Non-Gaussian Signatures in the Lens Deformations of the CMB Sky. A New Ray-Tracing Procedure

We work in the framework of an inflationary cold dark matter universe with cosmological constant, in which the cosmological inhomogeneities are considered as gravitational lenses for the CMB photons. This lensing deforms the angular distribution of the CMB maps in such a way that the induced deformations are not Gaussian. Our main goal is the estimation of the deviations with respect to Gaussianity appeared in the distribution of deformations. In the new approach used in this paper, matter is evolved with a particle-mesh N-body code and, then, an useful ray-tracing technique designed to calculate the correlations of the lens deformations induced by nonlinear structures is applied. Our appro…

Locating Objects Away from Earth Surface: Positioning Accuracy

The motion of the Galileo and GPS satellite constellations is simulated in Schwarzschild space-time, whereas photons travel in Minkowski space-time. This is a good enough approach to deal with the main goal of this paper: the study of positioning accuracy in the framework of the so-called relativistic positioning. Our study is based on numerical 4D simulations. In this meeting, the contribution of J.A. Morales-Lladosa contains some basic ideas which have been important to perform our numerical calculations. For four chosen emitters (satellites) of a certain constellation, many receivers located at different distances from Earth surface and in distinct directions are considered. Thus, we ver…

CMB anisotropies: cosmic confusion and polarization

Abstract Some physical effects producing Cosmic Microwave Background (CMB) anisotropies are briefly described. The CMB angular power spectrum is calculated -in appropriate cases- with the essential aim of estimating and comparing the effects produced by reionization and gravitational waves; thus a problem of Cosmic Confusion is pointed out. Accurate measurements of the CMB polarization could solve this problem in future. Some comments about the PLANCK mission —ESA project for anisotropy detection— are given.

General-relativistic approach to the nonlinear evolution of collisionless matter.

A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian…

Small Angular Scale Simulations of the Microwave Sky

We describe and compare two types of microwave sky simulations which are good for small angular scales. The first type uses expansions in spherical harmonics, and the second one is based on plane waves and the Fast Fourier Transform. The angular power spectrum is extracted from maps corresponding to both types of simulations, and the resulting spectra are appropriately compared. In this way, the features and usefulness of Fourier simulations are pointed out. For $\ell \geq 100$, all the simulations lead to similar accuracies; however, the CPU cost of Fourier simulations is $\sim 10$ times smaller than that for spherical harmonic simulations. For $\ell \leq 100$, the simulations based on sph…

Relativistic positioning: errors due to uncertainties in the satellite world lines

Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in the satellite world lines lead to dominant positioning errors. In this paper, a detailed analysis of these errors is developed inside a great region surrounding Earth. This analysis is performed in the framework of the so-called relativistic positioning systems. Our study is based on the Jacobian, J, of the transformation giving the emission coordinates in terms of the inertial ones. Around points of vanishing J, positioning errors are too large. We show …

A Frozen-Flow Approximation to the Evolution of Large-Scale Structures in the Universe

A new approximation to the evolution of large-scale structures in the Universe is proposed which is based on neglecting the role of particle inertia compared to the damping implied by the Hubble drag. We call this approximation frozen flow because particles move by updating at each step their velocity to the local value of the peculiar velocity field, here approximated by its growing linear mode: stream-lines are then frozen to their initial shape. The situation is quite different from that of the Zel'dovich algorithm, where the velocity is kept constant along each particle trajectory

Secondary gravitational anisotropies in open universes

The applicability of the potential approximation in the case of open universes is tested. Great Attractor-like structures are considered in the test. Previous estimates of the Cosmic Microwave background anisotropies produced by these structures are analyzed and interpreted. The anisotropies corresponding to inhomogeneous ellipsoidal models are also computed. It is proved that, whatever the spatial symmetry may be, Great Attractor-like objects with extended cores (radius $\sim 10h^{-1}$),located at redshift $z=5.9$ in an open universe with density parameter $\Omega_{0}=0.2$, produce secondary gravitational anisotropies of the order of $10^{-5}$ on angular scales of a few degrees. This aniso…

Evolution of polarization orientations in a flat universe with vector perturbations: CMB and quasistellar objects

Various effects produced by vector perturbations (vortical peculiar velocity fields) of a flat Friedmann-Robertson-Walker background are considered. In the presence of this type of perturbations, the polarization vector rotates. A formula giving the rotation angle is obtained and, then, it is used to prove that this angle depends on both the observation direction and the emission redshift. Hence, rotations are different for distinct quasars and also for the Cosmic Microwave Background (CMB) radiation coming along different directions (from distinct points of the last scattering surface). As a result of these rotations, some correlations could appear in an initially random field of quasar po…

The great attractor and the COBE quadrupole

A nonlinear model for the Great Attractor is built. It is based on the Tolman-Bondi solution of the Einstein equations. The angular temperature distribution of the Cosmic Microwave Background produced by the Great Attractor is numerically obtained. Several realizations of the Great Attractor are studied. In all the cases, the distance from the Great Attractor to the Local Group is ≈ 43h−1 Mpc, the density contrast reduces to a half of the central value at a radius of 9h−1 Mpc ⪯ Rc ⪯ 14h−1 Mpc, and the dipole due to the infall towards the inhomogeneity center is 1.33 × 10−3 ⪯ D ⪯ 1.8 × 10−3. A complete arbitrary background is assumed; the density parameter, Σ and the reduced Hubble constant,…

Gravitational waves from galaxy clusters: a new observable effect

A rich galaxy cluster showing strong resemblance with the observed ones is simulated. Cold dark matter spectrum, Gaussian statistics, flat universe, and two components -- baryonic gas plus dark matter particles -- are considered. We have calculated the gravitational-wave output during the epoch of the fully nonlinear and nonsymmetric cluster evolution. The amplitudes and frequencies of the resulting gravitational waves are estimated. Since frequencies are very small --of the order of $10^{-17} Hz$ -- a complete pulse cannot be observed during an admissible integration time; nevertheless, it is proved that these waves can produce an interesting secular effect which appears to be observable w…

Cosmological Applications of Extended Electromagnetism

Extended electromagnetism (EE) has been applied to cosmology in various papers. In all of them, the zero order energy density of the EE vector field plays the same role as vacuum energy. Perturbations of this field have been studied by using different approaches. Firstly, some basic equations and ideas are summarized and, then, the CMBFAST code is used to calculate the cosmic microwave background angular power spectrum for appropriate values of the EE parameters. Comparisons of the resulting spectra with a good observational one compatible with WMAP7 (Wilkinson map anisotropy probe 7 years data) seem to be promising. We are currently looking for a set of parameters leading to the best fitti…

On the microwave background anisotropy produced by big voids in open universes

The Tolman-Bondi solution of the Einstein equations is used in order to model the time evolution of the void observed in Bo\"otes. The present density contrast of the central region ($\sim -0.75$) and its radius ($\sim 30h^{-1} \ Mpc$) are fixed, while the density parameter of the Universe, the amplitude of the density contrast inside the void wall, the width of this wall and the distance from the void centre to the Local Group are appropriately varied. The microwave background anisotropy produced by Bo\"otes-like voids is estimated for a significant set of locations. All the voids are placed far from the last scattering surface. It is shown that the anisotropy generated by these voids stro…

Large‐Scale Vector Modes and the First CMB Temperature Multipoles

Recent observations have pointed out various anomalies in some multipoles (small $\ell $) of the cosmic microwave background (CMB). In this paper, it is proved that some of these anomalies could be explained in the framework of a modified concordance model, in which, there is an appropriate distribution of vector perturbations with very large spatial scales. Vector modes are associated with divergenceless (vortical) velocity fields. Here, the generation of these modes is not studied in detail (it can be done "a posteriori"); on the contrary, we directly look for the distributions of these vector modes which lead to both alignments of the second and third multipoles and a planar octopole. A …

ESTIMATING SMALL ANGULAR SCALE COSMIC MICROWAVE BACKGROUND ANISOTROPY WITH HIGH-RESOLUTIONN-BODY SIMULATIONS: WEAK LENSING

We estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background. Accurate calculation of large l multipoles requires N-body simulations and ray-tracing schemes with both high spatial and temporal resolution. To this end, we have developed a new code that combines a gravitational Adaptive Particle-Particle, Particle-Mesh solver with a weak-lensing evaluation routine. The lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps—rather than just a few outputs—are used in the lensing computations. The new code also includes a ray-tracing procedure that avoids periodicity effects in a univer…

Cosmological Vector Perturbations and CMB Anomalies

Recently, it has been proved that large scale vector modes could explain most of the CMB anomalies in the first temperature multipoles. Some divergenceless (vortical) velocity fields–which are superimpositions of vector modes–can explain both the alignment of the second and third multipoles and the planar character of the octopole. In this paper we comment: (a) some papers trying to account for the mentioned anomalies, (b) our explanation based on vector modes, and (c) some current ideas about the possible origin of these modes.

A relativistic approach to gravitational instability in the expanding Universe: second-order Lagrangian solutions

A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and geometric quantities and compared with the corresponding ones in the Newtonian approximation. Specifically, we compute the density, the volume expansion scalar, the shear, the ``electric" part, or tide, and the ``magnetic" part of the Weyl tensor. The evolution of the shear and the tide beyond the linear regime strongly depends on the ratio of the characteristic size of the perturbation to the cosmological horizon distance. For perturbations on sub--horizon scal…

Testing vector-tensor gravity with current cosmological observations

A certain vector-tensor theory of gravitation (VT) has been recently applied to cosmology (Phys. Rev. D, 89, 2014, 044035). It leads to encouraging results. The zero order energy density of the vector field accounts for the cosmological constant. It has been recently proved that the VT vector field cannot play the role of the electromagnetic field. The evolution of the scalar perturbations is different in VT and general relativity. Tensor fluctuations evolve in the same way in both theories. Here, the VT evolution equations of the scalar modes are appropriately written, and the initial conditions at high redshift - for numerical integration- are given. The codes COSMOMC and CAMB are modifie…

Non-Linear Relativistic Evolution of Cosmological Perturbations in Irrotational Dust

Beam deconvolution in noisy CMB maps

The subject of this paper is beam deconvolution in small angular scale CMB experiments. The beam effect is reversed using the Jacobi iterative method, which was designed to solved systems of algebraic linear equations. The beam is a non circular one which moves according to the observational strategy. A certain realistic level of Gaussian instrumental noise is assumed. The method applies to small scale CMB experiments in general (cases A and B), but we have put particular attention on Planck mission at 100 GHz (cases C and D). In cases B and D, where noise is present, deconvolution allows to correct the main beam distortion effect and recover the initial angular power spectrum up to the end…

Looking for the imprints of nonlinear structures on the cosmic microwave background

Abstract Many authors have estimated the anisotropies produced by one isolated cosmological non-linear inhomogeneity. This paper is an updated review about these estimates. The main methods used in order to deal with this problem are described. The limitations of these methods are analyzed. Results appear to be particularly interesting in the open non-linear case, in which a general treatment of the anisotropies produced by inhomogeneity distributions is very troublesome. The effects produced by very big structures such as the Great Attractor and the Bootes Void are studied in detail. Some generalities about the origin, detection and features of the Cosmic Microwave Background anisotropies …

A multidimensional hydrodynamic code for structure evolution in cosmology

A cosmological multidimensional hydrodynamic code is described and tested. This code is based on modern high-resolution shock-capturing techniques. It can make use of a linear or a parabolic cell reconstruction as well as an approximate Riemann solver. The code has been specifically designed for cosmological applications. Two tests including shocks have been considered: the first one is a standard shock tube and the second test involves a spherically symmetric shock. Various additional cosmological tests are also presented. In this way, the performance of the code is proved. The usefulness of the code is discussed; in particular, this powerful tool is expected to be useful in order to study…

The imprints of the Great Attractor and the Virgo cluster on the microwave background

A fully non-linear model based on the Tolman-Bondi solution of the Einstein equations is used to describe the Great Attractor and the Virgo cluster. The background is a Friedmann-Robertson-Walker universe, and the inhomogeneity develops from physically motivated initial profiles of the energy density and the peculiar velocity. Accurate numerical integrations of the field equations of the null geodesics are carried out, and thus the angular temperature distribution of the microwave background produced by the chosen overdensities is found. The observer is located in the Local Group. The quadrupole Q produced by each overdensity is computed and divided into two parts: the relativistic Doppler …

Deconvolving the Beam in Small Angular Scale CMB Experiments

This paper is concerned with experiments which measure CMB anisotropies on small angular scales. A certain coverage, a beam structure and a level of uncorrelated noise define each experiment. We focus our atention on the reversion of the beam average. In each experiment, we look for the best pixelization for reversion, namely, for the pixelization that -after reversion- leads to good maps containing right spectra for the most wide range of angular scales. Squared pixels having different sizes "smaller" than the beam radius are considered. For a given size, the following question arises: How well can we assign a temperature to each pixel? Various mathematical methods are used to show that, i…

On the sources of the late integrated Sachs-Wolfe effect

In some scenarios, the peculiar gravitational potential of linear and mildly nonlinear structures depends on time and, as a result of this dependence, a late integrated Sachs-Wolfe effect appears. Here, an appropriate formalism is used which allows us to improve on the analysis of the spatial scales and locations of the main cosmological inhomogeneities producing this effect. The study is performed in the framework of the currently preferred flat model with cosmological constant, and it is also developed in an open model for comparisons. Results from this analysis are used to discuss the contribution of Great Attractor-like objects, voids, and other structures to the CMB anisotropy.

More about a successful vector-tensor theory of gravitation

The vector-tensor (VT) theory of gravitation revisited in this article was studied in previous papers, where it was proved that VT works and deserves attention. New observational data and numerical codes have motivated further development which is presented here. New research has been planed with the essential aim of proving that current cosmological observations, including Planck data, baryon acoustic oscillations (BAO), and so on, may be explained with VT, a theory which accounts for a kind of dark energy which has the same equation of state as vacuum. New versions of the codes CAMB and COSMOMC have been designed for applications to VT, and the resulting versions have been used to get the…

Approaches to relativistic positioning around Earth and error estimations

In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the positioning errors due to uncertainties in the satellite world lines (U-errors). A distribution of U-errors was obtained, at various times, in a set of points covering a large region surrounding Earth. Here, the positioning errors associated to the simplifying assumption that photons move in Minkowski space-time (S-errors) are estimated and compared with the U-errors. Both errors have been calculated for the same points and times to make comparisons possib…

Topological defects and large-scale structure

Probing the creatable character of perturbed Friedmann-Robertson-Walker universes

We discuss whether some perturbed Friedmann-Robertson-Walker (FRW) universes could be creatable, i. e., could have vanishing energy, linear momentum and angular momentum, as it could be expectable if the Universe arose as a quantum fluctuation. On account of previous results, the background is assumed to be either closed (with very small curvature) or flat. In the first case, fully arbitrary linear perturbations are considered; whereas in the flat case, it is assumed the existence of: (i) inflationary scalar perturbations, that is to say, Gaussian adiabatic scalar perturbations having an spectrum close to the Harrison-Zel'dovich one, and (ii) arbitrary tensor perturbations. We conclude that…

On the Rees-Sciama effect: maps and statistics

Small maps of the Rees-Sciama (RS) effect are simulated by using an appropriate N-body code and a certain ray-tracing procedure. A method designed for the statistical analysis of cosmic microwave background (CMB) maps is applied to study the resulting simulations. These techniques, recently proposed --by our team-- to consider lens deformations of the CMB, are adapted to deal with the RS effect. This effect and the deviations from Gaussianity associated to it seem to be too small to be detected in the near future. This conclusion follows from our estimation of both the RS angular power spectrum and the RS reduced n-direction correlation functions for n<7.

Spherical symmetric dust collapse in a Vector-Tensor gravity

There is a viable vector-tensor gravity (VTG) theory, whose vector field produces repulsive forces leading to important effects. In the background universe, the effect of these forces is an accelerated expansion identical to that produced by vacuum energy (cosmological constant). Here, we prove that another of these effects arises for great enough collapsing masses which lead to Schwarzschild black holes and singularities in general relativity (GR). For these masses, pressure becomes negligible against gravitational attraction and the complete collapse cannot be stopped in the context of GR; however, in VTG, a strong gravitational repulsion could stop the falling of the shells towards the s…

Cosmological perturbations in extended electromagnetism. General gauge invariant approach

A certain vector-tensor (VT) theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which leads to both a modified Lorentz force and the true energy momentum tensor of the vector field. The theory is then applied to cosmology. A complete gauge invariant treatment of the scalar perturbations is presented. For appropriate gauge invariant variables describing the scalar modes of the vector field (A-modes), it is proved that the evolution equations of these modes do not involve the scalar modes appearing in General Relativity (GR-modes), which are…

Gravitational waves from galaxy encounters

We discuss the emission of gravitational radiation produced in encounters of dark matter galactic halos. To this aim we perform a number of numerical simulations of typical galaxy mergers, computing the associated gravitational radiation waveforms as well as the energy released in the processes. Our simulations yield dimensionless gravitational wave amplitudes of the order of $10^{-13}$ and gravitational wave frequencies of the order of $10^{-16}$ Hz, when the galaxies are located at a distance of 10 Mpc. These values are of the same order as those arising in the gravitational radiation originated by strong variations of the gravitational field in the early Universe, and therefore, such gra…

Great Attractor-like structures and large-scale anisotropy

On the estimation and detection of the Rees Sciama effect

Maps of the Rees–Sciama (RS) effect are simulated using the parallel N-body code, hydra, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstra…

Interpreting deviations between AR-VTG and GR

The cosmic microwave background (CMB) anisotropies predicted by two cosmological models are compared, one of them is the standard model of general relativity with cold dark matter and cosmological constant, whereas the second model is based on a consistent vector-tensor theory of gravitation explaining solar system and cosmological observations. It is proved that the resulting differences — between the anisotropies of both models — are due to the so-called late integrated Sachs–Wolfe effect and, consequently, cross-correlations between maps of CMB temperatures and tracers of the dark matter distribution could be used in future to select one of the above models. The role of reionization is …

Non-circular rotating beams and CMB experiments

This paper is concerned with small angular scale experiments for the observation of cosmic microwave background anisotropies. In the absence of beam, the effects of partial coverage and pixelisation are disentangled and analyzed (using simulations). Then, appropriate maps involving the CMB signal plus the synchrotron and dust emissions from the Milky Way are simulated, and an asymmetric beam --which turns following different strategies-- is used to smooth the simulated maps. An associated circular beam is defined to estimate the deviations in the angular power spectrum produced by beam asymmetry without rotation and, afterwards, the deviations due to beam rotation are calculated. For a cert…

On the viability of a certain vector-tensor theory of gravitation

A certain vector-tensor theory is revisited. Our attention is focused on cosmology. Against previous suggestions based on preliminary studies, it is shown that, if the energy density of the vector field is large enough to play the role of the dark energy and its fluctuations are negligible, the theory is not simultaneously compatible with current observations on: supernovae, the cosmic microwave background (CMB) anisotropy, and the power spectrum of the energy density fluctuations. However, for small enough energy densities of the vector field, the theory becomes compatible with all the above observations and, moreover, it leads to an interesting evolution of the so-called vector cosmologic…

Cosmology in a certain vector-tensor theory of gravitation

We study relevant cosmological topics in the framework of a certain vector-tensor theory of gravitation (hereafter VT). This theory is first compared with the so-called extended electromagnetism (EE). These theories have a notable resemblance and both explain the existence of a cosmological constant. It is shown that, in EE, a positive dark energy density requires a Lagrangian leading to quantum ghosts, whereas VT is free from these ghosts. On account of this fact, the remainder of the paper is devoted to study cosmology in the framework of VT. Initial conditions, at high redshift, are used to solve the evolution equations of all the VT scalar modes. In particular, a certain scalar mode cha…

Learning from observations of the microwave background at small angular scales

In this paper, we focus our attention on the following question: How well can we recover the power spectrum of the cosmic microwave background from the maps of a given experiment?. Each experiment is described by a a pixelization scale, a beam size, a noise level and a sky coverage. We use accurate numerical simulations of the microwave sky and a cold dark matter model for structure formation in the universe. Angular scales smaller than those of previous simulations are included. The spectrum obtained from the simulated maps is appropriately compared with the theoretical one. Relative deviations between these spectra are estimated. Various contributions to these deviations are analyzed. The…

Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando &amp; Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emissi…