Running gravitational couplings, decoupling, and curved spacetime renormalization

We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $\mu$. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.Comment: Some points clarified, misprints corrected; to appear in Phys. Rev.

Running couplings from adiabatic regularization

We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $\mu$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.Comment: Revised version. Some points clarified. New references added. 6 pages. To appear in Phys. Lett.

R-summed form of adiabatic expansions in curved spacetime

The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this (non-perturbative) property of the Schwinger-DeWitt series has a natural and equivalent counterpart in the adiabatic (Parker-Fulling) series expansion of the scalar modes in an homogeneous cosmological spacetime. The equivalence between both R-summed adiabatic expansions can be further extended when a background scalar field is also present.Comment: 13 pages. Minor changes. Misprints corrected. To appear in Phys. Rev.

Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes

We reexamine the regularization of the two-point function of a scalar field in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic regularization provides a set of subtraction terms in momentum space that successfully remove its ultraviolet divergences at coincident points, but can significantly distort the power spectrum at infrared scales, especially for light fields. In this work we propose, by using the intrinsic ambiguities of the renormalization program, a new set of subtraction terms that minimize the distortions for scales $k \lesssim M$, with $M$ an arbitrary mass scale. Our method is consistent with local covariance and equivalent to general regularization methods in curved spacetime. We apply our results to the regularization of the power spectrum in de Sitter space: while the adiabatic scheme yields exactly $\Delta_{\phi}^{\rm (reg)} = 0$ for a massless field, our proposed prescription recovers the standard scale-invariant result $\Delta_{\phi}^{\rm (reg)} \simeq H^2 /(4\pi^2)$ at super-horizon scales.Comment: Title changed with respect to first version. New section added on renormalization conditions and coupling constants (Sect. 3). It matches the published version in PLB. 6 pages + references, 1 figur

Adiabatic regularization and preferred vacuum state for the λϕ4\lambda \phi^4 field theory in cosmological spacetimes

We extend the method of adiabatic regularization by introducing an arbitrary parameter $\mu$ for a scalar field with quartic self-coupling in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime at one-loop order. The subtraction terms constructed from this extended version allow us to define a preferred vacuum state at a fixed time $\eta = \eta_0$ for this theory. We compute this vacuum state for two commonly used background fields in cosmology. We also give a possible prescription for an adequate value for $\mu$

Instantaneous vacuum and States of Low Energy for a scalar field in cosmological backgrounds

We construct the instantaneous vacuum state for a quantum scalar field coupled to another classical scalar field as described in [1]. We then compare it with the state of low energy constructed for a particular solution. We show that under physically motivated conditions they become very similar.Comment: 10 pages, 4 figures, contribution to the proceedings of the "Avenues of Quantum Field Theory in Curved Space-time" conference, Genova, September 202

Physical scale adiabatic regularization in cosmological spacetimes

We propose a new scheme to regularize the stress-energy tensor and the two-point function of free quantum scalar fields propagating in cosmological spacetimes. We generalize the adiabatic regularization method by introducing two additional mass scales not present in the standard program. If we set them to the order of the physical scale of the problem, we obtain ultraviolet-regularized quantities that do not distort the amplitude of the power spectra at the infrared momentum scales amplified by the non-adiabatic expansion of the universe. This is not ensured by the standard adiabatic method. We also show how our proposed subtraction terms can be interpreted as renormalization of coupling constants in the Einstein's equations. We finally illustrate our proposed regularization method in two scenarios of cosmological interest: de Sitter inflation and geometric reheating.Comment: 22 pages + references, 5 figure

Contribution to real time stability monitoring in waves based in FFT algorithm

[Abstract] This paper describes a methodology to implement and operate an automatic onboard device destined to compute ship stability in real time. The system comprises a software based set of instruments linked to a PC computer which measure roll motions in waves and process acquired data supplying a value related with ship stability by means of an algorithm based in the frequency domain analysis of ships motions related with sea state parameter