CMBfit: Rapid WMAP likelihood calculations with normal parameters

We present a method for ultra-fast confrontation of the WMAP cosmic microwave background observations with theoretical models, implemented as a publicly available software package called CMBfit, useful for anyone wishing to measure cosmological parameters by combining WMAP with other observations. The method takes advantage of the underlying physics by transforming into a set of parameters where the WMAP likelihood surface is accurately fit by the exponential of a quartic or sextic polynomial. Building on previous physics based approximations by Hu et.al., Kosowsky et.al. and Chu et.al., it combines their speed with precision cosmology grade accuracy. A Fortran code for computing the WMAP likelihood for a given set of parameters is provided, pre-calibrated against CMBfast, accurate to Delta lnL ~ 0.05 over the entire 2sigma region of the parameter space for 6 parameter ``vanilla'' Lambda CDM models. We also provide 7-parameter fits including spatial curvature, gravitational waves and a running spectral index.Comment: 14 pages, 8 figures, References added, accepted for publication in Phys.Rev.D., a Fortran code can be downloaded from http://space.mit.edu/home/tegmark/cmbfit

Relativistic models of two low-luminosity radio jets: B2 0326+39 and B2 1553+24

We apply the intrinsically symmetrical, decelerating relativistic jet model developed by Laing & Bridle for 3C 31 to deep, full-synthesis 8.4-GHz VLA imaging of the two low-luminosity radio galaxies B2 0326+39 and B2 1553+24. After some modifications to the functional forms used to describe the geometry, velocity, emissivity and magnetic-field structure, these models can accurately fit our data in both total intensity and linear polarization. We conclude that the jets in B2 0326+39 and B2 1553+24 are at angles of 64 +/- 5 deg and 7.7 +/- 1.3 deg to the line of sight, respectively. In both objects, we find that the jets decelerate from 0.7 - 0.8c to <0.2c over a distance of approximately 10 kpc, although in B2 1553+24 this transition occurs much further from the nucleus than in B2 0326+39 or 3C 31. The longitudinal emissivity profiles can be divided into sections, each fit accurately by a power law; the indices of these power laws decrease with distance from the nucleus. The magnetic fields in both objects are dominated by the longitudinal component in the high-velocity regions close to the nucleus and by the toroidal component further out, but B2 0326+39 also has a significant radial component at large distances, whereas B2 1553+24 does not. Simple adiabatic models fail to fit the emissivity variations in the regions of high velocity but provide good descriptions of the emissivity after the jets have decelerated. Given the small angle to the line of sight inferred for B2 1553+24, there should be a significant population of similar sources at less extreme orientations. Such objects should have long (>200 kpc), straight, faint jets and we show that their true sizes are likely to have been underestimated in existing images. (Slightly abridged.)Comment: 27 pages, 21 figures, accepted for publication in MNRA

Low scale gravity as the source of neutrino masses?

We address the question whether low-scale gravity alone can generate the neutrino mass matrix needed to accommodate the observed phenomenology. In low-scale gravity the neutrino mass matrix in the flavor basis is characterized by one parameter (the gravity scale M_X) and by an exact or approximate flavor blindness (namely, all elements of the mass matrix are of comparable size). Neutrino masses and mixings are consistent with the observational data for certain values of the matrix elements, but only when the spectrum of mass is inverted or degenerate. For the latter type of spectra the parameter M_{ee} probed in double beta experiments and the mass parameter probed by cosmology are close to existing upper limits.Comment: 10 pages, 1 figur

Wormholes and Ringholes in a Dark-Energy Universe

The effects that the present accelerating expansion of the universe has on the size and shape of Lorentzian wormholes and ringholes are considered. It is shown that, quite similarly to how it occurs for inflating wormholes, relative to the initial embedding-space coordinate system, whereas the shape of the considered holes is always preserved with time, their size is driven by the expansion to increase by a factor which is proportional to the scale factor of the universe. In the case that dark energy is phantom energy, which is not excluded by present constraints on the dark-energy equation of state, that size increase with time becomes quite more remarkable, and a rather speculative scenario is here presented where the big rip can be circumvented by future advanced civilizations by utilizing sufficiently grown up wormholes and ringholes as time machines that shortcut the big-rip singularity.Comment: 11 pages, RevTex, to appear in Phys. Rev.

Is cosmology consistent?

We perform a detailed analysis of the latest CMB measurements (including BOOMERaNG, DASI, Maxima and CBI), both alone and jointly with other cosmological data sets involving, e.g., galaxy clustering and the Lyman Alpha Forest. We first address the question of whether the CMB data are internally consistent once calibration and beam uncertainties are taken into account, performing a series of statistical tests. With a few minor caveats, our answer is yes, and we compress all data into a single set of 24 bandpowers with associated covariance matrix and window functions. We then compute joint constraints on the 11 parameters of the ``standard'' adiabatic inflationary cosmological model. Out best fit model passes a series of physical consistency checks and agrees with essentially all currently available cosmological data. In addition to sharp constraints on the cosmic matter budget in good agreement with those of the BOOMERaNG, DASI and Maxima teams, we obtain a heaviest neutrino mass range 0.04-4.2 eV and the sharpest constraints to date on gravity waves which (together with preference for a slight red-tilt) favors ``small-field'' inflation models.Comment: Replaced to match accepted PRD version. 14 pages, 12 figs. Tiny changes due to smaller DASI & Maxima calibration errors. Expanded neutrino and tensor discussion, added refs, typos fixed. Combined CMB data, window and covariance matrix at http://www.hep.upenn.edu/~max/consistent.html or from [email protected]

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm

Grand Unified Inflation Confronts WMAP

In a class of realistic four and five dimensional supersymmetric grand unified models, the scalar spectral index is found to be $n_s=0.98 (\pm 0.01)$, in excellent agreement with the values determined by several previous experiments and most recently by the Wilkinson Microwave Anisotropy Probe (WMAP). The models predict $dn_s/d{\rm ln}k\sim 10^{-3}$ and a negligible tensor-to-scalar ratio $r\sim 10^{-8}$. A new five dimensional supersymmetric SO(10) model along these is presented in which inflation is associated with the breaking of SO(10) to SU(5) at scale $M$, with $\delta T/T\propto (M/M_{\rm Planck})^2$, so that $M\simeq 10^{16}$ GeV. The inflaton decay leads to the observed baryon asymmetry via leptogenesis. We also discuss how the monopole problem is solved without the use of non-renormalizable terms.Comment: A new resolution of the monopole problem proposed. 1+9 page

Cosmological parameters from CMB and other data: a Monte-Carlo approach

We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.Comment: Quintessence results now include perturbations. Changes to match version accepted by PRD. MCMC code and data are available at http://cosmologist.info/cosmomc/ along with a B&W printer-friendly version of the pape

Primordial power spectrum from WMAP

The observed angular power spectrum of the cosmic microwave background temperature anisotropy, $C_l$, is a convolution of a cosmological radiative transport kernel with an assumed primordial power spectrum of inhomogeneities. Exquisite measurements of $C_l$ over a wide range of multipoles from the Wilkinson Microwave Anisotropy Probe (WMAP) has opened up the possibility to deconvolve the primordial power spectrum for a given set of cosmological parameters (base model). We implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from WMAP assuming a concordance cosmological model. The most prominent feature of the recovered $P(k)$ is a sharp, infra-red cut off on the horizon scale. The resultant $C_l$ spectrum using the recovered spectrum has a likelihood far better than a scale invariant, or, `best fit' scale free spectra ($\Delta\ln{\cal L}=25$ {\it w.r.t.} Harrison Zeldovich, and, $\Delta\ln{\cal L}=11$ {\it w.r.t.} power law with $n_s=0.95$). The recovered $P(k)$ has a localized excess just below the cut-off which leads to great improvement of likelihood over the simple monotonic forms of model infra-red cut-off spectra considered in the post WMAP literature. The recovered $P(k)$, in particular, the form of infra-red cut-off is robust to small changes in the cosmological parameters. We show that remarkably similar form of infra-red cutoff is known to arise in very reasonable extensions and refinements of the predictions from simple inflationary scenarios. Our method can be extended to other cosmological observations such as the measured matter power spectrum and, in particular, the much awaited polarization spectrum from WMAP.Comment: 20 pages, 12 figures, uses Revtex4, Matches version accepted to Phys. Rev. D. More extensive discussion of the method in the appendix, references added and typos correcte

Origin of the ring structures in Hercules A.: Sub-arcsecond 144 MHz to 7 GHz observations

Large scale structure and cosmologyGalaxie