non-local. [In other words, two or more objects in a quantum system that are correlated can no longer be described singularly.] Hence, one expects that systems near quantum critical points can be characterized in terms of entanglement. Recently, we showed a linear, higher-derivative scalar fields shows a discontinuity in entanglement entropy above a critical value of the "coupling" parameter. In the adjacent figure, for P = 10^(-5), the entropy jumps by few orders of magnitude. We are currently involved in understanding the physics behind this phenomena.

__Inflaton as a
spinor condensate__Top

Inflation is the name given to a period of accelerated expansion at ultra-high energies. It is currently the dominant paradigm for early universe cosmology. Phenomenologically, inflation has been highly successful. It not only provides answers to several questions that cannot be addressed in the standard Big Bang cosmology, but also provides a mechanism to generate the primordial density perturbations which ultimately lead to the formation of large scale structures in our Universe.

The predictions of inflation have been verified to great accuracy by cosmic microwave background (CMB) anisotropy experiments. Generically, single canonical scalar field slow roll inflation predicts that the primordial perturbations are Gaussian, adiabatic, and nearly scale invariant. WMAP 5-year data suggests that the observed power spectrum and scale invariance is consistent with the single scalar field inflation, however, the running of spectral index and large non-Gaussianity can not be explained by the single scalar field inflationary model.

For a realistic scenario of inflation, we need dynamical matter which is usually referred to as the inflaton. The inflaton can either be an elementary scalar field or a composite of particles (a condensate). Usually is it assumed that inflaton is a elemenatary field. My recent research has focused on the later. In other words, how robust are the predictions of inflation if the inflaton is a spinor condensate?

We have shown that a condensate of spinors (ELKOS), which behave like electrons but without any electrical charge, is a viable alternative to scalar-field driven models of inflation. I am currently working on signatures that could be used to distinguish spinor-driven inflation from standard inflationary models in the future CMB and gravitational wave observations.

__Trans-Planckian effects and
primordial spectrum__Top

Usually, the high-energy and low-energy effects are decoupled. In other words, to understand a low-energy phenomena one may ignore high-energy effects. For instance, to understand the motion of a cricket ball we assume that the ball can be described by Newton's laws of motion and not by Schrödinger equation. Besides, we assume that the ball is a point particle and ignore the internal forces which bind the solid ball.

However, it has been realised that high-energy and low-energy physics may not be decoupled during cosmological inflation due to the rapid expansion of the space-time. In other words, the high-energy (Planck-scale) effects do affect the inflationary predictions and, hence, the CMB fluctuations at an observable level. This is referred to as trans-Planckian problem of inflation. With the anisotropies in CMB being measured accurately, the detection of the imprints of these effects appear plausible. An observation of such an imprint in CMB will be a clear-cut evidence of new physics which may be inaccessible in terrestrial experiments.

Over the last few years, I have focused on two fronts:

- Construct toy models to understand the robustness of the corrections to the primordial power spectrum
- Use field theory, string theory and loop quantum gravity motivated models and confront them with the CMB data

__Black hole entropy and
quantum entanglement__Top

Black holes are exact solutions of Einstein's theory of general relativity. They are the remnant of the gravitational collapse of concentration of mass like stars, galaxies. Black holes are also the simplest macroscopic objects; they can be described by few parameters like mass, charge and angular momentum.

Classically (assuming that quantum mechanics can be neglected), black holes absorb all the matter around it and does not emit or radiate any particle i. e. black holes have infinite entropy and zero temperature. The concept of black hole entropy was introduced by Bekenstein to resolve thermodynamical paradoxes --- especially to preserve the universal applicability of the second-law of thermodynamics --- that arise in the presence of black holes.

The significance of this result became clear with Hawking's demonstration of black hole thermal radiation by investigating the properties of a quantum scalar field in the presence of a collapsing star forming a black-hole. He showed that the temperature of the radiation is inversely proportional to the mass of the black-hole which implies that the entropy of black-hole is one-quarter of the area of the horizon (in Planck units). However, it is still unclear why the black-holes behave this way? In other words, we don't know what microscopic quantum states are responsible for the statistical mechanics that lead to area law i. e. entropy proportional to horizon area.

Over the last few years, my focus has to been to show that quantum entanglement of the modes across the horizon can be the source of black-hole entropy. Quantum entanglement is a special correlation which exist between subsystems of a quantum system. In other words, two or more objects in a quantum system that are correlated can no longer be described singularly. One of the interesting consequence is that, once the correlation between subsystems is established, the correlation survives even when the subsystems are separated by large distances. Einstein referred this as spooky action at a distance.

So, why is quantum entanglement relevant to understand black hole entropy? Firstly, entanglement like black-hole entropy is a quantum effect with no classical analogue. Secondly, entanglement entropy and black-hole entropy are associated with the existence of horizon. To elaborate this, let us consider a scalar field on a background of a collapsing star. Before the collapse, an outside observer, at least theoretically, has all the information about the collapsing star. Hence, the entanglement entropy is zero. During the collapse and once the horizon forms, black-hole entropy is non-zero. The outside observers at spatial infinity do not have the information about the quantum degrees of freedom inside the horizon. Thus, the entanglement entropy is non-zero. In other words, both the entropies are associated with the existence of horizon. With Saurya Das and Sourav Sur, we have shown that:

- Entanglement entropy scales as area only if the quantum state is ground or coherent state
- For the superposition of ground and excited states, the entanglement entropy is sum of two terms --- one proportional to area and second term which is fractional power of area.
- The degrees of freedom which lead to the area law and the subleading corrections are not identical. This has important implications for identifying the correct degrees of freedom for black-hole entropy.

Hole

Einstein gravity

Hawking Entropy

Quantization

Dynamics

order parameter

mass gap