Dipayan Mukherjee

A fundamental assumption in the large-scale description of the Universe is symmetry: homogeneity and isotropy, the idea that the Universe looks the same everywhere and in every direction. For the cosmic microwave background (CMB), the symmetry assumption takes the form of statistical isotropy: the correlation between the CMB temperature at two points on the sky depends only on the angle between them. We explore how to detect and quantify possible violations of this symmetry.

The natural language for describing symmetry is group theory, and we use it to measure how symmetries are broken in the CMB. We average the correlation function of the CMB temperature fluctuations over all rotations, weighted by functions on the rotation group, so that any departure from isotropy shows up in the result. This also gives a physical, real-space counterpart to the BipoSH formalism, which is used to decompose a general two-point correlation function into harmonics.

For details, see Vaishali R, D. Mukherjee, A. Tyagi, T. Souradeep, Capturing Statistical Isotropy Violation with Rotational Averages, accepted in ApJ (2026)

We revisit a foundational but rarely scrutinised assumption in cosmology: that spatial averages over a single observable universe can stand in for the ensemble averages that theory actually predicts. This ergodic hypothesis is usually adopted as a “commonsense axiom,” but it is only guaranteed in the limit of infinite volume. We quantify the difference between the two averages, which we call the ergodicity bias, for finite volumes, and find that it is large on cosmological scales for curvature, density, and velocity perturbations. For density perturbations it exceeds 100% at separations of a few hundred Mpc, so it must be accounted for when comparing ensemble and volume averages in large-scale structure.

For details, see D. Mukherjee, S. Räsänen, Cosmic Variance and Ergodicity in Finite Systems with Correlations, arXiv:2608.30838 (2026)

We study what happens when the usual assumption of statistically homogeneous and isotropic primordial fluctuations is relaxed. Allowing perturbations to acquire a scale-dependent “primordial mean,” sourced by a coherent initial state rather than the vacuum, introduces violations of statistical homogeneity and isotropy that leave observable imprints: off-diagonal correlations in the CMB angular power spectrum, a non-vanishing bispectrum even for Gaussian fluctuations, and distinctive, potentially parity-violating signatures in scalar-induced gravitational waves.

For details, see H. V. Ragavendra, D. Mukherjee, S. K. Sethi, Cosmological Consequences of Statistical Inhomogeneity, Phys. Rev. D (2025);
D. Mukherjee, H. V. Ragavendra, S. K. Sethi, Scalar-Induced Gravitational Waves from Coherent Initial States, Phys. Rev. D (2026)

The classical Big Bang singularity signals a breakdown of general relativity, suggesting that quantum effects dominate at sufficiently small scales — but a full theory of quantum gravity remains elusive. We study an exactly solvable toy model: a spatially flat universe with pressureless dust and a dynamical cosmological constant, whose quantum description turns out to be mathematically equivalent to the non-relativistic hydrogen atom. For a positive cosmological constant the universe undergoes a smooth quantum bounce instead of a Big Bang; for a negative one, the solutions become discrete, giving a quantised cosmological constant and a cyclic universe in which both Big Bang and Big Crunch are resolved.

For details, see D. Mukherjee, H. S. Sahota, S. Shankaranarayanan, Quantum Cosmology as a Hydrogen Atom, Class. Quantum Grav. (2026);
H. S. Sahota, D. Mukherjee, S. Shankaranarayanan, Unitary Quantum Matter-Bounce in a Universe with a Positive Cosmological Constant, Eur. Phys. J. C (2026)

We study late-time cosmological models — including ΛCDM and scalar-field dark energy — as thermodynamic systems, in analogy with black hole thermodynamics, using a dynamical systems framework. We find that these models generically undergo thermodynamic phase transitions near their critical points, and that thermodynamic stability is closely tied to accelerated expansion; notably, standard ΛCDM and quintessence models fail the stability conditions, while phantom models satisfy them despite their other dynamical pathologies. The work is a critical assessment of applying thermodynamic notions to cosmological spacetimes.

For details, see D. Mukherjee, H. S. Sahota, S. Gavas, A Dynamical Systems Perspective on the Thermodynamics of Late-Time Cosmology, Fortsch. Phys. (2026)