Tensor Fluctuations Research Articles

Vacuum radiation pressure fluctuations on electrons

This paper is a continuation of a study of the properties and applications of quantum stress tensor fluctuations. Here we treat the vacuum fluctuations of the electromagnetic energy-momentum flux operator which has been averaged in space and time. The probability distribution of these fluctuations depends upon the details of this averaging and may allow fluctuations very large compared to the variance. The possibility of detecting their effects on electrons will be considered. The averaging of the flux operator will arise from the interaction of an electron with a wave packet containing real photons. The vacuum radiation pressure fluctuations can exert a force on the electron in any direction, in contrast to the effect of scattering by real photons. Some numerical estimates of the effect will be given. Published by the American Physical Society 2024

Correlated scalar perturbations and gravitational waves from axion inflation

Abstract The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the gravitational energy density, Ω GW , at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of ζ and by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of 10-4 ÷ 10-2.

Impact of dark sector preheating on CMB observables

The prediction of a nearly scale-invariant spectrum of curvature and tensor fluctuations is among the main features of cosmic inflation. The current measurements of the primordial fluctuations in the cosmic microwave background (CMB) provide tight constraints on the amplitude of the scalar and tensor spectra, and the scalar tilt. However, the precise connection between these observables and a given inflationary model, depends on the expansion history between the end of inflation and the beginning of the radiation dominated era, which corresponds to the reheating epoch. This mapping between horizon exit and reentry of fluctuations, parametrized by the number of e-folds N*, can therefore be affected by the presence of a transient epoch of non-perturbative particle production during reheating (preheating). Using a combination of perturbative and lattice computations, we quantify the impact of preheating in a non-equilibrated dark matter sector on the CMB observables, under the assumption of a simultaneous perturbative decay of the inflaton into Standard Model particles. Combined with structure formation constraints, this allows us to impose stringent bounds on the post-inflationary reheating temperature.

Interpretation of quantum theory in a cosmological perspective

We reconsider the problem of the interpretation of the quantum theory (QT) in the perspective of the entire universe and of the Bohr's idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. We distinguish a classical or macroscopic state, and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state is specified by a set of variables, a classical energy–momentum tensor and conserved currents, which are supposed to have always a well-defined value. The microscopic state and dynamics are expressed by the usual QT formalism. For the macroscopic variables, a basic distribution of probability is postulated in terms of quantum operators and a statistical operator, what replace the usual probability rule of QT. For the universe, a variance of the ΛCDM model with Ω=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega = 1$$\\end{document} is assumed, one inflaton, a Goldstone type potential, initial time at t=-∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t = - \\infty$$\\end{document}, expectation values of all fundamental fields vanishing for t→-∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t \ o - \\infty$$\\end{document}. The scalar fluctuations in the cosmic microwave background is correctly explained, but the absence of the tensor fluctuations remains not understood. This seems to suggest that gravity is a pure classical phenomenon what perhaps could be accommodated in our framework.

IKKT thermodynamics and early universe cosmology

Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. Recently, it was shown that space-time can emerge with a scale-invariant spectrum of cosmological perturbations which is sourced by thermal fluctuations of the BFSS model at finite temperature. Inspired by these results, we begin a study of the IKKT model at finite temperature. We find that in this model, which is closely related to the BFSS model at finite temperature, thermal fluctuations can also source a scale-invariant spectrum of scalar and tensor fluctuations.

Gravitational waves during Higgs inflation from complex geometrical scalar-tensor theory of gravity

In this paper we investigate tensor fluctuations of the metric at the end of a Higgs inflationary period in the context of a recently introduced complex geometrical scalar-tensor theory of gravity. In our model the Higgs field has a geometrical origin and the affine connection is determined by the Palatini’s principle. Additionally, we consider an extra contribution to the tensor-fluctuations equation coming from the vacuum term in the energy–momentum tensor associated to the Higgs field. The Higgs potential is rescaled by the non-canonicity function of the kinetic term of the field which is modified by the symmetry group of the background geometry. We obtain a nearly scale invariant spectrum and a scalar to tensor ratio in agreement with PLANCK 2018 cosmological results.

Tensor fluctuations in the early universe

In standard inflationary cosmology, scalar and tensor perturbations grew as the Universe expanded and froze when their wavelengths exceeded the Hubble horizon, producing a tell-tale signature in the fluctuation spectrum and amplitude of the cosmic microwave background (CMB). But there are now very good reasons to examine whether structure formation could also have begun via the seeding of quantum fluctuations in a non-inflationary field. In this Letter, we study and compare the scalar and tensor modes produced in these two scenarios, and demonstrate that upcoming observations to measure the B-mode polarization of the CMB may be able to differentiate between them. Whereas both scalar and tensor modes should be observable if the field was inflationary, only scalar modes would be present in the CMB if it were not. Should gravity be purely classical, however, the tensor modes would have avoided canonical quantization in all cases, resulting in unmeasurably weak gravitational waves. A non-detection of B-mode polarization would thus not completely rule out inflation.

Gravity and matter on a pure geometric thick polynomial f(R) brane

In this paper, the solutions of the pure geometric thick $f(R)$ brane are investigated. The formulation of $f(R)$ is chosen as $f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the brane solution can be calculated, and when $n=3$, $n=4$, and $n=10$, the thick brane solutions are presented. The solutions is stable under linear tensor fluctuation. The zero mode of gravity and scalar field can be localized on thick $f(R)$ branes naturally. The zero mode of vector field and left-chiral fermion can be localized on thick $f(R)$ branes by introducing the coupling with scalar curvature $R$ of spacetime, and the massive resonant modes can be quasilocalized on the brane with the large coupling coefficients.

The application of solution NMR spectroscopy to study dynamics of two-domain calcium-binding proteins

Protein dynamics due to flexible linkers connecting otherwise rigid domains may be critical for the functioning of a variety of biological systems, ranging from membrane transporters to calcium-signaling and the formation of intercellular junctions. Considering that NMR spectroscopy is extremely powerful to characterize dynamics at various time scales, this manuscript brings an overview of the main strategies that have been employed to characterize inter-domain dynamics in relevant biological systems. Emphasis was given to the calcium binding proteins: calmodulin, cadherin, and the Na+/Ca2+ exchanger calcium-sensor domain. The introduction of paramagnetic centers in diamagnetic proteins is seen as key to obtaining unambiguous information about inter-domain dynamics. This is because the self-alignment of one of the domains in multi-domain proteins avoids the problem of dealing with alignment tensor fluctuations in dynamic systems. The combination of residual dipolar couplings (RDCs) and pseudocontact shifts (PCSs) with computational strategies aiming to provide an ensemble description of protein dynamics is seen as the most powerful strategy to gain detailed atomistic information on inter-domain motions. It is noteworthy that the cadherin ectodomains and the Na+/Ca2+ exchanger calcium sensor respond in the same way upon calcium-binding: in the absence of calcium the two domains are flexibly linked to one another and may preferentially sample kinked inter-domain arrangements, while calcium binding stabilizes a rigid and extended inter-domain arrangement. It is thus remarkable that nature chose the same molecular mechanism to promote two very different biological functions that are triggered by calcium signaling: intercellular adhesion by the formation of cadherin dimers and the allosteric regulation of a membrane transporter in the case of the Na+/Ca2+ exchanger.

Missing one-loop contributions in secondary gravitational waves

We find several missing one-loop-order contributions in previous considerations about secondary gravitational waves induced at nonlinear order in cosmological perturbations. We consider a consistent perturbative expansion to third order in cosmological perturbations, including higher-order interactions and iterative solutions ignored in the previous literature. Tensor fluctuations induced by the source with two scalar and one tensor perturbations are correlated with the first-order tensor fluctuation and thus give a one-loop order correction to the tensor-power spectrum. The missing loop correction is scale invariant and negative in the superhorizon region, which secondarily reduces the initial primordial tensor-power spectrum prior to the horizon reentry. Such an IR behavior is very different from the autospectrum of second-order induced tensor modes discussed in the previous literature and can be important for the actual gravitational wave measurements. For a sharp peak of scalar fluctuations with ${A}_{\ensuremath{\zeta}}={10}^{\ensuremath{-}2}$ at ${k}_{*}={10}^{5}\text{ }h/\mathrm{Mpc}$ motivated by the LIGO/Virgo events, we show that the tensor-power spectrum at the cosmic microwave background scale reduces by at most 35%. Hence, the polarization B mode might not be seen because of the reduction of the original tensor spectrum due to the secondary effect of primordial black hole formation.

A hybrid map-Cℓ component separation method for primordial CMB B-mode searches

The observation of the polarised emission from the Cosmic Microwave Background (CMB) from future ground-based and satellite-borne experiments holds the promise of indirectly detecting the elusive signal from primordial tensor fluctuations in the form of large-scale B-mode polarisation. Doing so, however, requires an accurate and robust separation of the signal from polarised Galactic foregrounds. We present a component separation method for multi-frequency CMB observations that combines some of the advantages of map-based and power-spectrum-based techniques, and which is direcly applicable to data in the presence of realistic foregrounds and instrumental noise. We demonstrate that the method is able to reduce the contamination from Galactic foregrounds below an equivalent tensor-to-scalar ratio r FG ≲ 5 × 10-4, as required for next-generation observatories, for a wide range of foreground models with varying degrees of complexity. This bias reduction is associated with a mild ∼20–30% increase in the final statistical uncertainties, and holds for large sky areas, and for experiments targeting both the reionisation and recombination bumps in the B-mode power spectrum.

Frequency spectra analysis of space- and time-averaged quantum stress tensor fluctuations

Observing physical effects of large quantum stress tensor fluctuations requires knowledge of the interactions between the probe and the particles of the underlying quantum fields. The quantum stress tensor operators must first be averaged in time alone or space and time to confer meaningful results, the details of which may correspond to the physical measurement process. We build on prior results to characterize the particle frequencies associated with quantum fluctuations of different magnitudes. For the square of time derivatives of the massless scalar field in a spherical cavity, we find that these frequencies are bounded above in a power law behavior. Our findings provide a way to identify the largest quantum fluctuation that may be probed in experiments relying on frequency-dependent interactions.

Explicit spacetime-symmetry breaking and the dynamics of primordial fields

We study the effects of explicit spacetime-symmetry breaking on primordial tensor fluctuations using an effective-field theory for Lorentz/CPT violation. We find that the graviton is still massless, but that the propagation speed of tensor modes is modified, and we obtain a constraint on the coefficient determining the symmetry breaking on the order of $10^{-15}$ from the recent measurements of the speed of gravity. Due to the symmetry breaking, the de-Sitter phase is modified, and during this inflationary epoch, the power spectrum assumes a slow oscillation around the general-relativity limit; further, we find that the primordial tensor power spectrum retains its scale invariance, but that the amplitude is modified. We also find that the modes which become subhorizon during radiation domination acquire a phase shift proportional to the coefficient for Lorentz violation.

Bulk viscosity of hard sphere fluids by equilibrium and nonequilibrium molecular dynamics simulations.

The bulk viscosity, ηb, of the hard sphere (HS) fluid is computed by equilibrium and nonequilibrium molecular dynamics (NEMD) simulations, the latter using an adaptation of the time-stepping method for continuous potential systems invented by Hoover et al. [Phys. Rev. A 21, 1756 (1980)], which employs an imposed cyclic density variation on the system by affine scaling of the particle coordinates. The time-stepping method employed for HS is validated against exact event-driven hard sphere methodology for a series of equilibrium quantities over a wide density range, including the pressure, singular parts of the hard sphere viscosities, and the nonsingular parts of the shear viscosity time correlation functions. The time steps used are typically only a little smaller than those employed in continuous potential simulations. Exact pressure tensor fluctuation expressions are derived for the singular (or infinite limiting frequency) equilibrium parts of the viscosities, which were employed in the simulations. The values obtained agree well with the predictions of the Enskog theory for all densities considered. The bulk viscosity obtained by NEMD is shown to be noticeably frequency dependent for densities in excess of ∼0.8, decaying approximately exponentially to the Enskog and equilibrium simulation values at all densities considered for frequencies in excess of ∼5 in hard sphere units. Temperature profiles during the cycle and the effects of strain amplitude on the computed frequency dependent bulk viscosity are presented. The bulk viscosity increases with the maximum density amplitude.

Fractality in cosmic topology models with spectral action gravity

We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of spacetime. We show that the topology constrains the possible fractal structures, and in turn the correction terms to the spectral action due to fractality distinguish the various cosmic topology candidates, with effects detectable in a slow-roll inflation scenario, through the power spectra of the scalar and tensor fluctuations. We also discuss explicit effects of the presence of fractal structures on the gravitational waves equations.

CFTs blueshift tensor fluctuations universally

The strong constraints of conformal symmetry cause any nearly-conformal sector to blueshift tensor fluctuations in cosmology. Hidden sectors with approximate conformal symmetry, which may be quite large, are a well-motivated extension of physics beyond the Standard Models of particle physics and cosmology. They can therefore lead to a detectable shift in the tensor tilt for next-generation CMB and gravitational wave experiments. We compute the leading-order contribution to the in-in graviton two-point function from virtual loops in such sectors to demonstrate this universal effect. In units where a single conformally-coupled scalar is 1, limits from Stage-IV CMB experiments could bound the size of this extra sector to be smaller than ∼1015, under a plausible calculational assumption backed by a simple power counting argument. This would be sufficient to rule out N-Naturalness as a complete resolution of the hierarchy problem.

Parity violating non-Gaussianity from axion-gauge field dynamics

We study scalar-tensor-tensor and tensor-scalar-scalar three point cross correlations generated by the dynamics of a transiently rolling spectator axion-$\mathrm U(1)$ gauge field model during inflation. In this framework, tensor and scalar fluctuations are sourced by gauge fields at the non-linear level due to gravitational interactions, providing a chiral background of gravitational waves while keeping the level of scalar fluctuations at the observationally viable levels at CMB scales. We show that the gravitational couplings between the observable sector and gauge fields can also mediate strong correlations between scalar and tensor fluctuations, generating an amplitude for the mixed type three-point functions that is parametrically larger -- $f_{\rm NL} \simeq \mathcal{O}(1-10) (r/0.01)^{3/2}$-- compared to the single-field realizations of inflation. As the amplification of the gauge field sources are localized around the time of horizon exit, the resulting mixed bispectra are peaked {\it close} to the equilateral configurations. The shape dependence, along with the scale dependence and the parity violating nature of the mixed bispectra can serve as a distinguishing feature of the underlying axion-gauge field dynamics and suggest a careful investigation of their signatures on the CMB observables including cross correlations between temperature T and E,B polarization modes.

Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries

In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor Kμν. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of Kμν. Using these observationally consistent forms of Kμν, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard ΛCDM (Λ Cold Dark Matter) model.

Infrared effects in the late stages of black hole evaporation

As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of sim {M}_i^2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ {M}_i^{2/3} , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order sim {M}_i^2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ {M}_i^2/M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

Space and time averaged quantum stress tensor fluctuations

We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuum state, from which the underlying probability distribution can be constructed. For the normal-ordered square of the time derivative of a massless scalar field in a spherical cavity with finite degrees of freedom, analysis of the tails of these distributions confirms previous results based on the analytical treatment of the high moments. We find that the probability of large vacuum fluctuations is reduced when spatial averaging is included, but the tail still decreases more slowly than exponentially as the magnitude of the measured eigenvalues increases, suggesting vacuum fluctuations may not always be subdominant to thermal fluctuations and opening up the possibility of experimental observation under the right conditions.