Non-Linear Cosmic Structure Formation

with Prof Matthias Bartelmann, Heidelberg University

Matthias’s group is involved with Kinetic Field Theory, an analytic field theory of structure formation in classical particle ensembles and its applications in probing the origin of cosmic structures. Personally, I applied the formalism of KFT to original calculations of the non-linear cosmic power spectrum for a variety of modified gravity models incorporating screening mechanisms such as the Chameleon model, Vainshtein screening, k-mouflage mechanism and Yukawa suppression. I implemented these changes in code as well, generalizing it to include parametrizations of modified gravity models into a scale dependent effective gravitational constant to successfully plot the non-linear spectra for a variety of models. Currently, we are working on using a taylor approximation to obtaine in the non-linear spectra for midfied gravity models, as expanding it around the calcuated GR one.

The report can be found here.

Black Hole Mass Gap

with Prof Vikram Rentala, IITB

My main project, I started with Prof. Rentala in my third semester. I studied the onset of pair instability driven pulsations in PPISN, and the phenomenon of Pair Instability Supernovae (PISNe) for a theoretical understanding of the BHMG and the discovery of GW190521 by the LIGO-VIRGO detectors. I theoretically studied the effects of various astrophysical and particle physics parameters like metallicity, rotation, convective overshoot, wind mass loss, nuclear reaction rates, neutrino physics, dark matter annihilation, axionic emissions, and others on the Black Hole Mass Gap (BHMG). In addition, I Simuated the effects of these parameter dependencies on the blackhole masses using the 1D stellar evolutionary code MESA and it’s PPISN testsuites and analyzed the region of dynamical instability in massive stars in the core temperature and density plane using Wolfram Mathematica. Currently, I am analysing the effect of exotic Beyond Standard Model particles on the 12C(α, γ)16O rate, the major parameter impacting the lower edge of the BHMG, by adding extra resonances in excited states of O, and using the R-matrix formalism for the same.

The multiple reports can be found:

  1. The theory from Carrol and Ostille .
  2. The writeup containing our progress
  3. Our CO reaction work

Quantum gravity and Trace Dynamics

with Prof Tejinder Singh, TIFR I reviewed Teleparallel gravity, an equivalent construction of general relativity in the tetrad formalism, and the resulting Poincare algebra in the phase space of the theory. I mainly studied the details of a Quantum Gravity candidate, which utilizes matrix valued Lagrangian dynamics on an octionic spacetime evolving in Connes time, and the consequent recovery of classical space time and quantum field theory. I also studied the details of the emergence of standard model physics from the CO algebra from C. Furey’s thesis.

The work was mainly based on reviewing the following:

  1. C. Furey’s thesis
  2. Review article on the Quantum Gravity candidate

Differential Topology

with Prof Sugata Mondal, TIFR I mainly studied and completely solved Gullemin & Pollock for an introduction to manifolds, transversality and its applications in proving stability theorem, Sards Theorem, Morse Thoery, classification of one and two Manifolds, Jordan Brouwer Separation Theorem, Borsuk Ulam Theorem and others. This also included oriented intersection theory, specifically Lefschetz fixed point theory, Poincare-Hopf theorem, and differential forms, exterior derivatives, Stokes Theorem and integration on manifolds.

  1. The final report
  2. The presentation for completion of VSRP