Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions

The featured paper, 2309.15984, “Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions,” delves into the intricacies of matching conditions for primordial scalar perturbations across cosmological phase transitions. Lead author D. D. Dineen and Will Handley explore the validity of existing approximations, particularly the Contaldi approximation (2003JCAP…07..002C), in the context of physically motivated Israel junction conditions.

The paper challenges the conventional approach to matching primordial perturbations across epochs characterized by abrupt changes in the equation of state. It demonstrates that the commonly used joining conditions, which assume continuity of the Mukhanov variable and its derivative, are inconsistent with the Israel junction conditions. These conditions, derived from general relativity, ensure a smooth joining of spacetimes across a hypersurface.

The research highlights the importance of carefully choosing the hypersurface defining the phase transition. The authors examine two possibilities: a hypersurface of constant energy density and one of constant scalar field value. Applying these conditions to the Contaldi approximation yields significantly different power spectra, emphasizing the sensitivity of the results to the choice of hypersurface. The impact of various initial conditions for the perturbations, including Bunch-Davies and Hamiltonian diagonalization (2021PhRvD.104f3532G), is also investigated.

Furthermore, the paper introduces a novel semi-analytic model to generate the primordial power spectrum. This model smoothly connects the comoving horizon across the phase transition, avoiding the ambiguities associated with instantaneous transitions. This approach allows for greater control over the duration of the transition and provides a framework for comparing sudden, finite transitions to the instantaneous transitions inherent in the Contaldi approximation. The authors explore the implications of this model and its potential for reconstructing the inflationary potential using the Hamilton-Jacobi formalism. The work draws upon and expands on existing research on perturbation matching in various cosmological scenarios, such as transitions between inflation and slow-roll violating phases (1995PhRvD..52.5549D), and between inflation and reheating (PhysRevD.43.3802).

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