Gravitational Wave Power Research Articles

Tilt of primordial gravitational wave spectrum in a universe with sterile neutrinos

In this work, we constrain the spectral index $n_t$ of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the $\Lambda$CDM+$r$+$\nu_s$+$n_t$ model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of $n_t$. To constrain the parameters of sterile neutrino, we also utilize the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, and the cosmic shear data. We find that due to the fact that the BICEP2 data are most sensitive to the multipole $\ell\sim150$ corresponding to $k\sim0.01$ Mpc$^{-1}$, there exists a strong anticorrelation between $n_t$ and $r_{0.002}$ in the BICEP2 data, and this further results in a strongly blue-tilt spectrum. However, a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of $r_{0.002}$. By using the full data sets, we obtain $m_{\nu,{\rm{sterile}}}^{\rm{eff}}=0.48^{+0.11}_{-0.13}$ eV, $N_{\rm{eff}}=3.73^{+0.34}_{-0.37}$, and $n_t=0.96^{+0.48}_{-0.63}$ for the $\Lambda$CDM+$r$+$\nu_s$+$n_t$ model.

Gravitational waves from oscillon preheating

Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks.

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

Detecting a stochastic gravitational wave background, particularly radiation from individually unresolvable super-massive black hole binary systems, is one of the primary targets for Pulsar Timing Arrays. Increasingly more stringent upper limits are being set on these signals under the assumption that the background radiation is isotropic. However, some level of anisotropy may be present and the characterisation of the power at different angular scales carries important information. We show that the standard analysis for isotropic backgrounds can be generalised in a conceptually straightforward way to the case of generic anisotropic background radiation by decomposing the angular distribution of the gravitational wave power on the sky into multipole moments. We introduce the concept of generalised overlap reduction functions which characterise the effect of the anisotropy multipoles on the correlation of the timing residuals from the pulsars timed by a Pulsar Timing Array. In a search for a signal characterised by a generic anisotropy, the generalised overlap reduction functions play the role of the so-called Hellings and Downs curve used for isotropic radiation. We compute the generalised overlap reduction functions for a generic level of anisotropy and Pulsar Timing Array configuration. We also provide an order of magnitude estimate of the level of anisotropy that can be expected in the background generated by super-massive black hole binary systems.

Exact Scale-Invariant Background of Gravitational Waves from Cosmic Defects

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction.

Mass-energy and momentum extraction by gravitational wave emission in the merger of two colliding black holes: The non-head-on case

We examine numerically the post-merger regime of two nonspining holes in non-head-on collisions in the realm of nonaxisymmetric Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed and evolved via the Robinson-Trautman equation. The numerical integration is performed using a Galerkin spectral method which is sufficiently stable to reach the final configuration of the remnant black hole, when the gravitational wave emission ceases. The initial data contains three independent parameters, the ratio mass $\ensuremath{\alpha}$ of the individual colliding black holes, their initial premerger infalling velocity and the incidence angle of collision ${\ensuremath{\rho}}_{0}$. The remnant black hole is characterized by its final boost parameter, rest mass and scattering angle. The motion of the remnant black hole is restricted to the plane determined by the directions of the two initial colliding black holes, characterizing a planar collision. The net momentum fluxes carried out by gravitational waves are confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole for a large domain of initial data parameters. Our analysis is based on the Bondi-Sachs four-momentum conservation laws. The process of mass-energy extraction is shown to be less efficient as the initial data departs from the head-on configuration. Head-on collisions (${\ensuremath{\rho}}_{0}={0}^{o}$) and orthogonal collisions (${\ensuremath{\rho}}_{0}=90\ifmmode^\circ\else\textdegree\fi{}$) constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction. On the contrary, head-on collisions and orthogonal collisions constitute, respectively, lower and upper bounds for the momentum of the remnant. Distinct regimes of gravitational wave emission (bursts or quiescent emission) are characterized by the analysis of the time behavior of the gravitational wave power as a function of $\ensuremath{\alpha}$. In particular, the net gravitational wave flux is nonzero for equal-mass colliding black holes in non-head-on collisions. The momentum extraction and the patterns of the momentum fluxes, as a function of the incidence angle, are examined. The relation between the incidence angle and the scattering angle closely approximates a relation for the inelastic collision of classical particles in Newtonian dynamics.

Graviton production in the scaling of a long-cosmic-string network

In a previous paper [K. Kleidis, D. B. Papadopoulos, E. Verdaguer, and L. Vlahos, Phys. Rev. D 78, 024027 (2008).] we considered the possibility that (within the early-radiation epoch) there has been (also) a short period of a significant presence of cosmic strings. During this radiation-plus-strings stage the Universe matter-energy content can be modeled by a two-component fluid, consisting of radiation (dominant) and a cosmic-string fluid (subdominant). It was found that, during this stage, the cosmological gravitational waves---that had been produced in an earlier (inflationary) epoch---with comoving wave numbers below a critical value (which depends on the physics of the cosmic-string network) were filtered, leading to a distorsion in the expected (scale-invariant) cosmological gravitational wave power spectrum. In any case, the cosmological evolution gradually results in the scaling of any long-cosmic-string network and, hence, after a short time interval, the Universe enters into the late-radiation era. However, along the transition from an early-radiation epoch to the late-radiation era through the radiation-plus-strings stage, the time dependence of the cosmological scale factor is modified, something that leads to a discontinuous change of the corresponding scalar curvature, which, in turn, triggers the quantum-mechanical creation of gravitons. In this paper we discuss several aspects of such a process, and, in particular, the observational consequences on the expected gravitational-wave power spectrum.

Primordial power spectra from anisotropic inflation

We examine cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton, breaking conformal invariance. When the coupling between the gauge field and the inflaton takes a specific form, inflation becomes anisotropic and anisotropy can persist throughout inflation, avoiding Wald's no-hair theorem. After discussing scenarios in which anisotropy can persist during inflation, we calculate the dominant effects of a small persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra using the "in-in" formalism of perturbation theory. We find that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.

Stochastic gravitational waves from a new type of modified Chaplygin gas

We propose a new scenario for the early Universe where there is a smooth transition between an early de Sitter-like phase and a radiation-dominated era. In this model, the matter content is modeled by a new type of generalized Chaplygin gas [6] for the early Universe, with an underlying scalar field description. We study the gravitational waves generated by the quantum fluctuations. In particular, we calculate the gravitational-wave power spectrum, as it would be measured today, following the method of the Bogoliubov coefficients. We show that the high frequencies region of the spectrum depends strongly on one of the parameters of the model. On the other hand, we use the number of $e$ folds, along with the power spectra and spectral index of the scalar perturbations, to constrain the model observationally.

Semi-analytic calculation of the gravitational wave signal from the electroweak phase transition for general quartic scalar effective potentials

Upcoming gravitational wave (GW) detectors might detect a stochastic background of GWs potentially arising from many possible sources, including bubble collisions from a strongly first-order electroweak phase transition. We investigate whether it is possible to connect, via a semi-analytical approximation to the tunneling rate of scalar fields with quartic potentials, the GW signal through detonations with the parameters entering the potential that drives the electroweak phase transition. To this end, we consider a finite temperature effective potential similar in form to the Higgs potential in the Standard Model (SM). In the context of a semi-analytic approximation to the three dimensional Euclidean action, we derive a general approximate form for the tunneling temperature and the relevant GW parameters. We explore the GW signal across the parameter space describing the potential which drives the phase transition. We comment on the potential detectability of a GW signal with future experiments, and physical relevance of the associated potential parameters in the context of theories which have effective potentials similar in form to that of the SM. In particular we consider singlet, triplet, higher dimensional operators, and top-flavor extensions to the Higgs sector of the SM. We find that the addition of a temperature independent cubic term in the potential, arising from a gauge singlet for instance, can greatly enhance the GW power. The other parameters have milder, but potentially noticeable, effects.

A MODEL FOR GRAVITATIONAL WAVE EMISSION FROM NEUTRINO-DRIVEN CORE-COLLAPSE SUPERNOVAE

Abridged: Using a suite of progenitor models, neutrino luminosities, and two- dimensional (2D) simulations, we investigate the matter gravitational-wave (GW) emission from postbounce phases of neutrino-driven core-collapse supernovae (CCSNe). The relevant phases are prompt and steady-state convection, the standing accretion shock instability (SASI), and asymmetric explosions. For the stages before explosion, we propose a model for the source of GW emission. Downdrafts of the postshock-convection/SASI region strike the protoneutron star "surface" with large speeds and are decelerated by buoyancy forces. We find that the GW amplitude is set by the magnitude of deceleration and, by extension, the downdraft's speed and the vigor of postshock-convective/SASI motions. However, the characteristic frequencies, which evolve from ~100 Hz after bounce to ~300-400 Hz, are primarily independent of these speeds, but are set by the deceleration timescale, which is in turn set by the buoyancy frequency at the lower boundary of postshock convection. Consequently, the GW characteristic frequencies are dependent upon a combination of core structure attributes, specifically the dense-matter equation of state (EOS) and details that determine the gradients at the boundary, including the accretion-rate history, the EOS at subnuclear densities, and neutrino transport. During explosion, the high frequency signal wanes and is replaced by a strong low frequency, ~10s of Hz, signal that reveals the general morphology of the explosion (i.e. prolate, oblate, or spherical). However, current and near-future GW detectors are sensitive to GW power at frequencies >50 Hz. Therefore, the signature of explosion will be the abrupt reduction of detectable GW emission.

Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae

We present two-dimensional (axisymmetric) neutrino-hydrodynamic simulations of the long-time accretion phase of a 15 Mprogen- itor star after core bounce and before the launch of a supernova explosion, when non-radial hydrodynamic instabilities like convection occur in different regions of the collapsing stellar core and the standing accretion shock instability (SASI) leads to large-amplitude os- cillations of the stalled shock with a period of tens of milliseconds. Our simulations were performed with the Prometheus-Vertex code, which includes a multi-flavor, energy-dependent neutrino transport scheme and employs an effective relativistic gravitational potential. Testing the influence of a stiff and a soft equation of state for hot neutron star matter, we find that the non-radial mass motions in the supernova core impose a time variability on the neutrino and gravitational-wave signals with larger amplitudes, as well as higher frequencies in the case of a more compact nascent neutron star. After the prompt shock-breakout burst of electron neutrinos, a more compact accreting remnant produces higher neutrino luminosities and higher mean neutrino energies. The observ- able neutrino emission in the SASI sloshing direction exhibits a modulation of several ten percent in the luminosities and around 1 MeV in the mean energies with most power at typical SASI frequencies between roughly 20 and 100 Hz. The modulation is caused by quasi-periodic variations in the mass accretion rate of the neutron star in each hemisphere. At times later than ∼50-100 ms after bounce, the gravitational-wave amplitude is dominated by the growing low-frequency (<200 Hz) signal associated with anisotropic neutrino emission. A high-frequency wave signal results from nonradial gas flows in the outer layers of the anisotropically accreting neutron star. Right after bounce such nonradial mass motions occur due to prompt post-shock convection in both considered cases and contribute mostly to the early wave production around 100 Hz. Later they are instigated by the SASI and by convective overturn that vigorously stir the neutrino-heating and cooling layers, and also by convective activity developing below the neutrinosphere. The gravitational-wave power then peaks at about 300-800 Hz, connected to changes in the mass quadrupole moment on a timescale of milliseconds. Distinctively higher spectral frequencies originate from the more compact and more rapidly contracting neutron star. Both the neutrino and gravitational-wave emission therefore carry information that is characteristic of the properties of the nuclear equation of state in the hot remnant. The detectability of the SASI effects in the neutrino and gravitational-wave signals is briefly discussed.

Gravity waves signatures from anisotropic preinflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a preinflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary $e$-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole $\ensuremath{\ell}$ as ${\ensuremath{\ell}}^{\ensuremath{-}p}$, where $p$ depends on the slope of the initial GW power spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become nonlinear, they can significantly alter the geometry before the onset of inflation.

Imprints of cosmic strings on the cosmological gravitational wave background

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space-time can be treated as the Schrodinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding Universe with constant effective potential, there is a critical value (k_c) of the comoving wave-number which discriminates the metric perturbations into oscillating (k > k_c) and non-oscillating (k < k_c) modes. As a consequence, if the non-oscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a non-vanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (sub-dominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time (\Dl \ta) the Universe becomes radiation-dominated. The evolution of the non-oscillatory GW modes during \Dl \ta (while they were outside the horizon), results in the distortion of the GW power spectrum from what it is anticipated in a pure radiation-model, at present-time frequencies in the range 10^{-16} Hz < f < 10^5 Hz.

Large gravitational waves and the Lyth bound in multi-brane inflation

It is shown that multi-M5-brane inflation in heterotic M-theory gives riseto a detectable gravitational wave power spectrum with tensor fractionr typically larger than the projected experimental sensitivity,rexp = 0.01. A measurable gravitational wave power spectrum entails a large inflationary energy scaleand a super-Planckian inflaton variation. They present serious problems for particle theorymodel building as regards a reliable effective field theory description. These problems areeased or even absent in multi-brane inflation models and multi-M5-brane inflation, inparticular.

Gravitational waves from stochastic relativistic sources: Primordial turbulence and magnetic fields

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does not, in general, vanish on scales larger than the correlation scale. If the variable is a divergence-free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and they both peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.

Cosmic microwave background fluctuations from gravitational waves: An analytic approach

We develop an analytic approach to calculation of the temperature and polarisation power spectra of the cosmic microwave background due to inflationary gravitational waves. This approach complements the more precise numerical results by providing insight into the physical origins of the features in the power spectra. We explore the use of analytic approximations for the gravitational-wave evolution, making use of the WKB approach to handle the radiation-matter transition. In the process, we describe scaling relations for the temperature and polarisation power spectra. We illustrate the dependence of the amplitude, shape, and peak locations on the details of recombination, the gravitational-wave power spectrum, and the cosmological parameters, and explain the origin of the peak locations in the temperature and polarisation power spectra. The decline in power on small scales in the polarisation power spectra is discussed in terms of phase-damping. In an appendix we detail numerical techniques for integrating the gravitational-wave evolution in the presence of anisotropic stress from free-streaming neutrinos.

Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes

The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order perturbation theory have been shown to give the limits of applicability of the method without the need for comparison with numerical relativity results. Those second order calculations have been carried out in a fixed coordinate gauge, a method that entails conceptual and computational difficulties. Here we demonstrate a gauge invariant approach to such calculations. For a specific set of models (requiring head on collisions and quadrupole dominance of both the first and second order perturbations), we give a self contained gauge invariant formalism. Specifically, we give (i) wave equations and sources for first and second order gauge invariant wave functions; (ii) the prescription for finding Cauchy data for those equations from initial values of the first and second fundamental forms on an initial hypersurface; (iii) the formula for computing the gravitational wave power from the evolved first and second order wave functions.

Large primordial gravitational wave background in a class of BSI ΛCDM models

We consider the primordial gravitational wave (GW) background in a class of spatially flat inflationary cosmological models with cold dark matter (CDM), a cosmological constant, and a broken scale-invariant (BSI) step-like primordial (initial) spectrum of adiabatic perturbations produced in an exactly solvable inflationary model where the inflaton potential has a rapid change of its first derivative at some point. In contrast to inflationary models with a scale-free initial spectrum, these models may have a GW power spectrum the amplitude (although not the shape) of which is arbitrary for fixed amplitude and shape of the adiabatic perturbation power spectrum. In the presence of a positive cosmological constant, the models investigated here possess the striking property that a significant part of the large-angle cosmic microwave background (CMB) temperature anisotropy observed in the COBE experiment is a result of primordial GW. Confronting the models with existing observational data on CMB angular temperature fluctuations, galaxy clustering and peculiar velocities of galaxies, we find that, for the best parameter values ΩΛ≈0.7 and h≈0.7, the GW contribution to the CMB anisotropy can be as large as that of the scalar fluctuations.

Gravitational wave spectra from pole-like inflations based on generalized gravity theories

We present a general and unified formulation which can handle the classical evolution and quantum generation processes of the cosmological gravitational wave in a broad class of generalized gravity theories. Applications are demonstrated in several inflation models based on the scalar-tensor theory, the induced gravity and the low-energy effective action of string theories. The gravitational wave power spectra based on the vacuum expectation value of the quantized fluctuating metric during the pole-like inflation stages are derived in analytic forms. Assuming that the gravity theory transits to an Einstein one while the relevant scales remain in the superhorizon scale, we derive the consequent power spectra and the directional fluctuations of the relic radiation produced by the gravitational wave. The spectra seeded by the vacuum fluctuations in the pole-like inflation models based on the generalized gravity show a distinguished common feature ( spectrum) which differs from the scale-invariant one ( spectrum) generated in an exponential inflation in Einstein gravity which is supported by observations.

Confusion noise level due to galactic and extragalactic binaries

We have revised our earlier rough estimate of the combined galactic and extragalactic binary confusion noise level curve for gravitational waves. This was done to correct some numerical errors and to allow for roughly three frequency bins worth of information about weaker sources being lost for each galactic binary signal that is removed from the data. The results are still based on the spectral amplitude estimates for different types of galactic binaries reported by Hils et al in 1990, and assume that the gravitational wave power spectral densities for other galaxies are proportional to the optical luminosities. The estimated confusion noise level drops to the LISA instrumental noise level at between roughly 3 and 8 mHz.