The energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress and therefore generates gravitational waves. It has been argued in the literature (Caprini & Durrer \cite{CD}) that this gravitational wave production can be very strong and that back-reaction cannot be neglected. On the other hand, a gravitational wave background does affect the evolution of magnetic fields. It has also been argued (Tsagas et al. \cite{Tsagas:2001ak},\cite{Tsagas:2005ki}) that this can lead to very strong amplification of a primordial magnetic field. In this paper we revisit these claims and study back reaction to second order.
A mechanism for suppressing the cosmological constant is developed, based on an analogy with a superconducting phaseshift in which free fermions coupled perturbatively to a weak gravitational field are in an unstable false vacuum state. The coupling of the fermions to the gravitational field generates fermion condensates with zero momentum and a phase transition induces a nonperturbative transition to a true vacuum state by producing a positive energy gap $Δ$ in the vacuum energy, identified with $\sqrtΛ$, where $Λ$ is the cosmological constant. In the strong coupling limit a large cosmologica…
Similar to QCD, general relativity has a $Θ$ sector due to large diffeomorphisms. We make explicit, for the first time, that the gravitational CP violating $Θ$ parameter is non-perturbatively related to the cosmological constant. A gravitational pseudoscalar coupling to massive fermions gives rise to general relativity from a topological $B\wedge F$ theory through a chiral symmetry breaking mechanism. We show that a gravitational Peccei-Quinn like mechanism can dynamically relax the cosmological constant.
Several mechanisms exist for generating a stochastic background of gravitational waves in the period following inflation. These mechanisms are generally classical in nature, with the gravitational waves being produced from inhomogeneities in the fields that populate the early universe and not quantum fluctuations. The resulting stochastic background could be accessible to next generation gravitational wave detectors. We develop a framework for computing such a background analytically and computationally. As an application of our framework, we consider the stochastic background of gravitational…
Quantum fluctuation of unstable modes about gravitational instantons causes the instability of flat space at finite temperature, leading to the spontaneous process of nucleating quantum black holes. The energy-density of quantum black holes, depending on the initial temperature, gives the cosmological term, which naturally accounts for the inflationary phase of Early Universe. The reheating phase is attributed to the Hawking radiation and annihilation of these quantum black holes. Then, the radiation energy-density dominates over the energy-density of quantum black holes, the Universe started …
Cosmological constant problem (in its various versions) is arguably the deepest gap in our understanding of theoretical physics, the solution to which may very likely require revisiting the Einstein theory of gravity. In this letter, I argue that the simplest consistent way to decouple gravity from the vacuum energy (and hence solve the problem) is through the introduction of an incompressible gravitational aether fluid. The theory then predicts that gravitational constant for radiation is 33% larger than that of non-relativistic matter, which is preferred by most cosmological observations (wi…
Within the framework of the minimum quadratic Poincare gauge theory of gravity in the Riemann-Cartan spacetime we study the influence of gravitational vacuum energy density (a cosmological constant) on the dynamics of various gravitating systems. It is shown that the inclusion of the cosmological term can lead to gravitational repulsion. For some simple cases of spatially homogeneous cosmological models with radiation we obtain non-singular solutions in form of elementary functions and elliptic integrals.
We study the infrared effective theory of gravity that stems from the quantum trace anomaly. Quantum fluctuations of the metric induce running of the cosmological constant and the Newton constant at cosmological scales. By imposing the generalized Bianchi identity we obtain a prediction for the scale dependence of the dark matter and dark energy densities in terms of the parameters of the underlying conformal theory. For certain values of the model parameters the dark energy equation of state and the observed spectral index of the primordial density fluctuations can be simultaneously reproduce…
The aim of this contribution is to provide a short introduction to recently investigated models in which our accessible universe is a four-dimensional submanifold, or brane, embedded in a higher dimensional spacetime and ordinary matter is trapped in the brane. I focus here on the gravitational and cosmological aspects of such models with a single extra-dimension.
We analyze the bending of light by galaxies or clusters of galaxies in the presence of the cosmological term. Going over to the Friedmann-Robertson-Walker coordinates, used in fact for the description of actual observations, we demonstrate that the cosmological constant does not influence practically the lensing effect.
In a toy model we derive the gravitational equation on a self-gravitating curved D-brane. The effective theory on the brane is drastically changed from the ordinal Einstein equation. The net cosmological constant on the brane depends on a tuning between the brane tension and the brane charges. Moreover, non-zero matter stress tensor exists if the net cosmological constant is not zero. This fact indicates a direct connection between matters on the brane and the dark energy.
The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.
We study the propagation of axial gravitational waves in Friedman universes. The evolution equation is obtained in the Regge-Wheeler gauge. The gravitational waves obey the Huygens principle in the radiation dominated era, but in the matter dominated universe their propagation depends on their wavelengths, with the scale fixed essentially by the Hubble radius. Short waves practically satisfy the Huygens principle while long waves can backscatter off the curvature of a spacetime.
It has recently been suggested that collapse of neutron stars induced by a phase transition to quark matter can be a considerable source of gravitational waves with kHz frequencies. We demonstrate that if about one percent of all neutron stars undergo this process, the resulting cosmological gravitational wave background would reach about 10^-10 times the critical density. The background would peak at kHz frequencies and could have an observationally significant tail down to Hz frequencies. It would be comparable or higher than other astrophysical backgrounds, for example, from ordinary core c…
The mass function of primordial black holes created through the near-critical gravitational collapse is calculated in a manner fairly independent of the statistical distribution of underlying density fluctuation, assuming that it has a sharp peak on a specific scale. Comparing it with various cosmological constraints on their mass spectrum, some newly excluded range is found in the volume fraction of the region collapsing into black holes as a function of the horizon mass.
We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover…
We present the formalism for the covariant treatment of gravitational radiation in a magnetized environment and discuss the implications of the field for gravity waves in the cosmological context. Our geometrical approach brings to the fore the tension properties of the magnetic force lines and reveals their intricate interconnection to the spatial geometry of a magnetised spacetime. We show how the generic anisotropy of the field can act as a source of gravitational wave perturbations and how, depending on the spatial curvature distortion, the magnetic tension can boost or suppress waves pass…
The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the expanding universe, predicts something different for the propagation of gravity waves on cosmological distance scales. This analysis indicates that gravitational radiation may not propagate as an unattenuated wave where effects of the Hubble expansion are felt. In such cases the energy does not travel over such large length scales but is evanescent and dissipat…
Brane worlds are theories with extra spatial dimensions in which ordinary matter is localized on a (3+1) dimensional submanifold. Such theories could have interesting consequences for particle physics and gravitational physics. In this essay we concentrate on the cosmological constant (CC) problem in the context of brane worlds. We show how extra-dimensional scenarios may violate Lorentz invariance in the gravity sector of the effective 4D theory, while particle physics remains unaffected. In such theories the usual no-go theorems for adjustment of the CC do not apply, and we indicate a possib…
We reconsider the virial theorem in the presence of a positive cosmological constant Lambda. Assuming steady state, we derive an inequality of the form rho >= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from a spherically symmetric one. This, among others, indicates that flattened matter distributions like e.g. clusters or superclusters, with low density, cannot be in gravitational equilibrium.
The cosmological constant Lambda affects gravitational lensing phenomena. The contribution of Lambda to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study in the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Due to Lambda the unresolved images are slightly demagnified, the radius of the Einstein ring decreases and the time delay increases. The effect is however negligible for near lenses. In the case of null cosmological constant, we provide some updated results on lensing by a…
We study the effect of a cosmological constant $Λ$ on the propagation and detection of gravitational waves. To this purpose we investigate the linearised Einstein's equations with terms up to linear order in $Λ$ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on $Λ$. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny an…
The influence of spin in a system of classical particles on the propagation of gravitational waves is analyzed in the cosmological context of primordial thermal equilibrium. On a flat Friedmann-Robertson-Walker metric, when the precession is neglected, there is no contribution due to the spin to the distribution function of the particles. Adding a small tensor perturbation to the background metric, we study if a coupling between gravitational waves and spin exists that can modify the evolution of the distribution function, leading to new terms in the anisotropic stress, and then to a new sourc…
The spectrum of gravitational waves that have been produced in inflation is modified during cosmological transitions. Large drops in the number of relativistic particles, like during the QCD transition or at $e^+e^-$ annihilation, lead to steps in the spectrum of gravitational waves. We calculate the transfer function for the differential energy density of gravitational waves for a first-order and for a crossover QCD transition.
The cosmological stochastic gravitational-wave background produced by the mildly non-linear evolution of density fluctuations is analyzed, in the frame of an Einstein-de Sitter model, by means of a fully relativistic perturbation expansion up to second order. The form of these gravitational-instability-induced gravitational waves is gauge-dependent. In the synchronous gauge, where the second-order expansion is most easily carried out, the transverse and traceless tensor modes which are produced also contain a Newtonian and post-Newtonian piece, whose interpretation as gravitational waves is no…
We discuss the gravitational wave background generated by primordial density perturbations evolving during the radiation era. At second-order in a perturbative expansion, density fluctuations produce gravitational waves. We calculate the power spectra of gravitational waves from this mechanism, and show that, in principle, future gravitational wave detectors could be used to constrain the primordial power spectrum on scales vastly different from those currently being probed by large-scale structure. As examples we compute the gravitational wave background generated by both a power-law spectrum…
Cosmological simulation of gravitational weak lensing in open models is treated using the direct integration method, which is independent of the mult-lens-plane method. Statistical averages of optical quantuties (the convergencen shear and amplification) are derived for ray bundles passing through the clumpy universe, in which the initial state has the CDM spectrum with the power n = 1.
We show that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs). The characteristic frequency of these GWs for an extreme case of the phase transition model is around $10^{-3}$ --- $10^{-2}$ Hz with an energy density parameter as high as $10^{-12}$ --- $10^{-11}$. The possibility of detection is briefly discussed.
Recent observations suggest appreciable star formation activity in early-type galaxies down to redshift $z\sim 0.5$. If so, there is likely to be dust in these galaxies. We consider the possibility that obscuration by dust can reconcile the observed frequency of gravitational lensing of quasar images with the considerably larger rate predicted in a low density cosmologically flat universe dominated by a cosmological constant.
The paper presents results for deriving closed-form analytic solutions of the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the perturbations are outlined.
We study the phenomenological consequences of the recently proposed idea of a running gravitational coupling on macroscopic scales. When applied to the rotation curves of galaxies, we find that their flatness requires the presence of baryonic dark matter. Bounds on the variation of the gravitational coupling from primordial nucleosynthesis and the change of the period of binary pulsars are analysed. We also study constraints on the variations of $G$ with scale from gravitational lensing and the cosmic virial theorem, as well as briefly discuss the implications of such a scenario for structure …
Gravitational Lensing is an efficient tool to probe: the mass distribution of collapsed systems: galaxies and clusters; high redshift objects thanks to the gravitational amplification; and the geometry of the Universe. I will review here some important aspects of lensing and related issues in observational cosmology.
The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the perturbations are outlined.
Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent …
An injection of energy into the early Universe on a given characteristic length scale will result in turbulent motions of the primordial plasma. We calculate the stochastic background of gravitational radiation arising from a period of cosmological turbulence, using a simple model of isotropic Kolmogoroff turbulence produced in a cosmological phase transition. We also derive the gravitational radiation generated by magnetic fields arising from a dynamo operating during the period of turbulence. The resulting gravitational radiation background has a maximum amplitude comparable to the radiation…
We describe a new approach for the determination of cosmological parameters using gravitational lensing systems with multiple arcs, exploiting the fact that a given cluster can produce multiple arcs from sources over a broad range in redshift. The coupling between the critical radius of a single arc and the projected mass density of the lensing cluster can be avoided by considering the relative positions of two or more arcs. Cosmological sensitivity appears through the angular size-redshift relation. We consider simulated data constructed using a more general form for the potential, realistic …
The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of this contribution, and will then concentrate on several of the main applications in cosmology. Cluster lensing, and weak lensing, will constitute the main part of this review.
We investigate the potential of weak gravitational lensing maps to differentiate between distinct cosmological models, considering cosmic variance due to a limited map extension and the presence of noise. We introduce a measure of the differentiation between two models under a chosen lensing statistics. That enables one to determine in which circumstances (map size and noise level), and for which lensing measures two models can be differentiated at a desired confidence level. As an application, we simulate convergence maps for three cosmological models (SCDM, OCDM, and $Λ$CDM), calculate sever…
The cosmological expansion of the universe affects the behaviour of all physical systems and, in the case of gravitationally bound ones, could correspond to or mimic a time dependent Newton's constant. Here we discuss the case of a locally spherical mass distribution embedded in a generic Robertson Walker universe. Choosing the most appropriate metric tensor for the problem and assuming that the local time scale is much much lower than the cosmic one, we show that G is practically unaffected thus leaving the absolute magnitude of type Ia supernovae unaltered at all epochs.
An overview is presented of possible cosmologically distant sources of gravitational wave backgrounds, especially those which might produce detectable backgrounds in the LISA band between 0.1 and 100 mHz. Examples considered here include inflation-amplified vacuum fluctuations in inflaton and graviton fields, bubble collisions in first-order phase transitions, Goldstone modes of classical self-ordering scalars, and cosmic strings and other gauge defects. Characteristic scales and basic mechanisms are reviewed and spectra are estimated for each of these sources. The unique impact of a LISA dete…
Gravitational lensing, caused by matter perturbations along the line-of-sight to the last scattering surface, can modify the shape of the cosmic microwave background (CMB) anisotropy power spectrum. We discuss the detectability of lensing distortions to the temperature, polarisation and temperature-polarisation cross-correlation power spectra and we analyse how lensing might affect the estimation of cosmological parameters. For cold dark matter-like models with present-day matter power spectra normalised to match the abundances of rich clusters of galaxies, gravitational lensing causes detecta…
The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and robustness testing through numerical simulations---is discussed with relevance to a scheme originally introduced by Kochanek to avoid some of the uncertainties which plague other methods. The main result is that the observations at present---and probably in the future as well---are more indicative of intrinsic scatter than a hint of the correct cosmological model.
We investigate the interaction between the cosmological relic neutrinos, and primordial gravitational waves entering the horizon before the electroweak phase transition, corresponding to observable frequencies today nu_0 <= 10^-5 Hz. We give an analytic formula for the traceless transverse part of the anisotropic stress tensor, due to weakly interacting neutrinos, and derive an integro-differential equation describing the propagation of cosmological gravitational waves at these conditions. We find that this leads to a decrease of the wave intensity in the frequency region accessible to the LIS…
We estimate the sensitivity of lensing observables to the parameters in the lens model (isothermal sphere/Navarro-Frenk-White profile) parameters and to cosmological parameters. We find that the observables are primarily dependent on the lens model parameters, while the dependence on cosmological parameters is minor (especially so for the dark energy parameters). We demonstrate the lens model degeneracy by deriving both the projected mass density profile and the circular velocity profile. We also identify a possible source of the problem of fitting the averaged mass profile of CL 0024+1654 wit…
I show how weak gravitational lensing can be used to image the 3-D mass distribution in the Universe. An inverse relation to the lensing equation, relating the lensing potential evaluated at each source to the full 3-D Newtonian potential, is derived. I consider the normal modes of the lensing problem and clarify the equations using a small-angle approximation. Finally I consider the prospects of using this method to estimate the 3-D matter distribution from a realistic galaxy lensing survey.
We study the accumulation of errors in cosmological N-body algorithms that are caused by representing the continuous distribution of matter by massive particles, comparing the PPPM and Adaptive Multigrid codes. We use for this a new measure of two-body relaxation suitable for nonstationary gravitating systems. This measure is based on accumulated deflection angles of particle orbits and it does not saturate during evolution. We have found that the role of gravitational collisions in standard PPPM-models is rather high, and in order to avoid collision effects we recommend to use large comoving …
In the inflation models, the relic gravitational waves (RGW) generated in the inflation stage, and evolved in the Universe until now. In the different cosmological evolution models, one can get different gravitational waves power spectrum. In this paper, we give a simple formula to estimate this spectrum in a general cosmological model. From this formula, one can easily find the relation between this power spectrum and the cosmological evolution models. The spectrum includes all the information about the evolution of the scale factor $a$ from inflation to now. So RGW is a more clear fossil, wh…
