Non-adiabatic Perturbations Research Articles

TDiff invariant field theories for cosmology

We study scalar field theories invariant under transverse diffeomorphismsin cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar field theory with only kinetic term could drive inflation and generate a nearly scale invariant (red-tilted) spectrum of density fluctuations. We also present a detailed analysis of cosmological perturbations and show that the breaking of full Diff invariance generically induces new non-adiabatic pressure perturbations. A simple scalar field dark matter model based on a purely kinetic term that exhibits the same clustering properties as standard cold dark matter is also presented.

Opening the reheating box in multifield inflation

The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code.Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as ∼ 50%, while our semi-analytic estimates can reduce this error to ∼ 10%. We conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations.

Superadiabaticity in Jupiter and Giant Planet Interiors

Abstract Interior models of giant planets traditionally assume that at a given radius (i.e., pressure) the density should be larger than or equal to the one corresponding to a homogeneous, adiabatic stratification throughout the planet (referred to as the “outer adiabat”). The observations of Jupiter’s gravity field by Juno combined with the constraints on its atmospheric composition appear to be incompatible with such a profile. In this Letter, we show that the above assumption stems from an incorrect understanding of the Schwarzschild–Ledoux criterion, which is only valid on a local scale. In order to fulfill the buoyancy stability condition, the density gradient with pressure in a nonadiabatic region must indeed rise more steeply than the local adiabatic density gradient. However, the density gradient can be smaller than the one corresponding to the outer adiabat at the same pressure because of the higher temperature in an inhomogeneously stratified medium. Deep enough, the density can therefore be lower than the one corresponding to the outer adiabat. We show that this is permitted only if the slope of the local adiabat becomes shallower than the slope of the outer adiabat at the same pressure, as found in recent Jupiter models due to the increase of both specific entropy and adiabatic index with depth. We examine the dynamical stability of this structure and show that it is stable against nonadiabatic perturbations. The possibility of such an unconventional density profile in Jupiter further complicates our understanding of the internal structure and evolution of (extrasolar) giant planets.

Overshooting, critical Higgs inflation and second order gravitational wave signatures

The self coupling lambda of the Higgs boson in the Standard Model may show critical behavior, i.e. the Higgs potential may have a point at an energy scale sim 10^{17-18} GeV where both the first and second derivatives (almost) vanish. In this case the Higgs boson can serve as inflaton even if its nonminimal coupling to the curvature scalar is only {{mathcal {O}}}(10), thereby alleviating concerns about the perturbative unitarity of the theory. We find that just before the Higgs as inflaton enters the flat region of the potential the usual slow-roll conditions are violated. This leads to “overshooting” behavior, which in turn strongly enhances scalar curvature perturbations because of the excitation of entropic (non-adiabatic) perturbations. For appropriate choice of the free parameters these large perturbations occur at length scales relevant for the formation of primordial black holes. Even if these perturbations are not quite large enough to trigger copious black hole formation, they source second order tensor perturbations, i.e. primordial gravitational waves; the corresponding energy density can be detected by the proposed space-based gravitational wave detectors DECIGO and BBO.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Constant roll inflation in multifield models

Constant roll inflation is analyzed in the presence of multi scalar fields which are assumed to be described by a constant roll rate each. The different cases are studied and the corresponding potentials are reconstructed. The exact solutions are obtained, which show a similar behaviour to the single scalar field model. For one of the cases analyzed in the paper, the so-called adiabatic field also constant rolls while entropy perturbations become null, while the second case may lead to non-adiabatic perturbations. Both cases can fit well the Planck data by assuming the appropriate values for the free parameters of the models.

Cosmological constraints on nonadiabatic dark energy perturbations

The exact nature of dark energy is currently unknown and its cosmological perturbations, when dark energy is assumed not to be the cosmological constant, are usually modeled as adiabatic. Here we explore the possibility that dark energy might have a nonadiabatic component and we examine how it would affect several key cosmological observables. We present analytical solutions for the growth rate and growth index of matter density perturbations and compare them to both numerical solutions of the fluid equations and an implementation in the Boltzmann code CLASS, finding that they all agree to well below one percent. We also perform a Monte Carlo analysis to derive constraints on the parameters of the nonadiabatic component using the latest cosmological data, including the temperature and polarization spectra of the Cosmic Microwave Background as observed by Planck, the Baryon Acoustic Oscillations, the Pantheon type Ia supernovae compilation and lastly, measurements of Redshift Space Distortions (RSD) of the growth rate of matter perturbations. We find that the amplitude of the nonadiabatic pressure perturbation is consistent with zero within $1\sigma$. Finally, we also present a new, publicly available, RSD likelihood for MontePython based on the "Gold 2018" growth rate data compilation.

Acoustic Adiabatic Propagation Based on Topological Pumping in a Coupled Multicavity Chain Lattice

Stimulated adiabatic passage, as an efficient energy transfer in correlated systems, was intensively studied in condensed matter physics and quantum optics. Recently, a paradigm shift has been made to bring up quantum-classical analogs, giving rise to the acoustic version of stimulated Raman adiabatic passage and others. In this work, we focus on the adiabatic propagation of sound under topological protection, i.e., topological-pumping-based acoustic adiabatic propagation. We first study the topological pumping of sound in a two-state multicavity chain lattice, including the Su-Schrieffer-Heeger model, in which the acoustic energy is adiabatically transferred between the two topological end states under specific coupling interactions. Then, we consider the adiabatic propagation of sound via a dark mode in a three-state system. The three states correspond to two end states and one interface state in a heterostructured multicavity chain lattice, which is topologically protected. In a finite system, the three states strongly hybridize with the threefold energy degeneracy lifted. The hybridized states reside in the band gap of the systematic Hamiltonian spectrum in the topological pumping process, leading to a strong robustness against nonadiabatic perturbation, which allows for a faster and more efficient topological adiabatic propagation of acoustic waves.

Entropy production in affine inflation

Multiple scalar fields nonminimally interacting through pure affine gravity are considered to generate primordial perturbations during an inflationary phase. The couplings considered give rise to two distinct sources of entropy perturbations that may not be suppressed in the long wavelength limit. The first is merely induced by the presence of more than one scalar and arises even in the minimal coupling limit. The second source however is restricted to nonminimal interaction. Unlike the case of metric gravity, and due to the absence of anisotropic stresses, the second source disappears for single scalar, showing that nonminimal couplings become relevant to non-adiabatic perturbations only when more than one scalar field are considered. Hence the notion of adiabaticity is not affected by the transition to minimal coupling contrary to the metric gravity case where it is confused by changing the frames. Precise data that might be able to neatly track different sources of isocurvature modes, if any, must not only distinguish between different models of inflation but also determine the most viable approach to gravity which underlies the inflationary dynamics itself.

Baryon-CDM isocurvature galaxy bias with IllustrisTNG

We study the impact that baryon-CDM relative density perturbations δbc have on galaxy formation using cosmological simulations with the IllustrisTNG model. These isocurvature (non-adiabatic) perturbations can be induced primordially, if multiple fields are present during inflation, and are generated before baryon-photon decoupling when baryons did not comove with CDM. The presence of long-wavelength δbc perturbations in our simulations is mimicked by modifying the ratios of the cosmic densities of baryons Ωb and CDM Ωc, at fixed total matter density Ωm. We measure the corresponding galaxy bias parameter bδbc as the response of galaxy abundances to δbc. When selecting by total host halo mass, bδbc is negative and it decreases with mass and redshift. Stellar-mass selected simulated galaxies show a weaker or even the opposite trend because of the competing effects of δbc on the halo mass function and stellar-to-halo-mass relations. We show that simple modeling of the latter two effects describes bδbc for stellar-mass-selected objects well. We find bδbc =0.6 for M* = 1011 M⊙/h and z=0.5, which is representative of BOSS DR12 galaxies. For δbc modes generated by baryon-photon interactions, we estimate the impact on the DR12 power spectrum to be below 1%, and shifts on inferred distance and growth rate parameters should not exceed 0.1%.

The effect of anisotropic stress and non-adiabatic pressure perturbations on the evolution of the comoving curvature perturbation

We derive the equation for the evolution of the curvature perturbation on the comoving time slice, , in the presence of anisotropic and non-adiabatic terms in the energy–momentum tensor of matter fields. The equation is obtained by manipulating the perturbed Einstein’s equations in the comoving time slice. It could be used to study the evolution of the comoving curvature perturbations for systems with an anisotropic energy–momentum tensor, such as in the presence of vector fields, in the presence of entropy, such as in a multi-field system, or in modified gravity theories. As a simple application, after checking that the comoving time slice for a multi-field system does not coincide with the uniform field time slice in general, we use the equation in the case of two minimally coupled scalar fields and derive a closed set of equations for the curvature and entropy perturbations on the comoving time slice.

Precision tests of nonadiabatic perturbation theory with measurements on the DT molecule

This paper presents new measurements and calculations on the rovibrational transitions of DT, an istopolog of the hydrogen molecule composed of deuterium and tritium. The authors show an improved accuracy with respect to previous results and a good agreement between experiment and theory.

Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading $\alpha^5\,m$ and the next-to-leading $\alpha^6\,m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of $10^{-3}$--$10^{-7}$ cm$^{-1}$, and are provided by simple to use computer code.

Nonadiabatic relativistic correction in H2 , D2 , and HD

We calculate the nonadiabatic relativistic correction to rovibrational energy levels of H$_2$, D$_2$, and HD molecules using the nonadiabatic perturbation theory. This approach allows one to obtain nonadiabatic corrections to all the molecular levels with the help of a single effective potential. The obtained results are in very good agreement with the previous direct calculation of nonadiabatic relativistic effects for dissociation energies and resolve the reported discrepancies of theoretical predictions with recent experimental results.

Analog gravity in nonisentropic fluids

The analog acoustic metric has been originally derived for adiabatic acoustic perturbations propagating in an isentropic irrotational ideal fluid. In the framework of a Lagrangian hydrodynamic description we demonstrate that under certain conditions the usual acoustic metric can be derived for nonisentropic fluids. In a special case when the pressure takes a special form and the nonadiabatic perturbations are neglected the adiabatic acoustic perturbations corresponding to massless phonons propagate in an analog metric of the usual type.

Large-scale structure in mimetic Horndeski gravity

In this paper, we propose to use the mimetic Horndeski model as a model for the dark universe. Both cold dark matter (CDM) and dark energy (DE) phenomena are described by a single component, the mimetic field. In linear theory, we show that this component effectively behaves like a perfect fluid with zero sound speed and clusters on all scales. For the simpler mimetic cubic Horndeski model, if the background expansion history is chosen to be identical to a perfect fluid DE (PFDE) then the mimetic model predicts the same power spectrum of the Newtonian potential as the PFDE model with zero sound speed. In particular, if the background is chosen to be the same as that of LCDM, then also in this case the power spectrum of the Newtonian potential in the mimetic model becomes indistinguishable from the power spectrum in LCDM on linear scales. A different conclusion may be found in the case of non-adiabatic perturbations. We also discuss the distinguishability, using power spectrum measurements from LCDM N-body simulations as a proxy for future observations, between these mimetic models and other popular models of DE. For instance, we find that if the background has an equation of state equal to −0.95 then we will be able to distinguish the mimetic model from the PFDE model with unity sound speed. On the other hand, it will be hard to do this distinction with respect to the LCDM model.

Revealing the nonadiabatic nature of dark energy perturbations from galaxy clustering data

We study structure formation using relativistic cosmological linear perturbation theory in the presence of intrinsic and relative (with respect to matter) non-adiabatic dark energy perturbations. For different dark energy models we assess the impact of non-adiabaticity on the matter growth promoting a comparison with growth rate data. The dark energy models studied lead to peculiar signatures of the (non)adiabatic nature of dark energy perturbations in the evolution of the $f \sigma_{8}(z)$ observable. We show that non-adiabatic DE models become close to be degenerated with respect to the $\Lambda$CDM model at first order in linear perturbations. This would avoid the identification of the non-adiabatic nature of dark energy using current available data. Therefore, such evidence indicates that new probes are necessary to reveal the non-adiabatic features in the dark energy sector.

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer.

The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5)neV and 47.13(8)Å. The binding energy agrees with its first experimental determination of 151.9(13.3)neV [Zeller etal., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].

Perfect fluid in Lagrangian formulation due to generalized three-form field

A Lagrangian formulation of perfect fluid due to a noncanonical three-form field is investigated. The thermodynamic quantities such as energy density, pressure and the four velocity are obtained and then analyzed by comparing with the k-essence scalar field. The nonrelativistic matter due to the generalized three-form field with the equation of state parameter being zero is realized while it might not be possible for the k-essence scalar field. We also found that nonadiabatic pressure perturbations can be possibly generated. The fluid dynamics of the perfect fluid due to the three-form field corresponds to the system in which the number of particles is not conserved. We argue that it is interesting to use this three-form field to represent the dark matter for the classical interaction theory between dark matter and dark energy.

On the admissible range of the radial temperature gradient and Brünt-Väisäla frequency in the mantle and core: I. Main relations

The question of ambiguity in the solution of the inverse problem for determining the Brunt-Vaisala frequency in the Earth’s mantle from the entire set of the up-to-date data on seismicity, free oscillations, and forced nutations of the Earth, as well as the data on the Earth’s total mass and total moment of inertia, is considered. Based on the results of a series of numerical experiments, the band of admissible distributions of the Brunt-Vaisala frequency and mantle density with depth is calculated. This estimate is used for investigating the convective and gravitational stability of the different regions of the mantle against relatively small adiabatic and nonadiabatic perturbations. The generalization of the known Rayleigh criterion of convective stability of homogeneous and a nonself-gravitating incompressible viscous fluid for the case of a compressible self-gravitating fluid is given. A system of the ordinary eight-order differential equations with complex coefficients and homogeneous boundary conditions, whose eigenvalues determine the transition from the stable state to instability, is obtained. Examples of the numerical determination of these eignevalues are presented. For interpreting the data about the band of the admissible distributions of the Brunt-Vaisala frequency with depth, the notion of the effective bulk modulus of the medium at different depths is introduced. This quantity governs the depth changes in temperature in a convecting mantle and allows us to make a conclusion about the role of heat conduction and the radial heterogeneity of the mantle composition without imposing any constraints on the convection mechanism. It is shown that within the present-day observation errors in the frequencies of the Earth’s free oscillations, the simplest reasonable model is that in which the ratio of the effective bulk modulus to its adiabatic value in the lower and middle mantle is 1.043 ± 0.05. The closeness of this value to unity indicates that convection in the lower and middle mantle is fairly close to adiabatic. At the same time, when the analysis only relies on seismic data and on the information about the periods of the free oscillations of the Earth, there is a significant uncertainty in the models of the effective bulk modulus distribution in the upper mantle and crust. This uncertainty precludes us from making purely empirically derived conclusions that reliably and unambiguously describe the role of the effects of heat conduction and radially heterogeneous material composition in the convection in the upper mantle.