Markov Chain Monte Carlo Code Research Articles

Gravitational lensing from clusters of galaxies to test disformal couplings theories

In this study, we investigate the potential existence of a non-minimal coupling between dark matter and gravity using a compilation of galaxy clusters. We focus on the disformal scenario of a non-minimal model with an associated coupling length L. Within the Newtonian approximation, this model introduces a modification to the Poisson equation, characterized by a term proportional to L2∇2ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2 \ abla ^2 \\rho $$\\end{document}, where ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} represents the density of the DM field. We have tested the model by examining strong and weak gravitational lensing data available for a selection of 19 high-mass galaxy clusters observed by the CLASH survey. We have employed a Markov Chain Monte Carlo code to explore the parameter space, and two different statistical approaches to analyse our results: a standard marginalisation and a profile distribution method. Notably, the profile distribution analysis helps out to bypass some volume-effects in the posterior distribution, and reveals lower Navarro–Frenk–White concentrations and masses in the non-minimal coupling model compared to general relativity case. We also found a nearly perfect correlation between the coupling constant L and the standard Navarro–Frenk–White scale parameter rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_s$$\\end{document}, hinting at a compelling link between these two lengths.

Abell 1033: Radio halo and gently reenergized tail at 54 MHz

Context. Abell 1033 is a merging galaxy cluster of moderate mass (M500 = 3.24 × 1014 M⊙). It hosts a broad variety of diffuse radio sources that are linked to different astrophysical phenomena. The most peculiar phenomenon is an elongated feature with an ultra-steep spectrum that is the prototype of the category of gently reenergized tails (GReET). Furthermore, the cluster hosts sources that were previously classified as a radio phoenix and a radio halo. Aims. We aim to improve the understanding of the cosmic-ray acceleration mechanisms in galaxy clusters in a frequency and mass range that has been poorly explored so far. Methods. To investigate the ultra-steep synchrotron emission in the cluster, we performed a full direction-dependent calibration of a LOFAR observation centered at 54 MHz. We analyzed this observation together with recalibrated data of the LOFAR Two-meter Sky Survey at 144 MHz and an archival GMRT observation at 323 MHz. We performed a spectral study of the radio galaxy tail that is connected to the GReET to test whether the current interpretation of the source agrees with observational evidence below 100 MHz. Additionally, we employed a Markov chain Monte Carlo code to fit the halo surface brightness profile at different frequencies. Results. We report an extreme spectral curvature for the GReET. The spectral index flattens from α144 MHz323 MHz ≈ -4 to α144 MHz54 MHz ≈ -2 . This indicates the presence of a cutoff in the electron energy spectrum. At the cluster center, we detect the radio halo at 54, 144, and at lower significance at 323 MHz. We categorize it as an ultra-steep spectrum radio halo with a low-frequency spectral index α = −1.65 ± 0.17. Additionally, with a radio power of P150 MHz = 1.22 ± 0.13 × 1025 W Hz−1, it is found to be significantly above the correlations of radio power to cluster mass reported in the literature. Furthermore, the synchrotron spectrum of the halo is found to further steepen between 144 and 323 MHz, in agreement with the presence of a break in the electron spectrum, which is a prediction of homogeneous reacceleration models.

Scalar–fermion interaction as the driver of cosmic acceleration

We argue that an interacting scalar-fermion distribution can be used to demonstrate the cosmic acceleration in General Relativity. The interaction is of Yukawa nature and it drives the fermion density to decay with cosmic time. The consistency of the model is established through, (a) a generalization of the O m ( z ) parameter, the present matter density contrast of the universe and (b) a comparison of theoretical results with observational data, using a Markov Chain Monte Carlo code. A simple toy model of unified cosmic expansion history is also discussed, where the universe goes through transitions between subsequent epochs with different patterns of cosmic expansion. These patterns impose some constraints on the scalar-fermion interaction profile and on the overall cosmological dynamics.

Orbital Elements and Individual Component Masses from Joint Spectroscopic and Astrometric Data of Double-line Spectroscopic Binaries*

Abstract We present orbital elements, orbital parallaxes, and individual component masses for 14 spatially resolved double-line spectroscopic binaries derived doing a simultaneous fit of their visual orbit and radial velocity curve. This was done by means of a Markov Chain Monte Carlo code developed by our group that produces posterior distribution functions and error estimates for all of the parameters. Of this sample, six systems had high-quality previous studies and were included as benchmarks to test our procedures, but even in these cases, we could improve the previous orbits by adding recent data from our survey of southern binaries being carried out with the HRCam and ZORRO speckle cameras at the SOAR 4.1 m and Gemini South 8.1 m telescopes, respectively. We also give results for eight objects that did not have a published combined orbital solution, one of which did not have a visual orbit either. We could determine mass ratios with a typical uncertainty of less than 1%, mass sums with uncertainties of about 1%, and individual component masses with a formal uncertainty of 0.01 M ⊙ in the best cases. A comparison of our orbital parallaxes with available trigonometric parallaxes from Hipparcos and Gaia eDR3 shows a good correspondence, the mean value of the differences being consistent with zero within the errors of both catalogs. We also present observational H-R diagrams for our sample of binaries, which, in combination with isochrones from different sources, allowed us to assess their evolutionary status and the quality of their photometry.

A new look at local ultraluminous infrared galaxies: the atlas and radiative transfer models of their complex physics

ABSTRACT We present the ultraviolet to submillimetre spectral energy distributions (SEDs) of the HERschel Ultra Luminous Infrared Galaxy Survey (HERUS) sample of 42 local ultraluminous infrared galaxies (ULIRGs) and fit them with a Markov chain Monte Carlo code using the CYprus models for Galaxies and their NUclear Spectra (CYGNUS) radiative transfer models for starbursts, active galactic nucleus (AGN) tori, and host galaxy. The Spitzer IRS spectroscopy data are included in the fitting. Our Bayesian SED fitting method takes comparable time to popular energy balance methods but it is more physically motivated and versatile. All HERUS galaxies harbour high rates of star formation but we also find bolometrically significant AGN in all of the galaxies of the sample. We estimate the correction of the luminosities of the AGN in the ULIRGs due to the anisotropic emission of the torus and find that it could be up to a factor of ∼10 for nearly edge-on tori. We present a comparison of our results with the smooth torus model of Fritz et al. and the two-phase models of Siebenmorgen et al. and SKIRTOR. We find that the CYGNUS AGN torus models fit significantly better the SEDs of our sample compared to all other models. We find no evidence that strong AGN appear either at the beginning or end of a starburst episode or that starbursts and AGN affect each other. IRAS 01003−2238 and Mrk 1014 show evidence of dual AGNs in their SED fits, suggesting a minimum dual AGN fraction in the sample of 5 per cent.

Effect of pomegranate juice on vascular adhesion factors: A systematic review and meta-analysis

BackgroundCardiovascular diseases, obesity, and insulin resistance demonstrate elements of functional impairment of the endothelium. Treatment of endothelial dysfunction with natural products, such as pomegranate, can open new ways in the treatment of cardiovascular diseases. PurposeThe present meta-analysis provides information in highlighting the role of pomegranate in endothelial dysfunction. MethodsVarious databases, such as PubMed, Scopus, Web of Science, Cochrane, and Google Scholar, were searched up to July 2020 using relevant keywords. We have selected the studies that investigated the effects of pomegranate on vascular adhesion factors, including intercellular adhesion molecule 1 (ICAM-1), vascular cell adhesion molecule 1 (VCAM-1), E-selectin, and interleukin-6 (IL-6). MD with 95% CrI with 100,000 iterations by using Markov chain Monte Carlo code were used. ResultsPooled effect size of articles in human studies indicated that pomegranate juice was not significantly effective on ICAM-1 [MD: −0.42; CrI: (−1.01, 0.17)], VCAM-1 [MD: −0.20; CrI: (−1.95, 1.40)], and E-selectin [MD: −0.21; CrI: (−1.62, 1.21)] compared to the control group. But it can significantly reduce IL-6 [MD: −1.07; CrI: (−1.90, -0.19)]. ConclusionGenerally, present study showed that pomegranate juice has no significant effect on vascular adhesion factors, ICAM-1, VCAM-1, and E-selectin, but can reduce IL-6 significantly. Future prospective randomized clinical trials with longer intervention duration are warranted to obtain a precise conclusion.

The Sloan Digital Sky Survey Reverberation Mapping Project: Comparison of Lag Measurement Methods with Simulated Observations

Abstract We investigate the performance of different methodologies that measure the time lag between broad-line and continuum variations in reverberation mapping data using simulated light curves that probe a range of cadence, time baseline, and signal-to-noise ratio in the flux measurements. We compare three widely adopted lag-measuring methods: the interpolated cross-correlation function (ICCF), the z-transformed discrete correlation function (ZDCF), and the Markov chain Monte Carlo code JAVELIN, for mock data with qualities typical of multiobject spectroscopic reverberation mapping (MOS-RM) surveys that simultaneously monitor hundreds of quasars. We quantify the overall lag-detection efficiency, the rate of false detections, and the quality of lag measurements for each of these methods and under different survey designs (e.g., observing cadence and depth) using mock quasar light curves. Overall JAVELIN and ICCF outperform ZDCF in essentially all tests performed. Compared with ICCF, JAVELIN produces higher quality lag measurements, is capable of measuring more lags with timescales shorter than the observing cadence, is less susceptible to seasonal gaps and signal-to-noise ratio degradation in the light curves, and produces more accurate lag uncertainties. We measure the Hβ broad-line region size–luminosity (R–L) relation with each method using the simulated light curves to assess the impact of selection effects of the design of MOS-RM surveys. The slope of the R–L relation measured by JAVELIN is the least biased among the three methods and is consistent across different survey designs. These results demonstrate a clear preference for JAVELIN over the other two nonparametric methods for MOS-RM programs, particularly in the regime of limited light-curve quality as expected from most MOS-RM programs.

Fourier-series expansion of the dark-energy equation of state

The dark energy component of the universe still remains as a mystery, however, several papers based on observational data have shown that its equation of state may have an oscillatory behaviour. In this paper, we provide a general description for the dark-energy equation-of-state $w(z)$ in the form of Fourier series. This description generalises some previous dynamical dark energy models and is in agreement with the $w(z)$ reconstructions. We make use of a modified version of a simple and fast Markov Chain Monte Carlo code to constraint the model parameters. For the analysis we use data from supernovae type-Ia , baryon acoustic oscillations, $H(z)$ measurements and cosmic microwave background. We provide a comparison of the proposed model with $\Lambda$CDM, $w$CDM and the standard Taylor approximation. The Fourier series expansion of $w(z)$ is preferred from $\Lambda$CDM at more than $3\sigma$ significance level based on the improvement in the fit alone. We use the Akaike criteria to perform the model comparison and found that, even though there are extra parameters, there is a slight preference of the Fourier series compared with the $\Lambda$CDM model. The preferred shape of $w(z)$ found here puts in jeopardy the single scalar field models, as they as they cannot reproduce the crossing the phantom divide line $w=-1$.

Orbits for 18 Visual Binaries and Two Double-line Spectroscopic Binaries Observed with HRCAM on the CTIO SOAR 4 m Telescope, Using a New Bayesian Orbit Code Based on Markov Chain Monte Carlo*

Abstract We present orbital elements and mass sums for 18 visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of . Adopting published photometry and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere using the SOAR 4 m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov chain Monte Carlo (MCMC) algorithm that delivers maximum-likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric and radial velocity data (“orbital parallax”), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from 10 to seven dimensions—including parallax—in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our MCMC code.

Star formation and AGN activity in a sample of local luminous infrared galaxies through multiwavelength characterization

Nuclear starbursts and active galactic nucleus (AGN) activity are the main heating processes in luminous infrared galaxies (LIRGs) and their relationship is fundamental to understand galaxy evolution. In this paper, we study the star formation and AGN activity of a sample of 11 local LIRGs imaged with subarcsecond angular resolution at radio (8.4 GHz) and near-infrared (2.2 μm) wavelengths. This allows us to characterize the central kpc of these galaxies with a spatial resolution of ≃100 pc. In general, we find a good spatial correlation between the radio and the near-IR emission, although radio emission tends to be more concentrated in the nuclear regions. Additionally, we use an Markov Chain Monte Carlo code to model their multiwavelength spectral energy distribution (SED) using template libraries of starburst, AGN and spheroidal/cirrus models, determining the luminosity contribution of each component, and finding that all sources in our sample are starburst-dominated, except for NGC 6926 with an AGN contribution of ≃64 per cent. Our sources show high star formation rates (40–167 M⊙ yr−1), supernova rates (0.4–2.0 SN yr−1) and similar starburst ages (13–29 Myr), except for the young starburst (9 Myr) in NGC 6926. A comparison of our derived star-forming parameters with estimates obtained from different IR and radio tracers shows an overall consistency among the different star formation tracers. AGN tracers based on mid-IR, high-ionization line ratios also show an overall agreement with our SED model fit estimates for the AGN. Finally, we use our wide-band Very Large Array observations to determine pixel-by-pixel radio spectral indices for all galaxies in our sample, finding a typical median value (α ≃ −0.8) for synchrotron-powered LIRGs.

Assessment of the potential of the new Belgo-Moroccan telescope TRAPPIST-North for high-precision exoplanet transit photometry

We present the observation of a transit of the exoplanet TrES-3b by the newly commissioned robotic telescope TRAPPIST-North located at Oukaimeden Observatory (Morocco). The obtained light curve reaches a photometric precison 600 ppm. Its Bayesian analysis with a Markov Chain Monte Carlo code enables us to refine the radius of the planet to . These results demonstrate the high potential of TRAPPIST-North for high-photometry of exoplanet transits.

The Impact of Modeling Assumptions in Galactic Chemical Evolution Models

Abstract We use the OMEGA galactic chemical evolution code to investigate how the assumptions used for the treatment of galactic inflows and outflows impact numerical predictions. The goal is to determine how our capacity to reproduce the chemical evolution trends of a galaxy is affected by the choice of implementation used to include those physical processes. In pursuit of this goal, we experiment with three different prescriptions for galactic inflows and outflows and use OMEGA within a Markov Chain Monte Carlo code to recover the set of input parameters that best reproduces the chemical evolution of nine elements in the dwarf spheroidal galaxy Sculptor. This provides a consistent framework for comparing the best-fit solutions generated by our different models. Despite their different degrees of intended physical realism, we found that all three prescriptions can reproduce in an almost identical way the stellar abundance trends observed in Sculptor. This result supports the similar conclusions originally claimed by Romano & Starkenburg for Sculptor. While the three models have the same capacity to fit the data, the best values recovered for the parameters controlling the number of SNe Ia and the strength of galactic outflows, are substantially different and in fact mutually exclusive from one model to another. For the purpose of understanding how a galaxy evolves, we conclude that only reproducing the evolution of a limited number of elements is insufficient and can lead to misleading conclusions. More elements or additional constraints such as the Galaxy’s star-formation efficiency and the gas fraction are needed in order to break the degeneracy between the different modeling assumptions. Our results show that the successes and failures of chemical evolution models are predominantly driven by the input stellar yields, rather than by the complexity of the Galaxy model itself. Simple models such as OMEGA are therefore sufficient to test and validate stellar yields. OMEGA is part of the NuGrid chemical evolution package and is publicly available online at http://nugrid.github.io/NuPyCEE.

MAPS OF EVOLVING CLOUD STRUCTURES IN LUHMAN 16AB FROM HST TIME-RESOLVED SPECTROSCOPY

ABSTRACT WISE J104915.57-531906.1 is the nearest brown dwarf binary to our solar system, consisting of two brown dwarfs in the L/T transition: Luhman 16A and B. In this paper, we present the first map of Luhman 16A, and maps of Luhman 16B for two epochs. Our maps were created by applying Aeolus, a Markov-Chain Monte Carlo code that maps the top-of-the-atmosphere (TOA) structure of brown dwarf and other ultracool atmospheres, to light curves of Luhman 16A and B using the Hubble Space Telescope’s G141 and G102 grisms. Aeolus retrieved three or four spots in the TOA of Luhman 16A and B, with a surface coverage of 19%–32% (depending on an assumed rotational period of 5 hr or 8 hr) or 21%–38.5% (depending on the observational epoch), respectively. The brightness temperature of the spots of the best-fit models was ∼200 K hotter than the background TOA. We compared our Luhman 16B map with the only previously published map. Interestingly, our map contained a large TOA spot that was cooler (ΔT ∼ 51 K) than the background, which lay at low latitudes, in agreement with the previous Luhman 16B map. Finally, we report the detection of a feature reappearing in Luhman 16B light curves that are separated by tens of hundreds of rotations from each other. We speculate that this feature is related to TOA structures of Luhman 16B.

Correlated X-ray/ultraviolet/optical variability in NGC 6814

We present results of a 3-month combined X-ray/UV/optical monitoring campaign of the Seyfert 1 galaxy NGC 6814. The object was monitored by Swift from June through August 2012 in the X-ray and UV bands and by the Liverpool Telescope from May through July 2012 in B and V. The light curves are variable and significantly correlated between wavebands. Using cross-correlation analysis, we compute the time lag between the X-ray and lower energy bands. These lags are thought to be associated with the light travel time between the central X-ray emitting region and areas further out on the accretion disc. The computed lags support a thermal reprocessing scenario in which X-ray photons heat the disc and are reprocessed into lower energy photons. Additionally, we fit the lightcurves using CREAM, a Markov Chain Monte Carlo code for a standard disc. The best-fitting standard disc model yields unreasonably high super-Eddington accretion rates. Assuming more reasonable accretion rates would result in significantly under-predicted lags. If the majority of the reprocessing originates in the disc, then this implies the UV/optical emitting regions of the accretion disc are farther out than predicted by the standard thin disc model. Accounting for contributions from broad emission lines reduces the lags in B and V by approximately 25% (less than the uncertainty in the lag measurements), though additional contamination from the Balmer continuum may also contribute to the larger than expected lags. This discrepancy between the predicted and measured interband delays is now becoming common in AGN where wavelength-dependent lags are measured.

Constraints on the temperature of the intergalactic medium atz= 8.4 with 21-cm observations

We compute robust lower limits on the spin temperature, $T_{\rm S}$, of the $z=8.4$ intergalactic medium (IGM), implied by the upper limits on the 21-cm power spectrum recently measured by PAPER-64. Unlike previous studies which used a single epoch of reionization (EoR) model, our approach samples a large parameter space of EoR models: the dominant uncertainty when estimating constraints on $T_{\rm S}$. Allowing $T_{\rm S}$ to be a free parameter and marginalizing over EoR parameters in our Markov Chain Monte Carlo code 21CMMC, we infer $T_{\rm S}\ge3 {\rm K}$ (corresponding approximately to $1\sigma$) for a mean IGM neutral fraction of $\bar{x}_{\rm H{\scriptsize I}}\gtrsim0.1$. We further improve on these limits by folding-in additional EoR constraints based on: (i) the dark fraction in QSO spectra, which implies a strict upper limit of $\bar{x}_{\rm H{\scriptsize I}}[z=5.9]\leq 0.06+0.05 \,(1\sigma)$; and (ii) the electron scattering optical depth, $\tau_{\rm e}=0.066\pm0.016\,(1\sigma)$ measured by the Planck satellite. By restricting the allowed EoR models, these additional observations tighten the approximate $1\sigma$ lower limits on the spin temperature to $T_{\rm S} \ge 6$ K. Thus, even such preliminary 21-cm observations begin to rule out extreme scenarios such as `cold reionization', implying at least some prior heating of the IGM. The analysis framework developed here can be applied to upcoming 21-cm observations, thereby providing unique insights into the sources which heated and subsequently reionized the very early Universe.

AEOLUS: A MARKOV CHAIN MONTE CARLO CODE FOR MAPPING ULTRACOOL ATMOSPHERES. AN APPLICATION ON JUPITER AND BROWN DWARFHSTLIGHT CURVES

Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of a giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR.

The initial conditions of observed star clusters – I. Method description and validation

We have coupled a fast, parametrized star cluster evolution code to a Markov Chain Monte Carlo code to determine the distribution of probable initial conditions of observed star clusters, which may serve as a starting point for future $N$-body calculations. In this paper we validate our method by applying it to a set of star clusters which have been studied in detail numerically with $N$-body simulations and Monte Carlo methods: the Galactic globular clusters M4, 47 Tucanae, NGC 6397, M22, $\omega$ Centauri, Palomar 14 and Palomar 4, the Galactic open cluster M67, and the M31 globular cluster G1. For each cluster we derive a distribution of initial conditions that, after evolution up to the cluster's current age, evolves to the currently observed conditions. We find that there is a connection between the morphology of the distribution of initial conditions and the dynamical age of a cluster and that a degeneracy in the initial half-mass radius towards small radii is present for clusters which have undergone a core collapse during their evolution. We find that the results of our method are in agreement with $N$-body and Monte Carlo studies for the majority of clusters. We conclude that our method is able to find reliable posteriors for the determined initial mass and half-mass radius for observed star clusters, and thus forms an suitable starting point for modeling an observed cluster\rq{}s evolution.

Observational constraints from supernovae Ia and gamma-ray bursts on a clumpy universe

The luminosity distance describing the effect of local inhomogeneities in the propagation of light proposed by Zeldovich, Kantowski, Dyer, and Roeder is tested with two probes for two distinct ranges of redshifts: supernovae Ia in $0.015\ensuremath{\le}z\ensuremath{\le}1.414$ and gamma-ray bursts in $1.547\ensuremath{\le}z\ensuremath{\le}3.57$. Our analysis is performed by a Markov chain Monte Carlo code that allows us to constrain the matter density parameter ${\ensuremath{\Omega}}_{m}$ as well as the smoothness parameter $\ensuremath{\alpha}$ that measures the inhomogeneous-homogeneous rate of the cosmic fluid in a flat $\ensuremath{\Lambda}$ cold dark matter model. The obtained best fits are ${\ensuremath{\Omega}}_{m}={0.285}_{\ensuremath{-}0.018}^{+0.019}$, $\ensuremath{\alpha}={0.856}_{\ensuremath{-}0.176}^{+0.106}$ from supernovae Ia, and ${\ensuremath{\Omega}}_{m}={0.259}_{\ensuremath{-}0.028}^{+0.028}$, $\ensuremath{\alpha}={0.587}_{\ensuremath{-}0.202}^{+0.201}$ from gamma-ray bursts, while from the joint analysis the best fits are ${\ensuremath{\Omega}}_{m}={0.284}_{\ensuremath{-}0.020}^{+0.021}$, $\ensuremath{\alpha}={0.685}_{\ensuremath{-}0.171}^{+0.164}$ with ${\ensuremath{\chi}}_{\mathrm{red}}^{2}=0.975$. The value of the smoothness parameter $\ensuremath{\alpha}$ indicates a clumped universe; however, it does not have an impact on the amount of dark energy (cosmological constant) needed to fit the observations. This result may be an indication that the Dyer-Roeder approximation does not describe in a precise form the effects of clumpiness in the expansion of the Universe.

First cosmological constraints on the superfluid Chaplygin gas model

In this paper we set observational constraints of the superfluid Chaplygin gas model, which gives a unified description of the dark sector of the Universe as a Bose-Einstein condensate that behaves as dark energy while it is in the ground state and as dark matter when it is in the excited state. We first show and perform the various steps leading to a form of the equations suitable for the observational tests to be carried out. Then, by using a Markov Chain Monte Carlo code, we constrain the model with a sample of cosmology-independent long gamma-ray bursts calibrated using their type I fundamental plane, as well as the Union2.1 set and observational Hubble parameter data. In this analysis, using our cosmological constraints, we sketch the effective equation of state parameter and the deceleration parameter, and we also obtain the redshift of the transition from deceleration to acceleration ${z}_{t}$.

Analysis of simulated data for the KArlsruhe TRItium Neutrino experiment using Bayesian inference

The KATRIN (KArlsruhe TRItium Neutrino) experiment will be analyzing the tritium beta-spectrum to determine the mass of the neutrino with a sensitivity of 0.2 eV (90% C.L.). This approach to a measurement of the absolute value of the neutrino mass relies only on the principle of energy conservation and can in some sense be called model-independent as compared to cosmology and neutrino-less double beta decay. However by model independent we only mean in case of the minimal extension of the standard model. One should therefore also analyse the data for non-standard couplings to e.g. righthanded or sterile neutrinos. As an alternative to the frequentist minimization methods used in the analysis of the earlier experiments in Mainz and Troitsk we have been investigating Markov Chain Monte Carlo (MCMC) methods which are very well suited for probing multi-parameter spaces. We found that implementing the KATRIN chi squared function in the COSMOMC package - an MCMC code using Bayesian parameter inference - solved the task at hand very nicely.