On the renormalization procedure for quantum fields with modified dispersion relation in curved spacetimes

We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to $2s$ powers of the spatial momentum, the subtraction necessary to renormalize $$and$$ depends on $s$. We first describe our previous analysis for spatially flat Friedman-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.Comment: Talk given at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, July 200

Nonlinear effects of dark energy clustering beyond the acoustic scales

We extend the resummation method of Anselmi & Pietroni (2012) to compute the total density power spectrum in models of quintessence characterized by a vanishing speed of sound. For standard $\Lambda$CDM cosmologies, this resummation scheme allows predictions with an accuracy at the few percent level beyond the range of scales where acoustic oscillations are present, therefore comparable to other, common numerical tools. In addition, our theoretical approach indicates an approximate but valuable and simple relation between the power spectra for standard quintessence models and models where scalar field perturbations appear at all scales. This, in turn, provides an educated guess for the prediction of nonlinear growth in models with generic speed of sound, particularly valuable since no numerical results are yet available.Comment: 28 pages, 12 figure

Extreme parameter sensitivity in quasidilaton massive gravity

We reanalyze the behavior of Friedmann-Lema\^itre-Robertson-Walker cosmologies in the recently proposed quasidilaton massive-gravity model, and discover that the background dynamics present hitherto unreported features that require unexpected fine-tuning of the additional fundamental parameters of the theory for an observationally consistent background cosmology. We also identify new allowed regions in the parameters space and exclude some of the previously considered ones. The evolution of the mass of gravitational waves reveals non-trivial behavior, exhibiting a mass squared that may be negative in the past, and that presently, while positive, is larger than the square of the Hubble parameter. These properties of the gravity-wave mass have the potential to lead to observational tests of the theory. While quasidilaton massive gravity is known to have issues with stability at short distances, the current analysis is a first step toward the investigation of the more stable extended quasidilaton massive gravity theory, with some expectation that both the fine-tuning of parameters and the interesting behavior of the gravity-wave mass will persist.Comment: 10 pages, 7 figure

Massless Interacting Scalar Fields in de Sitter space

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.Comment: 8 pages. Summarized version of JHEP 09 (2016) 117 [arXiv:1606.03481]. Published in the Proceedings of the 19th International Seminar on High Energy Physics (QUARKS-2016

O(N)O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in $\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.Comment: 31 pages, 5 figures. Minor changes. Published versio

Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions

We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $\lambda\phi^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.Comment: 32 pages, 4 figure

Quantum backreaction of O(N)O(N)-symmetric scalar fields and de Sitter spacetimes at the renormalization point: renormalization schemes and the screening of the cosmological constant

We consider a theory of $N$ self-interacting quantum scalar fields with quartic $O(N)$-symmetric potential, with a coupling constant $\lambda$, in a generic curved spacetime. We analyze the renormalization process of the Semiclassical Einstein Equations at leading order in the $1/N$ expansion for different renormailzation schemes, namely: the traditional one that sets the geometry of the spacetime to be Minkowski at the renormalization point, and new schemes (originally proposed in [1,2]) which set the geometry to be that of a fixed de Sitter spacetime. In particular, we study the quantum backreaction for fields in de Sitter spacetimes with masses much smaller than the expansion rate $H$. We find that the scheme that uses the classical de Sitter background solution at the renormalization point, stands out as the most appropriate to study the quantum effects on de Sitter spacetimes. Adopting such scheme we obtain the backreaction is suppressed by $H^2/M_{pl}^2$ with no logarithmic enhancement factor of $\ln{\lambda}$, giving only a small screening of the classical cosmological constant due to the backreaction of such quantum fields. We point out the use of the new schemes can also be more appropriate than the traditional one to study quantum effects in other spacetimes relevant for cosmology.Comment: 14 pages, 3 figures; v2 agrees with the published version; in v2 we introduced new clarifications and we replaced the figures by new ones in order to fix a mistake in v1 and to provide additional details of the result