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Reconstructing homospectral inflationary potentials

A. G. Cadavid, A. E. Romano, A. R. Liddle

Purely geometrical arguments show that there exist classes of homospectral inflationary cosmologies, i.e., different expansion histories producing the same spectrum of comoving curvature perturbations. We develop a general algorithm to reconstruct the potential of minimally coupled single scalar fields from an arbitrary expansion history. We apply it to homospectral expansion histories to obtain the corresponding potentials, providing numerical and analytical examples. The infinite class of homospectral potentials depends on two free parameters, the initial energy scale and the initial value of the field, showing that, in general, it is impossible to reconstruct a unique potential from the curvature spectrum unless the initial energy scale and the field value are fixed, for instance, through observation of primordial gravitational waves.

Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology

Physical Review D
Volume 106, Issue 8
2022 October

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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia