## Research Interests

## 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. The following mind-map provides the broad outline of research carried out by the group:

- Primordial Magnetogenesis
- Quantum entanglement as the source of black-hole entropy
- Quantifing tools to distinguish Standard Cosmology and Modified gravity models
- Exact black hole solutions in modified gravity theories
- Generalized thermalization
- Fluid-Gravity Correspondence
- Entanglement signatures of quantum phase transistions
- Early Universe Cosmology/Inflation
- Higher order cosmological perturbations

__Primordial Magnetogenesis__Top

The origin of microGauss strength magnetic fields in the galaxies and clusters of galaxies is one of the long-standing problems in astrophysics and cosmology. These fields could have arisen from the dynamo amplification of seed fields. However, the dynamo mechanism needs seed magnetic fields. The key question is whether these seed magnetic fields were generated in the early Universe. The origin and detection of the seed magnetic fields is a subject of intense study.

Cosmological inflation has successfully provided a causal mechanism for generating large scale density perturbations and temperature fluctuations in the Cosmic microwave background. However, inflation can not provide the necessary amplitude for the seed magnetic field. One reason is that the
4-dimensional electromagnetic action is conformally invariant. Several mechanisms have been proposed in the literature to break the conformal invariance of the electromagnetic action. All these mechanisms either require coupling of 4-vector potential to scalar field or breaking of gauge invariance, or introducing ghosts.
The group has been working on different proposals to generate primordial magnetic field during inflation,
recombination and
superinflation.

Recently, we constructed a consistent Galileon scalar electrodynamics. This model is a promising candidate for primordial magnetic field generation.

Recently, we showed that the Riemann coupling of the Electromagnetic fields can lead to primordial helical fields during inflation.

__Black hole entropy and
quantum entanglement__Top

For more than a decade, I have been working on identifying the relation between
two quantum effects --- entanglement entropy and black-hole entropy. The review discusses
the deep connection between the two.

We identified new symmetries that entanglement entropy satisfies
which the Hamiltonian does not satisfy. These new symmetries play crucial role in removing the divergence
of entanglement entropy.

Recently, we showed that entropy divergence, which was previously considered to be a UV divergence, actually occurs due to the generation of zero-modes in the system. This is a fundamental property of entanglement that was not established previously in the literature. We showed that this feature is present in most well-known quantum systems, such as a two-coupled harmonic oscillator.

For the first time in literature, we established a one-to-one correspondence between entanglement energy, entropy, and temperature (entanglement mechanics) and the Komar energy, Bekenstein-Hawking entropy, and Hawking temperature of the horizon (black-hole thermodynamics), respectively. While this correspondence does not imply equality of their respective counterparts, they satisfy a universal relation, E=2TS, in perfect analogy with black-hole thermodynamics. By further extracting the Smarr-formula structure of black-holes directly from entanglement mechanics, we confirm that black-hole thermodynamics is of quantum origin.
You can listen to the talk I gave at IUCAA, here.

__Tools to distinguish standard cosmology and modified gravity__Top

Our current understanding of the cosmos is based on an enormous extrapolation of our limited knowledge of gravity since General Relativity has not been independently tested on galactic and cosmological scales. On the largest scales, the biggest surprise from observational cosmology has been that the current Universe is accelerating. The observations of Type Ia supernovae suggests that the current Universe is undergoing a phase of accelerated expansion which agrees with the observations of cosmic microwave background radiation.

Providing a fundamental understanding of the Universe's late-time accelerated expansion is one of the most challenging problems in cosmology. GR alone can not explain the late-time acceleration of the Universe with ordinary matter or radiation. The presence of an exotic matter source energy referred to as dark energy can explain the late-time accelerated expansion.

Recently, we considered a scenario where the accelerated expansion is due to modifications to gravity in the cosmological scales. Assuming that this is the same as the standard cosmology, we showed that the growth of structure formation would be different in these two cases.

To address the HO tension in cosmology, currently, we are looking at interacting dark energy (IDE) models, where dark matter (DM) and dark energy (DE) interact non-gravitationally. In the fluid picture, there is no restriction on the form of the interaction term. We addressed the important question: Can the field theory model provide correspondence to the fluid picture beyond the background expansion, i.e., at the level of cosmological perturbations?

__Exact BH solutions in modified gravity theories__Top

General Relativity continues to be, even after one hundred years, our best theory to describe gravitation. GR has passed every experimental test. However, GR can not explain some of the astrophysical and cosmological observations without introducing new concepts like dark matter and dark energy. Over time there have been various attempts to modify GR having as motivation different reasons, like the desire to quantize GR to be able to unify it with the other three elementary known forces: electromagnetic, weak, and strong nuclear forces. f(R) gravity theories are a class of theories that are obtained from GR by adding higher powers of the Ricci scalar to the standard GR action. Among the motivations for the study of f(R) theories is the fact that by adding suitable extra terms to the action, we can recover the evolution of the Universe as observed today without the need for dark matter and dark energy.
While these theories are simple, they contain non-linear higher-order derivatives of the metric, and hence, it is challenging to obtain non-trivial exact solutions in these models. Most of the earlier analyses use (i) approximate techniques or (ii) solutions that are similar to GR or (iii) obtain solutions to the Einstein frame by doing the conformal transformation. In this work, we do not use any of the above approaches and obtain exact vacuum solutions for a class of f(R) models. Our work is the first successful attempt to obtain non-trivial exact solutions.

Recently, we showed that the 4-D vacuum spherically symmetric space-time contains infinitely degenerate solutions. We then obtain two exact black-hole solutions that have the event-horizon at the same point. Thus, we confirmed that Birkhoff's theorem is violated for f(R) gravity theories.

__Tools to distinguish GR and modified gravity__Top

General Relativity is a hugely successful description of gravitation. However, both
theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field
limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational
waves. For quasi-normal modes of black-holes in General Relativity, the two polarisation states of gravitational waves have the same amplitude and frequency spectrum. Will this be valid for modified gravity theories and how can use this to distinguish GR and MG?

For spherically symmetric black-holes without charge, we showed that this equality is not maintained in F(R) and Chern-Simons theories and obtained a quantifying tool to distinguish the same. Recently, we extended the analysis for charged spherically symmetric black-holes and found a way to distinguish between the GR and modified theories of gravity. Using the principle of energy conservation , I showed that, the polarisations differ for modified gravity theories. We recently obtained a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.

__Fluid-Gravity Correspondence__Top

Many interesting features of gravity have arisen since the formal relation between the laws of thermodynamics and the laws of black hole dynamics were found. These relations allow the
possibility of extracting information about the microscopic degrees of freedom by providing statistical mechanical description of the
macroscopic properties of black hole horizons. In other words, one aims to arrive at the microscopic features of black holes from their semi-classical properties as we yet lack information about the quantum degrees of freedom of gravity.

Fluid/Gravity correspondence is another approach that aims to
associate fluid degrees of freedom to the horizon and, eventually, to the gravitational degrees of freedom. This correspondence
allows the connection between macroscopic and microscopic physics
by studying the statistical properties of the fluid on the
horizon of the black hole.

In a series of papers, taking the view-point that the horizon-fluid possesses some kind of physical reality
beyond the formal mathematical similarity, we have shown that
the entropy and energy of black holes, a well as their
bulk viscosity and negative specific heat
can be described as a critical point of a quantum fluid.

Recently, we showed that it is indeed possible to obtain a
microscopic model of the horizon-fluid. In the continuous limit,
the model is a perturbed CFT and has a Virasoro Algebra.
It reproduces the negative bulk viscosity.

__Entanglement and 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 ground state to another. Such phase transistions are induced by the change of a parameter that enhance quantum fluctuations. At the critical point, long-range correlations are developed. In many body quantum system, entanglement is non-local.
Hence, one expects that systems near quantum critical points
can be characterized in terms of entanglement.

We showed a linear, higher-derivative scalar fields shows a discontinuity in entanglement entropy above a critical value of the "coupling" parameter . In the figure, the entropy jumps by few orders of magnitude. We are currently involved in understanding the physics behind this phenomena.

__ Higher order cosmological perturbations__Top

The temperature fluctuations as observed in CMB is ~ 10^(-5),
hence order-by-order perturbation theory can be considered to match
with observations. There are two mathematical procedures that are currently used in the
literature to study gauge invariant cosmological perturbation theory:
Hamiltonian formulation and Lagrangian
formulation. While the Lagrangian formulation has been widely studied,
Hamiltonian framework in the context of cosmological perturbations is
not common.

Over the last few years, I have been concentrating
on Hamiltonian formalism and to provide a generalized Hamiltonian
approach for cosmological perturbations at all orders. We provided
a new technique to obtain Hamiltonian for generalized non-canonical
scalar fields and have also applied our Hamiltonian approach for the same. We also
applied our new approach to Galileon fields (fields whose action has
higher derivative terms, however, the equations of motion is still
second order).

__Generalized thermalization__Top

Thermalization of quantum systems over long time scales is an open issue in unitary quantum mechanics. Such a time irreversible phenomenon is understood through Gibbs Generalized Ensemble. Studies in finite-sized Hilbert space systems seem to support this understanding. In this work, we demonstrated thermalization of an infinite-dimensional Hilbert space system, which jumps between two integrable settings. Recently, we extended the analysis for breaking of a spin chain that has wide-ranged implications for quantum information, statistical mechanics, continuous variable systems, and also black hole physics.

__Early Universe cosmology (Inflation)__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 cosmology,
but also provides a mechanism to generate the primordial density
perturbations, which ultimately lead to the formation of large-scale structures in the Universe.

The predictions of inflation have been verified to great accuracy by
cosmic microwave background
anisotropy experiments. Generically, single canonical scalar field slow roll
inflation predicts that the primordial perturbations are Gaussian,
adiabatic, and nearly scale-invariant. Within General Relativity,
near scale-invariance imposes a condition that the canonical scalar
field potential should be almost flat so that the quantum fluctuations that exit the horizon
during inflation is nearly scale-invariant. While these flat
potentials are phenomenologically successful; however, the scalar
field sector of action deviates much from the standard model of
particle physics.

Over the last few years, I have been interested in constructing inflationary models
in modified gravity --- Gauss-Bonnet, F(R)
and F(R,Φ) --- where the canonical scalar field potential does not
deviate much from the standard model of particle physics.