Small Sound Speed Research Articles

Unified dark fluid with constant adiabatic sound speed: Including entropic perturbations

In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Because of the relations between the adiabatic sound speed and equations of state ${c}_{s,ad}^{2}(a)=w(a)\ensuremath{-}d\mathrm{ln}(1+w(a))/3d\mathrm{ln}a$, the equation of state can be determined up to an integration constant, in principle, when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its microscale properties are characterized by its equations of state or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscillation, and WMAP 7-yr data of cosmic background radiation, to constrain the possible entropic perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo method. The results show that the cosmic observations favor a small effective sound speed ${c}_{s,\mathrm{eff}}^{2}={0.00155}_{\ensuremath{-}0.00155}^{+0.000319}$ in the $1\ensuremath{\sigma}$ region.

Insensitivity of Sub-Kelvin Electron-Phonon Coupling to Substrate Properties

We have examined the role of the substrate on electron-phonon coupling in normal-metal films of Mn-doped Al at temperatures below 1 K. Normal metal-insulator-superconductor junctions were used to measure the electron temperature in the films as a function of Joule heating power and phonon temperature. Theory suggests that the distribution of phonons available for interaction with electrons in metal films may depend on the acoustic properties of the substrate, namely, that the electron-phonon coupling constant Σ would be larger on the substrate with smaller sound speed. In contrast, our results indicate that within experimental error (typically ±10%), Σ is unchanged among the two acoustically distinct substrates used in our investigation.

NON-GAUSSIANITY FROM THE BISPECTRUM IN GENERAL MULTIPLE FIELD INFLATION

We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We derive the three-point function for the curvature perturbation which depends on both adiabatic and entropy perturbations, in the small sound speed limit and at leading order in the slow-roll expansion. The contribution from the entropy perturbations has a different momentum dependence if the sound speed for the entropy perturbations is different from the adiabatic one, which provides a possibility to distinguish the multi-field models from single field models.

One-loop corrections to the power spectrum in general single-field inflation

We perfom a thorough computation of the one-loop corrections from both scalar and tensor degrees of freedom to the power spectrum of curvature fluctuations for non-canonical Lagrangians in single-field inflation. We consider models characterized by a small sound speed cs, which produce large non-Gaussianities. As expected, the corrections turn out to be inversely proportional to powers of cs; evaluating their amplitudes it is then possible to derive some theoretical bounds on the sound speed by requesting the conditions necessary for perturbation theory to hold.

Rotating a curvaton brane in a warped throat

In this paper we study a curvaton model obtained by considering a probeanti-D3-brane with angular motion at the bottom of a KS throatwith approximate isometries. We calculate the spectrum ofcurvature perturbations and the non-Gaussianities of this model.Specifically, we consider the limit of relativistic rotation ofthe curvaton brane which leads to a small sound speed, and thus itcan be viewed as an implementation of the DBI-curvaton mechanism. We findthat the primordial power spectrum is nearly scale-invariant whilethe non-Gaussianity of local type is sizable and that ofequilateral type is usually large and negative. Moreover, we studyboth the theoretical and observational constraints on this model,and find that there exists a sizable allowed region for the phasespace of this model.

Bispectrum signatures of a modified vacuum in single field inflation with a small speed of sound

Deviations from the Bunch-Davies vacuum during an inflationary period can leave a testable imprint on the higher-order correlations of the CMB and large scale structures in the Universe. The effect is particularly pronounced if the statistical non-Gaussianity is inherently large, such as in models of inflation with a small speed of sound, e.g. DBI. First reviewing the motivations for a modified vacuum, we calculate the non-Gaussianity for a general action with a small speed of sound. The shape of its bispectrum is found to most resemble the `orthogonal' or `local' templates depending on the phase of the Bogolyubov parameter. In particular, for DBI models of inflation the bispectrum can have a profound `local' template feature, in contrast to previous results. Determining the projection into the observational templates allows us to derive constraints on the absolute value of the Bogolyubov parameter. In the small sound speed limit, the derived constraints are generally stronger than the constraint obtainable from the power spectrum. The bound on the absolute value of the Bogolyubov parameter ranges from the 10−6 to the 10−3 level for H/Λc = 10−3, depending on the specific details of the model, the sound speed and the phase of the Bogolyubov parameter.

Full trispectrum in single field DBI inflation

We compute the tree-level connected four-point function of the primordial curvature perturbation for a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This model includes K-inflation and DBI-inflation as particular cases. We show that, at the leading order in the slow-roll expansion and in the small sound speed limit, there are two important tree-level diagrams for the trispectrum. One is a diagram where a scalar mode is exchanged and the other is a diagram where the interaction occurs at a point, i.e. a contact interaction diagram. The scalar exchange contribution is comparable to the contact interaction contribution. For the DBI-inflation model, in the so-called equilateral configuration, the scalar exchange trispectrum is maximized when the angles between the four momentum vectors are equal and in this case the amplitude of the trispectrum from the scalar exchange is one order of magnitude higher than the contact interaction trispectrum.

Lorentz boost and non-Gaussianity in multifield DBI inflation

We show that higher-order actions for cosmological perturbations in the multifield Dirac-Born-Infeld (DBI) inflation model are obtained by a Lorentz boost from the rest frame of the brane to the frame where the brane is moving. We confirm that this simple method provides the same third- and fourth-order actions at leading order in slow roll and in the small sound speed limit as those obtained by the usual Arnowitt-Deser-Misner formalism. As an application, we compute the leading order connected four-point function of the primordial curvature perturbation coming from the intrinsic fourth-order contact interaction in the multifield DBI-inflation model. At third order, the interaction Hamiltonian arises purely by the boost from the second-order action in the rest frame of the brane. The boost acts on the adiabatic and entropy modes in the same way, thus there exists a symmetry between the adiabatic and entropy modes. But at fourth order this symmetry is broken due to the intrinsic fourth-order action in the rest frame and the difference between the Lagrangian and the interaction Hamiltonian. Therefore, contrary to the three-point function, the momentum dependence of the purely adiabatic component and the components including the entropic contributions are different in the four-point function. This suggests that the trispectrum can distinguish the multifield DBI-inflation model from the single field DBI-inflation model.

Rapidly-varying speed of sound, scale invariance and non-Gaussian signatures

We show that curvature perturbations acquire a scale invariant spectrum for any constant equation of state, provided thefluid has a suitably time-dependent sound speed. In order for modes to exit the physical horizon, and in orderto solve the usual problems of standard big bang cosmology, we argue that the only allowed possibilities are inflationary(albeit not necessarily slow-roll) expansion or ekpyrotic contraction. Non-Gaussianities offer many distinguish features.As usual with a small sound speed, non-Gaussianity can be relatively large, around current sensitivity levels.For DBI-like lagrangians, the amplitude is negative in the inflationary branch, and can be either negative or positive in the ekpyrotic branch.Unlike the power spectrum, the three-point amplitude displays a large tilt that, in the expanding case, peaks on smallest scales. While the shape is predominantly of the equilateral type in the inflationary branch, as in DBI inflation, it is of the local form in the ekpyrotic branch. The tensor spectrum is also generically far from scale invariant.In the contracting case, for instance, tensors are strongly blue tilted, resulting in an unmeasurably small gravity wave amplitude oncosmic microwave background scales.

Loop corrections to cosmological perturbations in multi-field inflationary models

We investigate one-loop quantum corrections to the power spectrum of adiabatic perturbation from entropy modes/adiabatic mode cross-interactions in multiple DBI inflationary models. We find that due to the non-canonical kinetic term in DBI models, the loop corrections are enhanced by slow-varying parameter ϵ and small sound speed cs. Thus, in general the loop-corrections in multi-DBI models can be large. Moreover, we find that the loop-corrections from adiabatic/entropy cross-interaction vertices are IR finite.

The acoustic field in biomedical tissue with midscale inhomogeneities

Biomedical ultrasound is often used for investigations within and close to tissue inhomogeneities, such as lesions and plaques, that are midsized compared with the ultrasound wavelength. The scaled wavenumber is typically in the range 1 to 100. Even with small (less than 10%) sound speed variations, such objects are associated with very complicated diffractive field magnitude modulations. The corresponding phase modulations are much more regular, and this observation is the basis for the method described in this paper. The acoustic field can be expressed in terms of a scattering integral. For biomedical parameters, calculations with the widely used Born approximation give accurate results in only very limited circumstances. In this paper we demonstrate the importance of the initial phase estimate, and introduce the Phase Corrected Scattering Integral (PCSI) method. We show that remarkably accurate results for the acoustic field can be obtained from a single evaluation of the scattering integral if this incorporates an initial estimate of the phase modulation imposed by the inhomogeneity. A simple ray model can be used to find the phase correction. The PCSI method deals very effectively with scattering due to small changes in sound speed and irregular geometry, both characteristic of biomedical problems.

Kinematic Density Waves in Accretion Disks

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain nonintersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655–40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetimes, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.

Primordial perturbations and non-Gaussianities in DBI and general multifield inflation

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

Primordial Fluctuations and Non-Gaussianities in Multifield Dirac-Born-Infeld Inflation

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.

Non-Gaussianity from the bispectrum in general multiple field inflation

We study the non-Gaussianity from the bispectrum in multi-field inflation models with ageneral kinetic term. The models include multi-field K-inflation and multi-fieldDirac–Born–Infeld (DBI) inflation as special cases. We find that, in general, the soundspeeds for the adiabatic and entropy perturbations are different and they canbe smaller than 1. Then the non-Gaussianity can be enhanced. Multi-field DBIinflation is shown to be a special case where both sound speeds are the samedue to a special form of the kinetic term (Langlois et al 2008 Preprint 0804.3139[hep-th]). We derive the exact second-and third-order actions including metricperturbations. In the small sound speed limit and at leading order in the slow-rollexpansion, we derive the three-point function for the curvature perturbation whichdepends on both adiabatic and entropy perturbations. The contribution fromthe entropy perturbations has a different momentum dependence if the soundspeeds for the entropy and adiabatic perturbations are different, which provides apossibility to distinguish multi-field models from single-field models. On the otherhand, in the multi-field DBI case, the contribution from the entropy perturbationshas the same momentum dependence as the pure adiabatic contributions andit only changes the amplitude of the three-point function (Langlois et al 2008Preprint 0804.3139 [hep-th]). This could help to ease the constraints on the DBI-inflationmodels.

Observational signatures and non-Gaussianities of general single-field inflation

We perform a general study of primordial scalar non-Gaussianities in single-fieldinflationary models in Einstein gravity. We consider models where the inflaton Lagrangianis an arbitrary function of the scalar field and its first derivative, and the sound speed isarbitrary. We find that under reasonable assumptions, the non-Gaussianity iscompletely determined by five parameters. In special limits of the parameter space, onefinds distinctive ‘shapes’ of the non-Gaussianity. In models with a small soundspeed, several of these shapes would become potentially observable in the nearfuture. Different limits of our formulae recover various previously known results.

DBI inflation in the tip region of a warped throat

Previous work on DBI inflation, which achieves inflation through the motion of a $D3$ brane as it moves through a warped throat compactification, has focused on the region far from the tip of the throat. Since reheating and other observable effects typically occur near the tip, a more detailed study of this region is required. To investigate these effects we consider a generalized warp throat where the warp factor becomes nearly constant near the tip. We find that it is possible to obtain 60 or more e-folds in the constant region, however large non-gaussianities are typically produced due to the small sound speed of fluctuations. For a particular well-studied throat, the Klebanov-Strassler solution, we find that inflation near the tip may be generic and it is difficult to satisfy current bounds on non-gaussianity, but other throat solutions may evade these difficulties.

Approximating acoustic field uncertainty in underwater sound channels

Precise acoustic field prediction relies on accurate knowledge of many environmental parameters. Uncertainty in any of the inputs to a propagation routine leads to uncertainty in the predicted field. The most accurate but time-consuming method of assessing the resulting field uncertainty is Monte Carlo simulation, which requires calculating the field with many possible combinations of inputs. This presentation covers a method to approximately determine the uncertainty in the predicted field, using only one additional field calculation for each uncertain parameter, when the input uncertainties are relatively small. The method relies on identifying how variations in uncertain input parameters can be mapped into spatial displacements in the original field calculation. Simultaneous uncertainty in multiple input parameters is handled using a net effective spatial displacement. In addition to expected values and standard deviations, the method allows for the generation of complete probability density functions for the uncertain predicted field. Calculated field amplitude results for both ideal and more realistic range-independent sound channels having small depth and sound speed uncertainty are shown and compared to Monte Carlo simulations at several source-receiver ranges. [Work sponsored by the Office of Naval Research, Code 321OA.]

Growth of perturbations in dark matter coupled with quintessence

We consider the evolution of linear perturbations in models with a nonminimal coupling between dark matter and scalar field dark energy. Growth of matter inhomogeneities in two examples of such models proposed in the literature are investigated in detail. Both of these models are based on a low-energy limit of effective string theory action, and have been previously shown to naturally lead to late acceleration of the universe. However, we find that these models can be ruled out by taking properly into account the impact of the scalar field coupling on the formation of structure in the dark matter density. In particular, when the transition to acceleration in these models begins, the interaction with dark energy enchances the small scale clustering in dark matter much too strongly. We discuss the the role of an effective small scale sound speed in such models with a coupled dark sector.

A multifrequency scintillation probing of current in a stratified ocean

Transverse flow of inhomogeneous fluid produces fluctuation of the acoustic signal passing through it. These fluctuations vary with the CW signal frequency change due to variation of the Fresnel zone and diffraction angles. Respectively, the fluctuations of signals at two different frequencies are coherent in a low frequency range of the spectrum and noncoherent in the high-frequency band. The frequency cutoff of the correlation function of the signal fluctuation depends upon the flow velocity at given fine structure of the flow. Measurement of the cutoff frequency allows one therefore to determine the flow velocity of the fluid. The principles of this approach in application to the probing of current in the homogeneous in average ocean were considered previously [J. Fuks, K. Naugolnykh, and M. Charnotskii, J. Acoust. Soc. Am. 109, 2730–2738 (2001)]. In a stratified ocean the sound field has a modal structure connected with the fact that rays tend to bend toward region of smaller sound speed. The features of the multifrequency method of current measurements in a stratified ocean when the fine structure of the flow is determined by the realistic spectrum of internal waves and the sound field is presented as a modal set are considered in the present paper.