General Relativity and Beyond: Modified Gravity and Quantum Gravity.

The accelerated expansion of the Universe.

A number of cosmological observations [1] indicate that the expansion of the universe began to accelerate some five billion years ago. Such observations can only be accomodated within the framework of General Relativity if dark matter and a non-zero cosmological constant (or some other source of dark energy) are introduced on the right hand side of Einstein's equations. The inferred amounts of dark sources imply that only about 5 percent of the total matter-energy budget of the universe is in the form of matter-energy sources found in laboratory. This fact is raising growing interest on alternative theories of gravity that can justify those observations without the introduction of dark sources. Particular cases of interest that have attracted much attention in recent years correspond to the so called f(R) theories of gravity [2]. These theories have been explored from many different points of view and it has been found that solar system and laboratory tests together with cosmological perturbation theory can pose severe constraints on the parameters of infrared- corrected models [3,4]. Though it has been claimed that the metric version of these theories could escape local constraints by means of the so called ?chameleon mechanism? [5], the Palatini version is clearly incompatible with observations due to the implementation of the infrared corrections via a curvature scale [3]. However, recent proposals coming from the modified gravity approach to dark matter [6] suggest that new ways to implement infrared modifications of gravity using the Palatini formalism are possible, which opens a new window to the consideration of dark matter and dark energy questions from this approach. Exploring this possibility will require a careful understanding of the different ways in which Newtonian gravity can be recovered from a geometric theory of gravity involving metrics and connections, of the different ways infrared modifications can be implemented to produce the desired phenomenology, and of the way those theories can be made fully covariant and relativistic in order to be used in a cosmological setting. Those aspects will be fully investigated.

Quantum gravity phenomenology and effective dynamics.

Non-perturbative quantization techniques have allowed in the last few years important progress in the understanding of quantum cosmologies and the origin of the Universe. In particular, it has been found that within the framework of loop quantum cosmology [1] (LQC) the big bang singularity can be avoided at early times by means of a bounce from a contracting phase to an expanding phase that at late times recovers the usual Friedmann evolution of GR. The dynamical equations describing this evolution have been exactly reproduced using an f(R) theory with ultraviolet curvature corrections in the Palatini formalism [2]. More recent investigations [3] have shown that bouncing cosmologies are quite generic within the Palatini approach, and bouncing solutions have been found in isotropic and anisotropic (Bianchi-I) universes filled with different types of sources, including well-known sources such as radiation and dust. The theories that predict this cosmic evolution also predict that the spacetime metric depends on the local energy-momentum densities [4], an aspect that had already been predicted using ad-hoc approaches to quantum gravity phenomenology [5]. We will devote part of our efforts to the study of this type of theories and their generalizations with a double goal, namely, to implement the effective dynamics of cosmological and black hole quantum models, and to find a geometric theory of gravity free from singularities. We will also consider the Hamiltonian formulation of these theories and their quantization.

Conformal symmetry and fundamental physics.

Conformal symmetry and black holes.

An outstanding result of the theory of quantized fields in curved spacetimes [1] is the thermal creation of particles by black holes [2]. According to this result, a black hole behaves as a thermodynamic system possessing both temperature and entropy. The thermal character of the radiation emitted is deeply linked to the presence of the event horizon. One characteristic of the even horizon is the existence of an unbounded gravitational blueshift that a quantum with a given energy at infinity experience as it approaches the horizon. This blueshift sweeps away any physical scale present in the field theory and makes conformal symmetry arise in a rather natural way. It has long been argued that the flux of thermal radiation is deeply connected to anomalies related to the conformal symmetry arising near the horizon [3]. Hints indicating that conformal symmetry suffices to yield the full spectrum (not only the flux) of thermal radiation emitted by Schrwarzschild black holes were obtained in [4]. Higher-order moments of the Planck distribution were obtained in [5] through an involved analysis of higher-spin currents. Furthermore, it has been argued that the near-horizon conformal symmetry [6] is at the heart of the entropy of black holes. Recently, the approach based on near-horizon asymptotic symmetries [7] has been extended to rotating (Kerr) black holes, suggesting an holographic duality between extremal and near-extremal Kerr black holes and a two-dimensional CFT [8]. A further step has appeared in [9] where a (finite-dimensional) conformal symmetry has been shown to exist for the wave equation of a massless scalar field (in the so-called near region) for a generic non-extremal Kerr black hole. This finite dimensional SO(2,2) symmetry accounts for classical superradiance. More recently we have shown that conformal symmetry alone is enough to determine the Hawking effect itself (providing the full spectrum of radiation) of a generic rotating black hole [10]. We shall investigate the relationship between both approaches. In particular, we shall study ways to enlarge the SO(2,2) symmetry, realized in the three-dimensional space (t, r, axial angle) of the Kerr black hole, to the full two-dimensional conformal group. This will certainly provide new and important hints on the understanding of the role of conformal invariance in black hole physics, including the details of the backscattering aspects.

2-dimensional symmetric sigma models.

We have discovered a method to construct a lagrangian 2D sigma models with WZ term on coset spaces which keep the exact symmetry under left translations. Although the definition is coordinate independent, we use solvable (i. e. based on the Iwasawa decomposition) coordinates to parametrize the coset manifold, which leads to a relatively simple form of the Lagrangian. No gauging procedure is employed, and by means of generalized contractions one is able to generate hierarchies of sigma models. One can compute the beta function, although generically it is not zero and the models are then not conformal at the quantum level. Our aim is to relate this contraction procedure with other procedures based on the gauging of isometries. Gauging, generically, does not produce conformal models, except in some situations. We are interested in investigating the conformal points on our theory space, as well as the properties of the generic case under the renormalization group.

Supersymmetry, supergravity and deformations.

Deformation of Minkowski and conformal superspaces. Non commutative supersymmetric field theories.

The deformation of Minkowski space and superspace has been treated in many references. The idea is to formulate supersymmetric theories on a space or superspace which is non commutative. Nevertheless, there are problems when trying to conciliate supersymmetry with the idea of deformation [1,2]. In [3] we designed a way for putting together both ingredients, which at the end reduces to the known deformations of quantum matrices. The idea is very appealing because one starts by quantizing a superconformal symmetry from which the super Poincare? follows. The super Minkowski space is a big cell inside the superconformal space, which is a Grassmannian supermanifold, for the case of chiral superfields. Although much more simple in the calculations than the case of generic superfields, the quantization of the super Grassmannian offers a natural definition of quantum chiral superfileds, definition that escaped up to know to all attempts of compatibilizing supersymmetry with chirality. Our goal is now to extend this approach to generic superfileds, which involves the quantization of a flag supermanifold which is much more complicated. Also, we want to obtain explicitly the deformation in Minkowski space, which can be done by means of a star product. Partial calculations of the star products have already been performed and an explicit formula is possible. Then, we want to formulate deformed field theories with the use of the star product. In particular, by using the quantum chiral superfields we will be able to obtain a new deformation of super Yang- Mills. In D=4 and for N=4 it is a superconformal theory, which in the deformed case, will presumably show in our approach.

Compactifications of supersymmetric theories and supergravity on three dimensional manifolds.

We are interested in studying the compactification of supergravity theories over 3 dimensional smooth flat manifolds. These manifolds are classified according to crystalografic groups. We have already partial results in some particular manifold. The novelty is that we use exclusively smooth manifolds (not orbifolds nor ?orientifolds) a priory, although orientifold planes or singularities could be introduced at a later stage. Fortunately these manifolds possess a spin structure so solutions of supergravity are available with these topologies. We are interested in comparing these results with the compactifications over non flat manifolds with torsion. Altough in [2] we showed that, locally, both theories are identical, since when compactifying the global properties of the internal manifold are relevant, we expect to obtain a sharp difference in regard to the surving modes and number of supersymmetries.

Attractor mechanism in Supergravity

A lot of work has been done in the study of this phenomenon in the context of the bosonic sector of N=2 supergravity. It has been proved that it is manifested by supersymmetric [1] as well as non-supersimmetric [2] extremal single-center and multicenter black holes. When supersymmetry is conserved the solutions (sometimes expressed in a symplectic covariant form known as ?stabilization equations? ) to the first-order flow equations of the scalars, have been well understood [3], in the non-supersymmetric case not always general clear final results have been achieved. Recently stabilization equations for non-supersymmetric configurations seem to have been found for single- center black holes [4] but a generalization without assumptions to the multicenter case is needed (see [5] for black holes with parallel charge vectors and trivial axions). At the same time it would be interesting to see how this formalism applies to non-extremal black holes. It is known that they do not experience the attractor mechanism but nevertheless the evolution of the scalars turns out to be still described by first-order equations [6]. It arises then naturally the question if an analogue to the stabilization equations in this background exists or not.

Quantum black holes, quantum gravity and holography.

Holographic description of quantum black-hole physics.

The goal of this research is to deepen our understanding of evaporating black holes by using a combination of braneworlds and AdS/CFT techniques as considered in [1,2] where, in particular, it was conjectured that a classical 5D braneworld black hole is dual to a 4D quantum corrected black hole on the brane. In the static case for what concerns the correction to Newtonian potential on the brane, the classical computation in AdS_5 in [3] was matched with a semiclassical 4D numerical calculation of the large-distance quantum corrections to the Schwarzschild spacetime due to matter fields in the Boulware vacuum [4] (an analytical technique to derive this result has been developed recently [5]). The time dependent case is more involved and more interesting. An interesting conjecture relating horizons in braneworld models, following [6], and the horizons of an evaporating black hole was put forward in [7], where a possible classical 5D mechanism at the base of the Hawking effect was also proposed [8]. Our aim is to continue the research in this direction by trying to understand, with the help of numerical and analytical techniques, what are the features of 5D time-dependent configurations dual to 4D evaporating black holes, with possible clues on the endpoint of the evaporation.

Hawking radiation and the Planck scale.

Semiclassical gravity predicts the radiation of quanta by black holes [1]. The deep connection of this result with thermodynamics and, in particular, with a generalized second law strongly supports its robustness. However, Hawking's derivation requires the validity of relativistic quantum field theory on all scales. Therefore, the microscopic structure offered by any quantum gravity theory could leave some imprint or signal in the emission rate. However, the results of string theory seem to agree with Hawking's prediction (for the emission of low- energy quanta and for some particular near-extremal charged black holes, when one can actually compare both approaches). Hints from acoustic black holes also support this viewpoint [2]. We are currently investigating this issue: the range of validity of Hawking radiation and the underlying symmetry condition (i.e., Lorentz invariance) that makes it robust against Planck-scale physics (for not very-high energy emission) [3]. We will further analyze this question aiming to relate it with dynamical aspects of quantum gravity. In particular, in order to approach the problem of Hawking radiation within loop quantum gravity it is mandatory to incorporate dynamics in the description. This will very likely require us to go beyond the present black hole models, based on the use of isolated horizons, and introduce dynamical elements. This goal can possibly be achieved by extending the present model to dynamical horizons. The successful implementation of this extension will require a careful understanding of the Hamiltonian description for this kind of models and, crucially, of the role of quantum matching conditions in the construction of the Hilbert space. It may be actually necessary to use toy models to understand in a stepwise manner the incorporation of dynamics to the existing static descriptions. It is worthwhile to add that there is some hope that mini-black holes can be produced in the LHC at CERN. In that case, due to the closeness of the fundamental Planck length and the gravitational radius, the effects of trans-Planckian physics will be very important.

Testing Hawking radiation in Bose-Einstein condensates via correlation measurements.

The Hawking effect in correlations in acoustic black holes

The crucial feature of gravitational black holes is the existence of an event horizon, a surface separating two causally disconnected regions: the exterior and the black hole. In the gravitational collapse of a star leading to a black hole the initial quantum vacuum state of matter fields is `distorted' in such a way that it becomes a two- mode squeezed vacuum state [1] entangling the external and the black hole regions. Restricting to the exterior region, as Hawking did, we need to trace over the inaccessible black hole degrees of freedom and the result is the famous thermal emission he discovered in 1974 [2]. Our proposal to study the Hawking signal in density-density correlations in BECs [3] is based on the hydrodynamical approximation of the theory where QFT in curved space techniques can be applied. The crucial observation in this respect is that the initial vacuum state contains local correlations (before the black hole forms) that are converted, in the course of time evolution, to nonlocal correlations between the black hole and the exterior regions. Such correlations have a typical form that characterizes the Hawking effect. This, in turn, reflects the fact that Hawking particles are created in pairs, one reaching infinity (Hawking quanta) and the other (the partner) being trapped inside the black hole [4]. Unlike in gravity, the acoustic nature of the horizon does not forbid the measurement of these correlations. The richness of the numerical results in [5] requires a considerable amount of work to explain them. The quantitative comparison of the main Hawking quanta-partner signal with its hydrodynamical approximation (proportional to \kappa^2, \kappa being the horizon?s surface gravity) is excellent for acoustic black hole configurations with small enough surface gravities. Once dispersion effects (parameterised by the condensate healing length \xi) become important a new analytic technique, based on step-like discontinuities, was introduced in [6] (for a spectral analysis see [7]). We started in [8,9] an analysis to understand the effects of the temporal formation of acoustic black holes (as opposed to the stationary calculations in [6]). We see that in the infinite surface gravity limit the correlators are finite and go as 1/\xi. It would be interesting to find an analytical formula interpolating between these two (hydrodynamic and deep dispersive) regimes and to understanding thoroughly the effects of the temporal formation. The numerical results show the presence of a subleading peak inside the horizon which is also due to Hawking radiation. It is interpreted as arising from the backscattering of the Hawking quanta created in the exterior region. We were not able to capture this feature in our hyrodynamical analysis in [3] because there we considered a conformal field approximation for the phase fluctuation field of our condensate allowing to extract analytical formulas but eliminating backscattering. We shall perform a numerical analysis of backscattering effects at the hydrodynamic/gravitational analogy level and compare them with the numerical simulations.

Acoustic white holes and black hole-white hole systems

Unlike in gravity, acoustic white holes are easily realisable in the laboratory (see for instance [1]). They are seen as a kind of time-reversal of black holes. For what concerns the Hawking effect, this implies that, in hydrodynamic/relativistic regime, the Hawking quanta and the partner pile up along the horizon with an arbitrarily-high frequency. Therefore, while Hawking radiation from black holes is believed to be robust against modifications in the short-distance behaviour of the theory (the so called transplanckian problem [2]) in the case of white holes the signal depends crucially in its high-energy features. For the case of Bose-Einstein condensates the supersonic characher of the phonon?s dispersion relation is such that both the Hawking quanta and the partner do not accumulate along, but enter the white hole horizon. The density correlations patterns [3] show a checkerboard-type feature inside the horizon with an amplitude that grows in time (logarithmically in zero temperature case, and linear with T different from zero). This contrasts the stationary character of the Hawking signal from (acoustic) black holes. The physical implications of this result, whether or not it leads to a `mild? instability of white holes, needs to be better understood. We shall thoroughly study all the numerical features making use of analytical techniques and we shall also focus on the effects of the temporal formation. Indeed, being the found signal nonstationary, it could be more sensitive than the black hole to the details of its formation. In addition, we shall also study the type of radiation emitted in the exterior region. The other physical situation of interest are systems with a black hole and a white hole horizon (such as the ring-shaped configuration considered in [4]). In them, an incident wavepacket is able to trigger a dynamical instability leading to exponentially growing perturbations. This phenomenon is thought to lead to the laser effect [5,6]. Besides studying the correlations patterns, as well as the radiation emitted, we shall also consider the phonon?s backreaction on the condensate. This analysis will help clarify which are the experimental features, such as the predicted amplification of the Hawking effect, to be expected in these systems.

Connecting with the experimental search.

Density correlation measurements appear to be very promising for an experimental verification of the Hawking effect in the near future. Inserting number for existing experiments, one expects normalized correlations of the order 10^(-3), small but non-negligible. Cornell [1] proposed a method to amplify the signal by a significant factor by following the formation of the formation of the acoustic black hole with a period of free expansion. We shall study the details of this interesting proposal (a similar amplification of dynamical Casimir-type transient features present in [2] was studied in [3]) and more in general of the various theoretical issues the experimental search will have to face. Experimental and theoretical issues (a first experimental attempt to create an acoustic black hole in a BEC was reported in [4] and recent interesting results on the detection of Hawking radiation in other systems appeared in [5, 6]) will be discussed at the workshop `New trends in the physics of the quantum vacuum: gravitation, cosmology and condensed matter? that we shall organize in Trento in June 2011. Condensates in free expansion are interesting also because the long wavelength acoustic geometry felt by the phonons is of cosmological type with a cosmic horizon. Using our techniques it will be interesting to study the amplification of the initial quantum fluctuations of the phonon modes, which could give observable effects in the density correlations patterns (see for instance [7]). Finally, on a more speculative level, our results and the many available in the literature make us confident that Hawking radiation exists in gravity as well, and that the semiclassical results are valid up to scales of the order of the Planck length. Provided black holes evaporate according to unitary rules, we may be able to measure peculiar correlations between the particles emitted at early and late time for instance from miniblack holes at LHC.

Quantum fields in the primordial universe: observable signatures.

The impact of ultraviolet divergences on the observable consequences of inflation.

A sufficiently long period of accelerated expansion in the very early universe is able to solve the questions raised by the standard big bang cosmology and, at the same time, offers a predictive mechanism to account for the small observed inhomogeneities responsible for the structure formation in the universe and the anisotropies present in the cosmic microwave background (CMB) [1]. Inflation predicts the production of primordial density perturbations and relic gravitational waves as amplifications of vacuum fluctuations together with a quantum-to- classical transition at the scale of Hubble sphere crossing. Primordial perturbations leave an imprint in the CMB anisotropies, which are, therefore, of major importance for understanding our universe and its origin [2]. The potential-energy density of a scalar (inflaton) field is assumed to cause the inflationary expansion, and the amplification of its quantum fluctuations and those of the metric are inevitable consequences in an expanding universe. The metric fluctuations provide the initial conditions for the acoustic oscillations of the plasma at the onset of the subsequent radiation-dominated epoch. The detection of the effects of primordial gravitational waves in future high-precision measurements of the CMB anisotropies, as for instance in the PLANCK satellite mission, will serve as a highly non-trivial test for inflation. Therefore, it is particularly important to scrutinize, from all points of view, the standard predictions of inflation. A disturbing aspect of the spectra of scalar and tensorial perturbations generated during inflation is that they have a divergent variance. In the case of classical perturbations, divergences of the variance are usually removed by means of window functions that filter out the wavelengths that cause the problem. However, the primordial spectra have a quantum origin and their divergences should be removed, on grounds of theoretical consistency, by means of the well established methods of quantum field renormalization in curved spaces [3]. Recently we have shown that the renormalization of the variance of scalar and tensorial perturbations during inflation has a nontrivial impact on the primordial power spectra of those fields [4]. The renormalized power spectra are independent of the renormalization scheme. The adiabatic Parker-Fulling renormalization turns out to be equivalent to the Bunch-Parker renormalization [5]. Though the resulting spectra are almost scale free within the slow-roll approximation, the relation between spectral indices and the slow-roll parameters is significantly changed as compared to the standard derivation. The consistency condition of single-field inflation, which involves the tensor-to-scalar ratio r and the tensorial index n_t, is then transformed into a more involved relation [4-5]. We plan to further study this question and perform a model-by-model analysis. However, since the renormalized consistency conditions involve the tensorial index and its running, it is very unlikely that current experiments may determine them with precision. Therefore, we also want to carry out a bootstrap approach, of the type performed in [6], to determine precise relations among observable quantities. These may allow strong tests of the assumed inflationary epoch in the very early universe.

Observable signatures of the stimulated creation of quanta/perturbations during inflation: non- gaussianities.

The idea that our universe experienced a period of accelerated expansion [1], known as inflation, in the early stages of its evolution came out as a mechanism able to dilute some of the important problems of the Big Bag model, namely the so called flatness and horizon problem. However, it was soon realized [2] that the most valuable achievement of the inflationary mechanism is that it is able to generate, in a physically compelling way, a spectrum of primordial density perturbations that accounts successfully for the spectrum of temperature fluctuations that is observed in the Cosmic Microwave Background. The inflationary expansion of the early universe is able to generate a spectrum of density perturbations as the result of the gravitationally-induced spontaneous creation of perturbations from vacuum fluctuations of the scalar field producing inflation, the inflaton. Therefore, by adding to the original hypothesis the fact that the state of inflaton perturbations at the onset of inflation was the vacuum state (i.e., the so-called Bunch-Davies vacuum [3]), inflation is able to account for the observed inhomogeneities of the CMB. The election of the vacuum state describing the state of inflaton perturbations can seem unnatural due to our ignorance of the physics in the early universe before inflation. However, it is consistent with the argument that the exponential expansion of the universe during inflation will dilute any possible quanta present in the initial state and will drive any arbitrary state to the vacuum state. That justifies the vacuum state as the most natural choice. However, recently we have shown [4] that, if there exist perturbations already present in the initial state, i.e. the initial state is not the vacuum, the effect of these perturbations is not diluted by inflation and survives to its end, and beyond. This happens because there is a gravitationally-induced stimulated creation of quanta that amplify the initial perturbation by the same quantum amplification factor as is responsible for the spontaneous particle creation from the vacuum. The existence of a non-vacuum state of inflaton perturbation is compatible with the present observations of the power spectrum of the distribution of temperature fluctuations of the CMB. But remarkably, the deviations from a Gaussian distribution, the so called non-gaussianities of the CMB temperature distribution, are much more sensitive than the power spectrum to the presence of initial inflaton perturbation at the onset of inflation. Therefore, the study of non-gaussianities offers a sharp tool that can provide valuable information regarding the initial state of inflaton perturbations. We plan to complete the analysis made in [4] by extending it in several directions. We want to study in detail how the effect produced by the presence of initial inflaton perturbation can be distinguished from other sources of non-gaussianities. On the other hand, we want to extend the analysis to other models of inflation with a more generic kinetic term in the inflaton Lagrangian (the so called K-inflationary models) and to the presence of more than one field driving inflation (the so called hybrid inflation). The enhancement of non-gaussianities may be different for different models and it would be very interesting to be able to differentiate among them. The new generation of observational projects, with the PLANCK mission among them, are expected to provide detailed information regarding the non-gaussianities in the CMB temperature distribution. Therefore, the analysis that we propose can be very valuable to extract information about the initial state of inflaton perturbations at the onset of inflation and about the mechanism driving inflation itself.

Primordial perturbations and quantum gravity.

At the present time, physicists have some confidence about the physics taking place at energy scales reached by current particles accelerators. However, at higher energies we enter into the speculative regime. In particular, at present there is not agreement about the physical processes governing the behaviour of the very early universe. Our uncertainty about the physics at the beginning and before inflation prevents us from making predictions about the state of the universe at that time. Concretely, we do not have any information about the initial quantum state of inflaton perturbations. As pointed out in the previous item, we have shown [1] that the non-gaussianities present in the distribution of temperature of the CMB may reflect the characteristics of this quantum state, and therefore, one could use the observation of non-gaussianities to rule out models for the physics taking place before the onset of inflation. Nowadays there exist proposals for quantum gravity theories that are able to provide a consistent picture of the very early universe. This is the case of Loop Quantum Gravity, the canonical quantization of GR using the so-called Ashtekar-Barbero variables [2]. The application of the techniques of Loop Quantum Gravity to the dynamics of the early universe, so called Loop Quantum Cosmology, has provided a consistent picture that is able to resolve the big bang singularity, in a robust way, due to quantum effects [3]. This scenario provides a complete picture of the history of the universe previous to the onset of inflation. Our objective is to use the generic features provided by quantum cosmology to compute the properties of the quantum state of inflaton perturbations at the onset of inflation. The form of this state is expected to reflect the peculiarities of the theoretical model. This initial state for inflaton perturbation will produce a particular spectrum of non-gaussianities in the CMB due to the process of gravitationally-induced stimulated particle creation during inflation that can be eventually compared to the upcoming observational data. This analysis can open a window for testing the phenomenological consequences of quantum cosmology.

Quantum-to-classical transition for primordial perturbations.

Primordial fluctuations in the very early universe acquire classical properties when their wavelengths become larger than the Hubble radius. As each mode crosses outside the Hubble horizon, it decouples from the microphysics and freezes as a classical fluctuation [1]. There are several ways one could think this process. One way is to think the gravitational field as making a measurement of each mode of the inflaton fluctuation field a few Hubble times of its exit from the Hubble sphere. If this measurement of the inflaton dispersion spectrum is similar to standard measurements in quantum mechanics (i.e, quantum state reduction), then it should proceed almost instantaneously at the time when the measurement is carried out. If the process is regarded in the open system approach, with environment-induced decoherence, the decoherence time (for modes with wavelengths bigger than the Hubble radius) is of order of the Hubble time during inflation [2]. This effect can also been understood due to the huge squeezing of the initial quantum state. This makes the process indistinguishable from a classical stochastic process. In any case, the field amplitude emerges then as the robust pointer basis [3]. One of our aims is to further investigate this issue since it may be closely related, in a deep way, to the observable properties of the cosmic microwave background. For instance, the precise way quantum fluctuations are converted into classical perturbations (i.e., the location of the Heisenberg's cut) may have an impact of the role of ultraviolet divergences on the physical power spectra for wavelengths that today are at observable scales.