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arXiv · 2505.16863

Unitary quantum matter-bounce in a universe with a positive cosmological constant

Harkirat Singh Sahota·Dipayan Mukherjee·S. Shankaranarayanan
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Abstract

We analyze the Wheeler-DeWitt quantization of a spatially flat Friedmann-Lema\^itre-Robertson-Walker universe containing pressureless dust and a positive cosmological constant ($\Lambda > 0$). Following relational time framework, we establish a direct mathematical correspondence between the cosmological Hamiltonian and the radial Schr\"odinger equation for the scattering states of the non-relativistic hydrogen atom. This exact solvability allows us to rigorously construct the physical Hilbert space and ensure the self-adjointness of the Hamiltonian. As a concrete result, we show that the wave packets unitarily evolve depicting a non-singular quantum bounce, systematically replacing the classical Big Bang singularity. Finally, we discuss the physical relevance of this exact solution within the matter-bounce scenario. We demonstrate that this framework provides a robust quantum origin for a bounce during a dust-dominated contracting phase -- a necessary prerequisite for generating a scale-invariant spectrum of primordial perturbations -- derived from the unitary dynamics of the quantized background.

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Harkirat Singh Sahota, Dipayan Mukherjee, S. Shankaranarayanan. 2025-05-22. Unitary quantum matter-bounce in a universe with a positive cosmological constant. https://doi.org/10.1140/epjc%2Fs10052-026-16168-z

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