The Fourier Space Statistics of Seedlike Cosmological Perturbations

We propose a new test for distinguishing observationally cosmological models based on seed-like primordial perturbations (like cosmic strings or textures), from models based on Gaussian fluctuations. We investigate analytically the {\it Fourier space} statistical properties of temperature or density fluctuation patterns generated by seed-like objects and compare these properties with those of Gaussian fluctuations generated during inflation. We show that the proposed statistical test can easily identify temperature fluctuations produced by a superposition of a small number of seeds per horizon scale for {\it any} observational angular resolution and {\it any} seed geometry. However, due to the Central Limit Theorem, the distinction becomes more difficult as the number of seeds in the fluctuation pattern increases.Comment: 12 pages plus 1 Figure (available upon request). Use LaTeX. To appear in M.N.R.A.S., preprint No. CfA-359

On the Statistics of CMB Fluctuations Induced by Topological Defects

We use the analytical model recently introduced in Ref. \cite{lp92}, to investigate the statistics of temperature fluctuations on the cosmic microwave background (CMB), induced by topological defects. The cases of cosmic strings and textures are studied. We derive analytically the characteristic function of the probability distribution for ${\delta T}\over T$ and use it to obtain the lowest twelve moments including the skewness and the kurtosis. The distribution function is also obtained and it is compared with the Gaussian distribution thus identifying long non-Gaussian tails. We show that for both cosmic strings and textures all odd moments (including skewness) vanish while the relative deviation from the Gaussian for even moments increases with the order of the moment. The non-Gaussian signatures of textures, derived from the distribution function and the moments, are found to be much more prominent than the corresponding signatures for strings. We discuss the physical origin of this result.Comment: 18 pages plus 7 figures (available upon request), submitted to Phys. Rev. D, use late

Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy

A wide range of large scale observations hint towards possible modifications on the standard cosmological model which is based on a homogeneous and isotropic universe with a small cosmological constant and matter. These observations, also known as "cosmic anomalies" include unexpected Cosmic Microwave Background perturbations on large angular scales, large dipolar peculiar velocity flows of galaxies ("bulk flows"), the measurement of inhomogenous values of the fine structure constant on cosmological scales ("alpha dipole") and other effects. The presence of the observational anomalies could either be a large statistical fluctuation in the context of {\lcdm} or it could indicate a non-trivial departure from the cosmological principle on Hubble scales. Such a departure is very much constrained by cosmological observations for matter. For dark energy however there are no significant observational constraints for Hubble scale inhomogeneities. In this brief review I discuss some of the theoretical models that can naturally lead to inhomogeneous dark energy, their observational constraints and their potential to explain the large scale cosmic anomalies.Comment: 42 pages, 15 figures, Invited Review published in 'Galaxies' at http://www.mdpi.com/2075-4434/2/1/2

Large Scale Structure by Global Monopoles and Cold Dark Matter

A cosmological model in which the primordial perturbations are provided by global monopoles and in which the dark matter is cold has several interesting features. The model is normalized by choosing its single parameter within the bounds obtained from gravitational wave constraints and by demanding coherent velocity f1ows of about 600km/sec on scales of $50 h^{-1} Mpc$. Using this normalization, the model predicts the existence of dominant structures with mass $2\times 10^{16} M_\odot$ on a scale $35 h^{-1}Mpc$ i.e. larger than the horizon at $t_{eq}$. The magnitude of the predicted mass function in the galactic mass range is in good agreement with the observed Schechter function.Comment: 9 pages, 2 Figures (available upon request), use late

CMB Maximum Temperature Asymmetry Axis: Alignment with Other Cosmic Asymmetries

We use a global pixel based estimator to identify the axis of the residual Maximum Temperature Asymmetry (MTA) (after the dipole subtraction) of the WMAP 7 year Internal Linear Combination (ILC) CMB temperature sky map. The estimator is based on considering the temperature differences between opposite pixels in the sky at various angular resolutions (4 degrees-15 degrees and selecting the axis that maximizes this difference. We consider three large scale Healpix resolutions (N_{side}=16 (3.7 degrees), N_{side}=8 (7.3 degrees) and N_{side}=4 (14.7 degrees)). We compare the direction and magnitude of this asymmetry with three other cosmic asymmetry axes (\alpha dipole, Dark Energy Dipole and Dark Flow) and find that the four asymmetry axes are abnormally close to each other. We compare the observed MTA axis with the corresponding MTA axes of 10^4 Gaussian isotropic simulated ILC maps (based on LCDM). The fraction of simulated ILC maps that reproduces the observed magnitude of the MTA asymmetry and alignment with the observed \alpha dipole is in the range of 0.1%-0.5%$ (depending on the resolution chosen for the CMB map). The corresponding magnitude+alignment probabilities with the other two asymmetry axes (Dark Energy Dipole and Dark Flow) are at the level of about 1%. We propose Extended Topological Quintessence as a physical model qualitatively consistent with this coincidence of directions.Comment: 8 pages, 6 figures. Typos corrected, references added. The data, Mathematica and Healpix-IDL program files used for the numerical analysis files may be downloaded from http://leandros.physics.uoi.gr/mt

Stabilizing the Semilocal String with a Dilatonic Coupling

We demonstrate that the stability of the semilocal vortex can be significantly improved by the presence of a dilatonic coupling of the form e^\frac{q | \Phi |^2}{\eta^2} F_{\mu \nu}F^{\mu \nu} with q>0 where \eta is the scale of symmetry breaking that gives rise to the vortex. For q=0 we obtain the usual embedded (semilocal) Nielsen-Olesen vortex. We find the stability region of the parameter \beta = (\frac{m_\Phi}{m_A})^2 (m_\Phi and m_A are the masses of the scalar and gauge fields respectively). We show that the stability region of \beta is 0<\beta<\beta_{max}(q) where \beta_{max}(q=0)=1 (as expected) and \beta_{max}(q) is an increasing function of q. This result may have significant implications for the stability of the electroweak vortex in the presence of a dilatonic coupling (dilatonic electroweak vortex).Comment: 4 pages, 4 Figures. The numerical analysis files are available by e-mail upon reques

Evolution of the fσ8f\sigma_8 tension with the Planck15/Λ\LambdaCDM determination and implications for modified gravity theories

We construct an updated extended compilation of distinct (but possibly correlated) $f\sigma_8(z)$ Redshift Space Distortion (RSD) data published between 2006 and 2018. It consists of 63 datapoints and is significantly larger than previously used similar datasets. After fiducial model correction we obtain the best fit $\Omega_{0m}-\sigma_8$ $\Lambda$CDM parameters and show that they are at a $5\sigma$ tension with the corresponding Planck15/$\Lambda$CDM values. Introducing a nontrivial covariance matrix correlating randomly $20\%$ of the RSD datapoints has no significant effect on the above tension level. We show that the tension disappears (becomes less than $1\sigma$) when a subsample of the 20 most recently published data is used. A partial cause for this reduced tension is the fact that more recent data tend to probe higher redshifts (with higher errorbars) where there is degeneracy among different models due to matter domination. Allowing for a nontrivial evolution of the effective Newton's constant as $G_{\textrm{eff}}(z)/G_{\textrm{N}} = 1 + g_a \left(\frac{z}{1+z}\right)^2 - g_a \left(\frac{z}{1+z}\right)^4$ ($g_a$ is a parameter) and fixing a \plcdm background we find $g_a=-0.91\pm 0.17$ from the full $f\sigma_8$ dataset while the 20 earliest and 20 latest datapoints imply $g_a=-1.28^{+0.28}_{-0.26}$ and $g_a=-0.43^{+0.46}_{-0.41}$ respectively. Thus, the more recent $f\sigma_8$ data appear to favor GR in contrast to earlier data. Finally, we show that the parametrization $f\sigma_8(z)=\lambda \sigma_8 \Omega(z)^\gamma /(1+z)^\beta$ provides an excellent fit to the solution of the growth equation for both GR ($g_a=0$) and modified gravity ($g_a\neq 0$).Comment: Version published in Phys. Rev. D 97, 103503 (3 May 2018). 17 pages, 11 figures. Added a Table indicating the consistency of RSD data with other growth of perturbation probes (weak lensing). The Mathematica files with the numerical analysis may be downloaded from http://leandros.physics.uoi.gr/growth-tomograph