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We study the mode decomposition of a unitarily evolving wave packet that represents the quantum dynamics of the dust cloud in Lema\^itre-Tolman-Bondi geometry. We showed that the infrared sector of the dust profile predominantly contributes to the emission during the collapsing phase and therefore, is most relevant for the Hawking radiation.

We investigate the status of the conformal map between Einstein and Jordan frames of a scalar-tensor theory at the quantum level with the focus on the apparent paradox: the classical conformal map allows an always expanding Einstein frame to map to a Jordan frame that is always contracting, and at some point, the formalism maps a classical system (fluctuations are ignorable) to a quantum system (fluctuations are not ignorable). We find that the conformal map holds at the quantum level, and despite having drastically different cosmological evolution, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart.

We investigate the viability of an effective quantum-corrected spacetime defined by expectation value of the metric variables in quantum cosmology. For this effective geometry, we ask; how the ordering choice affects this notion, what are the quantum fluctuations in this {\it quantum geometry}, and whether its observables have any correspondence with the true {\it quantum observables}. Surprisingly, we find that the ordering choices not only affect physics near singularity but creep well into the classical regime.

Sharply peaked quantum states are conjectured to be conducive to the notion of a quantum-corrected spacetime. We investigate this conjecture for a flat-FLRW model with perfect fluid, where a generalized ordering scheme is considered for the gravitational Hamiltonian. We study the implications of different ordering choices on the dynamics of the quantum Universe. We demonstrate that the imprints of the operator ordering ambiguity are minimal, and quantum fluctuations are small in the case of sharply peaked states, leading to a consistent notion of a quantum-corrected spacetime defined via the expectation value of the scale factor. Surprisingly, the ordering imprints survive far away from the singularity through the quantum fluctuations in the quantum-corrected spacetime for broadly peaked states.

We explore the question, whether the accelerated detector is sensitive to the Planck order shift in its causal domain? This question is addressed in the context of a nested sequence of Rindler observers, where the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. The Bogoliubov analysis relies on the global notion of the quantum field theory and turns out to be insensitive to the local character of these horizon shifts. We investigate this system by means of the Unruh-DeWitt detector and show that this local probe of the quantum field theory is sensitive enough to capture the horizon shifts of the order of the Planck scale.

We perform exact half-line path integral quantization of flat, homogeneous cosmological models containing a perfect fluid acting as an internal clock, in a D + 1 dimensional minisuperspace setup.

Quantum correlations across the horizon could be pivotal in unveiling the puzzles surrounding quantum aspects of black holes and Hawking radiation. The peaks in the equal time correlation function are typically attributed to the entangled particle excitations. In this work, we investigate the evolution of the correlations of a test quantum field on a dynamical background spacetime undergoing gravitational collapse. In the case of super-critical collapse, as the black hole and its horizon forms, correlated peaks are seen to appear across the horizon, representing an entangled Hawking pair. The outside peak moves away from the horizon as the system evolves, possibly representing outgoing Hawking flux. The implications of these non-local correlations are discussed in light of information paradox, quantum atmosphere and analogue black holes.

Building upon our recently established correspondence between quantum cosmology and the hydrogen atom (Sahota et al 2025 arXiv:2505.16863 [gr-qc]), we investigate the specific sector of a negative cosmological constant (Λ<0Λ<0) in a flat FLRW Universe with dust. While the positive Λ sector (Sahota et al 2025 arXiv:2505.16863 [gr-qc]) yields a continuous spectrum and a single bounce, we show here that the negative Λ sector leads to a discrete spectrum of energy eigenvalues, effectively quantizing the cosmological constant. Within this dual description, the operator-ordering ambiguity parameter appears as the azimuthal quantum number of the hydrogen atom. A skewed Bohr correspondence emerges for the bound states, matching classical evolution at large volumes but deviating near the bounce. By constructing wave packets from these bound states, we demonstrate that the classical Big Bang and Big Crunch singularities are resolved, and the Universe oscillates between quantum bounces and classical turnaround points. The expectation values of the observables indicate a cyclic Universe—with vanishing Hubble parameter at turnarounds—undergoing quantum bounces. This exactly solvable model offers a tractable setting to explore quantum gravitational effects in cosmology. We analyze the properties of this cyclic Universe, contrasting its bound-state dynamics with the scattering states of the de Sitter case.

A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, similar to black hole thermodynamics. We investigate the thermodynamic properties of late-time cosmological evolution using the dynamical systems approach, focusing on ΛΛCDM model and scalar field models with exponential potentials. Thermodynamic quantities obtained through the Hayward-Kodama formalism are mapped onto the phase-space of these models. Specifically, we express the thermodynamic quantities as functions of the phase-space variables, allowing us to study the thermodynamic behavior across the phase space, particularly at the critical points. We focus on thermodynamic stability and phase transitions, analyzed in an initial condition-independent manner. In these models, the universe inevitably undergoes a thermodynamic phase transition, marked by diverging specific heats, irrespective of its initial configuration. We further demonstrate that the thermodynamic stability can occur only during an accelerating phase of the universe. For ΛΛCDM and quintessence models, the necessary stability conditions are never satisfied anywhere in the phase space, rendering both models thermodynamically unstable within the Hayward-Kodama framework and the canonical ensemble based stability criteria. Interestingly, the phantom models, although dynamically unstable, allow for the universe to attain thermodynamic stability in its asymptotic future. This can indicate the limitations of applying canonical ensemble based thermodynamic stability criteria to cosmological horizons. Through these archetypal descriptions of late-time cosmology, we show that the dynamical system approach is a robust framework to probe the thermodynamic aspects of cosmological evolution.

Collaborators

Teaching assistance for lab and theory courses during PhD at Indian Institute of Science Education and Research Mohali.

Teaching assistance for online NPTEL course, ‘Foundations of quantum theory: Relativistic approach’.