Search Results (43 total)

Gravitational wave production from bubble collisions was calculated in the early 1990s using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulas for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.

A primordial gravitational wave background with positive (blue) spectral index is expected in several nonstandard inflationary cosmologies where the stress-energy tensor violates the null energy condition. Here we show that a sizable amount of blue gravitational waves is compatible with current cosmological and astrophysical data. So far most of the works on parameter estimation from cosmic microwave background data have assumed a negative or negligible spectral index. The present limits on cosmological parameters, especially on the scalar spectral index, widen up considerably when one allows also for blue tilts of the tensor spectrum. Since the amplitude of the cosmic microwave background (CMB) B-mode polarization is larger in these models, future data from Planck are likely to provide crucial measurements.

It has been shown that generalized Einstein-Aether theories may lead to significant modifications to the nonrelativistic limit of the Einstein equations. In this paper we study the effect of a general class of such theories on the Solar System. We consider corrections to the gravitational potential in negative and positive powers of distance from the source. Using measurements of the perihelion shift of Mercury and time delay of radar signals to Cassini, we place constraints on these corrections. We find that a subclass of generalized Einstein-Aether theories is compatible with these constraints.

We consider a two-brane system in five-dimensional anti–de Sitter space-time. We study particle creation due to the motion of the physical brane which first approaches the second static brane (contraction) and then recedes from it (expansion). The spectrum and the energy density of the generated gravitons are calculated. We show that the massless gravitons have a blue spectrum and that their energy density satisfies the nucleosynthesis bound with very mild constraints on the parameters. We also show that the Kaluza-Klein modes cannot provide the dark matter in an anti–de Sitter braneworld. However, for natural choices of parameters, backreaction from the Kaluza-Klein gravitons may well become important. The main findings of this work have been published in the form of a Letter [R. Durrer and M. Ruser, Phys. Rev. Lett. 99, 071601 (2007)].

In braneworld cosmology the expanding Universe is realized as a brane moving through a warped higher-dimensional spacetime. Like a moving mirror causes the creation of photons out of vacuum fluctuations, a moving brane leads to graviton production. We show that, very generically, Kaluza-Klein (KK) particles scale like stiff matter with the expansion of the Universe and can therefore not represent the dark matter in a warped braneworld. We present results for the production of massless and KK gravitons for bouncing branes in five-dimensional anti–de Sitter space. We find that for a realistic bounce the back reaction from the generated gravitons will be most likely relevant. This Letter summarizes the main results and conclusions from numerical simulations which are presented in detail in a long paper [M. Ruser and R. Durrer, arXiv:0704.0790].

We investigate microlensing in the case where the lens is considered as an extended object. We use a multipolar expansion of the lens potential and show that the time-varying nature of the quadrupole contribution allows to separate it from the mass and spin contributions and leads to specific modulations of the amplification signal. As example we study the case of binary system lenses in our galaxy. The modulation is observable if the rotation period of the system is smaller than the time over which the amplification is significant and if the impact parameter of the passing light ray is sufficiently close to the Einstein radius so that the amplification is large. Observations of this modulation can reveal important information on the quadrupole and thus on the gravitational radiation emitted by the binary lens. Even if not observed directly, because of their importance the quadrupole modulation has to be included in the error budget for high magnification (μ≤7) microlensing events.

We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.

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.

We demonstrate that if k-essence can solve the coincidence problem and play the role of dark energy in the Universe, the fluctuations of the field have to propagate superluminally at some stage. We argue that this implies that successful k-essence models violate causality. It is not possible to define a time ordered succession of events in a Lorentz invariant way. Therefore, k-essence cannot arise as a low energy effective field theory of a causal, consistent high energy theory.

We show that the dipole of the luminosity distance is a useful observational tool which allows us to determine the Hubble parameter as a function of redshift H(z). We determine the number of supernovae needed to achieve a given precision for H(z) and to distinguish between different models for dark energy. We analyze a sample of nearby supernovae and find a dipole consistent with the cosmic microwave background at a significance of more than 2σ.

We derive an expression for the luminosity distance in a perturbed Friedmann universe. We define the correlation function and the power spectrum of the luminosity distance fluctuations and express them in terms of the initial spectrum of the Bardeen potential. We present semianalytical results for the case of a pure CDM (cold dark matter) universe. We argue that the luminosity distance power spectrum represents a new observational tool which can be used to determine cosmological parameters. In addition, our results shed some light into the debate whether second order small scale fluctuations can mimic an accelerating universe.

We consider supergravity models in which the lightest supersymmetric particle (LSP) is a stable gravitino. The next-to-lightest supersymmetric particle (NLSP) freezes out with its thermal relic density and then decays after (10⁵–10¹⁰)sec⁡, injecting high-energy photons into the cosmic plasma. These photons heat up the electron plasma which then thermalizes with the cosmic microwave background (CMB) via Compton scattering, bremsstrahlung and double-Compton scattering. Contrary to previous studies which assume instantaneous energy injection, we solve the full kinetic equation for the photon number density with a source term describing the decay of the NLSP. This source term is based on the requirement that the injected energy be almost instantaneously redistributed by Compton scattering, hence leading to a time-dependent chemical potential. We investigate the case of a stau NLSP and determine the constraints on the gravitino and stau masses from observations of the CMB spectrum by assuming that all gravitino LSPs come from stau NLSP decays. Unlike the analytical approximations, we find that there may be a stau mass below which the constraint from the CMB spectrum vanishes.

We study braneworlds in a five-dimensional bulk, where cosmological expansion is mimicked by motion through AdS₅. We show that the five-dimensional graviton reduces to the four-dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, the massless four-dimensional graviton obeys the usual 4D equation and is therefore also not generated in a radiation-dominated universe.

In their recent paper, Kosowsky et al. commented about our earlier work in which we derived very stringent limits on the amplitude of a primordial magnetic field from gravitational wave production. They argue that our limits are erroneous. In this short Comment we defend our result.

We show that scalar as well as vector and tensor metric perturbations in the Randall-Sundrum II braneworld allow normalizable tachyonic modes, i.e., possible instabilities. These instabilities require nonvanishing initial anisotropic stresses on the brane. We show with a specific example that within the Randall-Sundrum II model, even though the tachyonic modes are excited, no instability develops. We argue, however, that in the cosmological context instabilities might in principle be present. We conjecture that the tachyonic modes are due to the singularity of the orbifold construction. We illustrate this with a simple but explicit toy model.

We study the effect of a helicity component of a primordial magnetic field on the tensor part of the cosmic microwave background temperature anisotropies and polarization. We give analytical approximations for the tensor contributions induced by helicity, discussing their amplitude and spectral index in dependence of the power spectrum of the primordial magnetic field. We find that an helical magnetic field creates a parity odd component of gravity waves inducing parity odd polarization signals. However, only if the magnetic field is close to scale invariant and if its helical part is close to maximal, the effect is sufficiently large to be observable. We also discuss the implications of causality on the magnetic field spectrum.

We investigate both analytically and numerically the evolution of scalar perturbations generated in models which exhibit a smooth transition from a contracting to an expanding Friedmann universe. If the perturbation equations are formulated as second order equations for either the Bardeen potential Ψ or the curvature perturbation on uniform comoving hypersurfaces ζ, at best one of them can stay regular during the transition. We find that the resulting spectral index in the late radiation dominated universe depends on which of these two variables passes regularly through the transition. The results can be parametrized by the exponent q defining the rate of contraction of the universe, or equivalently through the equation of state w=(2-q)/3q of the background fluid. For q>~-1 / 2 we find that there are no stable cases where both Ψ and ζ are regular during the transition. In particular, for 0<q≪1, we find that the resulting spectral index is close to scale invariant if Ψ is regular, whereas it has a steep blue behavior if ζ is regular. We also show that as long as q<~1 and we are in the regime where corrections can be ignored, perturbations remain small during contraction in the sense that there exists a gauge in which all the metric and matter perturbation variables are small. This work has important implications for the current debate concerning the nature of perturbations evolving through a collapsing regime into an expanding one: it shows that if in the ekpyrotic model, where 0<q≪1, the Bardeen potential passes regularly through the transition, this leads to a nearly scale invariant spectrum with n=1-2q, whereas in the case of dilaton-driven string cosmology we have the opposite situation. There it is assumed that ζ passes regularly through the transition, leading to a very blue spectrum of highly suppressed perturbations.

We investigate in detail the question of whether a nonvanishing cosmological constant is required by the present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are taken into account. We also discuss the differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the Cosmic Background Explorer (COBE)-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies. We find that in a flat universe the Bayesian analysis requires Ω_Λ≠0 to more than 3σ, while in the frequentist approach Ω_Λ=0 is still within 3σ for a value of h<~0.48. Both conclusions hold regardless of the initial conditions.

At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre-big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase. We show that, under certain physically motivated and quite generic assumptions on the high energy corrections, one obtains n=0 for the spectrum of scalar perturbations in the original pre-big bang model (with a vanishing potential). With the same assumptions, when an exponential potential for the dilaton is included, a scale invariant spectrum (n=1) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre-big bang and ekpyrotic scenario. We also derive the resulting spectrum for arbitrary power law scale factors matched to a radiation-dominated era.

We compute the gravity waves induced by anisotropic stresses of stochastic primordial magnetic fields. The nucleosynthesis bound on gravity waves is then used to derive a limit on the magnetic field amplitude as a function of the spectral index. The obtained limits are extraordinarily strong: If the primordial magnetic field is produced by a causal process, leading to a spectral index n>~2 on superhorizon scales, galactic magnetic fields produced at the electroweak phase transition or earlier have to be weaker than B_λ<~10^-27 G. If they are induced during an inflationary phase (reheating temperature T∼10¹⁵ GeV) with a spectral index n∼0, the magnetic field has to be weaker than B_λ<~10^-39 G. Only very red magnetic field spectra, n∼-3, are not strongly constrained. We also find that a considerable amount of the magnetic field energy is converted into gravity waves. The gravity wave limit derived in this work rules out most of the proposed processes for primordial seeds for the large scale magnetic fields observed in galaxies and clusters.

In the light of the recent high quality data of the cosmic microwave background anisotropies, several estimations of cosmological parameters have been published. We study to what extent these estimations depend on assumptions about the initial conditions of the cosmological perturbations, which are usually supposed to be adiabatic. We show that, for more generic initial conditions, not only the best fit values are very different but the allowed parameter range enlarges dramatically. This raises the question which cosmological information (matter content of the Universe vs physics of inflation) can be reliably extracted from these data.

We derive dynamical equations to describe a single 3-brane containing fluid matter and a scalar field coupling to the dilaton and the gravitational field in a five-dimensional bulk. First, we show that a scalar field or an arbitrary fluid on the brane cannot evolve to cancel the cosmological constant in the bulk. Then we show that the Randall-Sundrum model is unstable under small deviations from the fine-tuning between the brane tension and the bulk cosmological constant and even under homogeneous gravitational perturbations. Implications for brane world cosmologies are discussed.

During recent years it has become clear that global O(N) defects and U(1) cosmic strings do not lead to the pronounced first acoustic peak in the power spectrum of anisotropies of the cosmic microwave background (CMB) which has recently been observed to high accuracy. Inflationary models cannot easily accommodate the low second peak indicated by the data. Here we construct causal scaling seed models which reproduce the first and second peak. Future, more precise CMB anisotropy and polarization experiments will however be able to distinguish them from the ordinary adiabatic models.

We present an alternative scenario for cosmic structure formation where initial fluctuations are due to Kalb-Ramond axions produced during a pre-big bang phase of inflation. We investigate whether this scenario, where the fluctuations are induced by seeds and therefore are of isocurvature nature, can be brought in agreement with present observations by a suitable choice of cosmological parameters. We also discuss several observational signatures which can distinguish axion seeds from standard inflationary models. We finally discuss the gravitational wave background induced in this model and we show that it may be well within the range of future observations.

We compute the energy spectra for massless Kalb-Ramond axions in four-dimensional anisotropic string cosmology models. We show that, when integrated over directions, the four-dimensional anisotropic model leads to infrared divergent spectra similar to the one found in the isotropic case.