In any case, the way we look back into the past, whether we are looking back a billion years, or ten billion years, or before the big bang, is essentially the same way.
To look back we use a model of the universe that we can TEST because it makes predictions about things we can measure in the present.
If we can validate the model, then we extrapolate back to conditions in the past by running the model backwards in time.
The vintage 1915 model, as it happened, broke down at a certain point when you ran it back. People got over-impressed by that and thought because the model broke that time didn't extend back any further
But since 2001 or so, models have been developed that don't break down and to go back prior to the big bang. And they fit the available data as far as we can tell, so far. More testing is in order.
But that is Quantum Cosmology. It eliminates the singularity and goes back before the big bang. Typically the QC model says there was a contracting phase and a bounce.
A lot of this work was in fact done at Penn State starting in 2001 by Bojowald and Ashtekar and their many collaborators.
I believe the two people you mentioned are or have been at Penn State and worked with Ashtekar's group. But I need to check this.
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Yeah, Madhavan Varadarajan and Ashtekar go way back. They collaborated already in 1994.
Here are some of the 25 papers by Varadarajan which the arxiv lists:
22. arXiv:gr-qc/9507044 [ps, pdf, other]
Title: Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation
Authors: J. Fernando Barbero G., Madhavan Varadarajan
Comments: 31 pages, latex
Journal-ref: Nucl.Phys. B456 (1995) 355-376
Subjects: General Relativity and Quantum Cosmology (gr-qc)
23. arXiv:gr-qc/9503006 [ps, pdf, other]
Title: On the gauge fixing of 1 Killing field reductions of canonical gravity: the case of asymptotically flat induced 2-geometry
Authors: Madhavan Varadarajan
Comments: 25 pages, LaTex
Journal-ref: Phys.Rev. D52 (1995) 2020-2029
Subjects: General Relativity and Quantum Cosmology (gr-qc)
24. arXiv:gr-qc/9406040 [ps, pdf, other]
Title: A Striking Property of the Gravitational Hamiltonian
Authors:
Abhay Ashtekar, Madhavan Varadarajan
Comments: 22, CGPG-94/6-3
Journal-ref: Phys.Rev. D50 (1994) 4944-4956
Subjects: General Relativity and Quantum Cosmology (gr-qc)
25. arXiv:gr-qc/9307006 [ps, pdf, other]
Title: The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation
Authors: J. Fernando Barbero G., Madhavan Varadarajan
Comments: 19 pages, preprint# SU-GP-93/64
Journal-ref: Nucl.Phys. B415 (1994) 515-532
Subjects: General Relativity and Quantum Cosmology (gr-qc)