Bonus properties of states of low energy

Abstract

States of Low Energy (SLEs) are exact Hadamard states defined on arbitrary Friedmann–Lemaître spacetimes. They are constructed from a fiducial state by minimizing the Hamiltonian’s expectation value after averaging with a temporal window function. We show the SLE to be expressible solely in terms of the (state independent) commutator function. They also admit a convergent series expansion in powers of the spatial momentum, both for massive and for massless theories. In the massless case, the leading infrared behavior is found to be Minkowski-like for all scale factors. This provides a new cure for the infrared divergences in Friedmann–Lemaître spacetimes with accelerated expansion. As a consequence, massless SLEs are viable candidates for pre-inflationary vacua, and in a soluble model, they are shown to entail a qualitatively correct primordial power spectrum.

Non-Oscillatory Power Spectrum From States of Low Energy in Kinetically Dominated Early Universes

“…We have applied this reasoning to the NO vacuum state, that had previously been shown to be at least of fourth order (Elizaga Navascués et al, 2018b). We find that, in the ultraviolet limit of large wave numbers, the asymptotic expansion that the NO vacuum satisfies (found in (Elizaga Navascués et al, 2020)) agrees exactly with that of the SLE (Banerjee and Niedermaier, 2020) (no matter the test function chosen to define it). As a consequence, the β coefficients of the transformation between the two will be identically zero in the ultraviolet.…”

“…We were motivated by the fact that they were proven to be Hadamard states that minimized the regularized energy density when smeared along the time-like curve of an isotropic observer via a test function. Furthermore, they had been shown to provide a qualitative behavior in the ultraviolet (UV) and infrared regimes of the primordial power spectra of scalar and tensor perturbations that agrees with observations in models where a period of kinetic dominance precedes inflation (Banerjee and Niedermaier, 2020), which is the case in LQC. However, in (Martín-Benito et al, 2021) we have only considered test functions that could be seen as natural choices within LQC, namely, ones with support on the high curvature regime.…”

“…with G 0 1. Remarkably, in (Banerjee and Niedermaier, 2020), the SLEs are found to have the same asymptotic expansion ( 22), regardless of the choice of the test function. Therefore, the β coefficients of the Bogoliubov transformation between the SLE and NO vacuum are identically zero in the UV.…”

“…One remarkable property of the SLEs that is usually not explicitly proven for other vacua proposals is that they are of Hadamard type (Olbermann, 2007;Banerjee and Niedermaier, 2020). This guarantees that computations such as that of the expectation value of the renormalized stress-energy tensor will be well defined.…”

“…In this work, by comparing with SLEs, we show that indeed this is the case. To do so, we resort to their UV expansions, obtained for SLEs in (Banerjee and Niedermaier, 2020) and for the NO vacuum in (Elizaga Navascués et al, 2020).…”