Dynamical measurements of deviations from Newton's 1/r21/r^2 law

In a previous work (arXiv:1609.05654v2), an experimental setup aiming at the measurement of deviations from the Newtonian $1/r^2$ distance dependence of gravitational interactions was proposed. The theoretical idea behind this setup was to study the trajectories of a "Satellite" with a mass $m_{\rm S} \sim {\cal O}(10^{-9})$ $\mathrm{g}$ around a "Planet" with mass $m_{\rm P} \in [10^{-7},10^{-5} ]$ $\mathrm{g}$, looking for precession of the orbit. The observation of such feature induced by gravitational interactions would be an unambiguous indication of a gravitational potential with terms different from $1/r$ and, thus, a powerful tool to detect deviations from Newton's $1/r^2$ law. In this paper we optimize the proposed setup in order to achieve maximal sensitivity to look for {\em Beyond-Newtonian} corrections. We study in detail possible background sources that could induce precession and quantify their impact on the achievable sensitivity. We conclude that a dynamical measurement of deviations from newtonianity can test Yukawa-like corrections to the $1/r$ potential with strength as low as $\alpha \sim 10^{-2}$ for distances as small as $\lambda \sim 10 \, \mu\mathrm{m}$.Comment: Two-column format (26 pages), 18 figure

Low-energy states and CPT invariance at the big bang

In this paper, we analyze the quantum vacuum in a radiation-dominated and CPT-invariant universe by further imposing the quantum states to be ultraviolet regular i.e., satisfying the Hadamard/adiabatic condition. For scalar fields, this is enforced by constructing the vacuum via the states of low-energy proposal. For spin-12 fields, we extend this proposal for a FLRW spacetime and apply it for the radiation-dominated and CPT-invariant universe. We focus on minimizing the smeared energy density around the big bang and give strong evidence that the resulting states satisfy the Hadamard/adiabatic condition. These states are then self-consistent candidates as effective big bang quantum vacuum from the field theory perspective.This work is supported by the Spanish Grants No. PID2020–116567 GB-C2-1 funded by MCIN/AEI/10.13039/501100011033, and PROMETEO/ 2020/079 (Generalitat Valenciana). S. N. is supported by the Universidad de Valencia, within the Atracció de Talent Phd Fellowship No. UV-INV- 506 PREDOC19F1- 1005367. S. P. is supported by the Leverhulme Trust, Grant No. RPG-2021-299

Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this paper we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well-established adiabatic regularization method