arXiv subjects

Pia Mukherjee

Publications and source records attributed to Pia Mukherjee.

36 records · Page 2Linked to original sources

arXiv2006

Robust Dark Energy Constraints from Supernovae, Galaxy Clustering, and Three-Year Wilkinson Microwave Anisotropy Probe Observations

Type Ia supernova (SN Ia), galaxy clustering, and cosmic microwave background anisotropy (CMB) data provide complementary constraints on the nature of the dark energy in the universe. We find that the three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations give a CMB shift parameter of R = (Ω_m H_0^2)^{1/2} \int_0^{z_{CMB}} dz'/H(z')= 1.70 \pm 0.03. Using this new measured value of the CMB shift parameter, together with the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS), and SN Ia data from the HST/GOODS program and the first year Supernova Legacy Survey, we derive model-independent constraints on the dark energy density rho_X(z) and the cosmic expansion rate H(z). We also derive constraints on the dark energy equation of state w_X(z)=w_0+w'z (with cutoff at z=2) and w_X(a)=w_0+(1-a)w_a. We find that current data provide slightly tighter constraints on rho_X(z) and H(z) as free functions in redshift, and roughly a factor of two improvement in constraining w_X(z). A cosmological constant remains consistent with data, however, uncertainties remain large for model-independent constraints of dark energy. Significant increase in the number of observed SNe Ia between redshifts of 1 and 2, complemented by improved BAO and weak lensing cosmography measurements (as expected from the JEDI mission concept for the Joint Dark Energy Mission), will be required to dramatically tighten model-independent dark energy constraints.

astro-ph↗

arXiv2006

A Bayesian model selection analysis of WMAP3

We present a Bayesian model selection analysis of WMAP3 data using our code CosmoNest. We focus on the density perturbation spectral index $n_S$ and the tensor-to-scalar ratio $r$, which define the plane of slow-roll inflationary models. We find that while the Bayesian evidence supports the conclusion that $n_S \neq 1$, the data are not yet powerful enough to do so at a strong or decisive level. If tensors are assumed absent, the current odds are approximately 8 to 1 in favour of $n_S \neq 1$ under our assumptions, when WMAP3 data is used together with external data sets. WMAP3 data on its own is unable to distinguish between the two models. Further, inclusion of $r$ as a parameter weakens the conclusion against the Harrison-Zel'dovich case (n_S = 1, r=0), albeit in a prior-dependent way. In appendices we describe the CosmoNest code in detail, noting its ability to supply posterior samples as well as to accurately compute the Bayesian evidence. We make a first public release of CosmoNest, now available at http://www.cosmonest.org.

astro-ph↗

arXiv2006

Model selection forecasts for the spectral index from the Planck satellite

The recent WMAP3 results have placed measurements of the spectral index n_S in an interesting position. While parameter estimation techniques indicate that the Harrison-Zel'dovich spectrum n_S=1 is strongly excluded (in the absence of tensor perturbations), Bayesian model selection techniques reveal that the case against n_S=1 is not yet conclusive. In this paper, we forecast the ability of the Planck satellite mission to use Bayesian model selection to convincingly exclude (or favour) the Harrison-Zel'dovich model.

astro-ph↗

arXiv2006

Model selection as a science driver for dark energy surveys

A key science goal of upcoming dark energy surveys is to seek time evolution of the dark energy. This problem is one of {\em model selection}, where the aim is to differentiate between cosmological models with different numbers of parameters. However, the power of these surveys is traditionally assessed by estimating their ability to constrain parameters, which is a different statistical problem. In this paper we use Bayesian model selection techniques, specifically forecasting of the Bayes factors, to compare the abilities of different proposed surveys in discovering dark energy evolution. We consider six experiments -- supernova luminosity measurements by the Supernova Legacy Survey, SNAP, JEDI, and ALPACA, and baryon acoustic oscillation measurements by WFMOS and JEDI -- and use Bayes factor plots to compare their statistical constraining power. The concept of Bayes factor forecasting has much broader applicability than dark energy surveys.

astro-ph↗

arXiv2006

Cosmic microwave background multipole alignments in slab topologies

Several analyses of the microwave sky maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have drawn attention to alignments amongst the low-order multipoles. Amongst the various possible explanations, an effect of cosmic topology has been invoked by several authors. We focus on an alignment of the first four multipoles (\ell = 2 to 5) found by Land and Magueijo (2005), and investigate the distribution of their alignment statistic for a set of simulated cosmic microwave background maps for cosmologies with slab-like topology. We find that this topology does offer a modest increase in the probability of the observed value, but that even for the smallest topology considered the probability of the observed value remains below one percent.

astro-ph↗

arXiv2006

A Nested Sampling Algorithm for Cosmological Model Selection

The abundance of new cosmological data becoming available means that a wider range of cosmological models are testable than ever before. However, an important distinction must be made between parameter fitting and model selection. While parameter fitting simply determines how well a model fits the data, model selection statistics, such as the Bayesian Evidence, are now necessary to choose between these different models, and in particular to assess the need for new parameters. We implement a new evidence algorithm known as nested sampling, which combines accuracy, generality of application and computational feasibility, and apply it to some cosmological datasets and models. We find that a five-parameter model with Harrison-Zel'dovich initial spectrum is currently preferred.

astro-ph↗

arXiv2006

Primordial Power Spectrum Reconstruction

In order to reconstruct the initial conditions of the universe it is important to devise a method that can efficiently constrain the shape of the power spectrum of primordial matter density fluctuations in a model-independent way from data. In an earlier paper we proposed a method based on the wavelet expansion of the primordial power spectrum. The advantage of this method is that the orthogonality and multiresolution properties of wavelet basis functions enable information regarding the shape of $P_{\rm in}(k)$ to be encoded in a small number of non-zero coefficients. Any deviation from scale-invariance can then be easily picked out. Here we apply this method to simulated data to demonstrate that it can accurately reconstruct an input $P_{\rm in}(k)$, and present a prescription for how this method should be used on future data.

astro-ph↗

arXiv2004

Wavelets and WMAP non-Gaussianity

We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows. We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations amongst wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parametrized by the non-linearity parameter $f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain $f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99% confidence.

astro-ph↗

arXiv2004

Looking for Cosmological Alfven Waves in WMAP Data

A primordial cosmological magnetic field induces and supports vorticity or Alfven waves, which in turn generate cosmic microwave background (CMB) anisotropies. A homogeneous primordial magnetic field with fixed direction induces correlations between the $a_{l-1,m}$ and $a_{l+1,m}$ multipole coefficients of the CMB temperature anisotropy field. We discuss the constraints that can be placed on the strength of such a primordial magnetic field using CMB anisotropy data from the WMAP experiment. We place 3 $σ$ upper limits on the strength of the magnetic field of $B < 15$ nG for vector perturbation spectral index $n=-5$ and $B<1.7$ nG for $n=-7$.

astro-ph↗

arXiv2004

Model-Independent Constraints on Dark Energy Density from Flux-averaging Analysis of Type Ia Supernova Data

We reconstruct the dark energy density $ρ_X(z)$ as a free function from current type Ia supernova (SN Ia) data (Tonry et al. 2003; Barris et al. 2003; Knop et al. 2003), together with the Cosmic Microwave Background (CMB) shift parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure (LSS) growth factor from 2dF galaxy survey data. We parametrize $ρ_X(z)$ as a continuous function, given by interpolating its amplitudes at equally spaced $z$ values in the redshift range covered by SN Ia data, and a constant at larger $z$ (where $ρ_X(z)$ is only weakly constrained by CMB data). We assume a flat universe, and use the Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that the dark energy density $ρ_X(z)$ is constant for $0 \la z \la 0.5$ and increases with redshift $z$ for $0.5 \la z \la 1$ at 68.3% confidence level, but is consistent with a constant at 95% confidence level. For comparison, we also give constraints on a constant equation of state for the dark energy. Flux-averaging of SN Ia data is required to yield cosmological parameter constraints that are free of the bias induced by weak gravitational lensing \citep{Wang00b}. We set up a consistent framework for flux-averaging analysis of SN Ia data, based on \cite{Wang00b}. We find that flux-averaging of SN Ia data leads to slightly lower $Ω_m$ and smaller time-variation in $ρ_X(z)$. This suggests that a significant increase in the number of SNe Ia from deep SN surveys on a dedicated telescope \citep{Wang00a} is needed to place a robust constraint on the time-dependence of the dark energy density.

astro-ph↗

arXiv2003

COBE-DMR-Normalized Dark Energy Cosmogony

Likelihood analyses of the COBE-DMR sky maps are used to determine the normalization of the inverse-power-law-potential scalar field dark energy model. Predictions of the DMR-normalized model are compared to various observations to constrain the allowed range of model parameters. Although the derived constraints are restrictive, evolving dark energy density scalar field models remain an observationally-viable alternative to the constant cosmological constant model.

astro-ph↗

arXiv2003

Direct Wavelet Expansion of the Primordial Power Spectrum

In order to constrain and possibly detect unusual physics during inflation, we allow the power spectrum of primordial matter density fluctuations, P_{in}(k), to be an arbitrary function in the estimation of cosmological parameters from data. The multi-resolution and good localization properties of orthogonal wavelets make them suitable for detecting features in P_{in}(k). We expand P_{in}(k) directly in wavelet basis functions. The likelihood of the data is thus a function of the wavelet coefficients of P_{in}(k), as well as the H_0, Ω_b h^2, $Ω_c h^2 and the τ_{ri}, in a flat $Λ$CDM cosmology. We derive constraints on these parameters from CMB anisotropy data (WMAP, CBI, and ACBAR) and large scale structure (LSS) data (2dFGRS and PSCZ) using the Markov Chain Monte Carlo (MCMC) technique. The direct wavelet expansion method is different and complimentary to the wavelet band power method of Mukherjee & Wang (2003a,b), and results from the two methods are consistent. In addition, as we demonstrate, the direct wavelet expansion method has the advantage that once the wavelet coefficients have been constrained, the reconstruction of P_{in}(k) can be effectively denoised, i.e., P_{in}(k) can be reconstructed using only the coefficients that, say, deviate from zero at greater than 1σ. In doing so the essential properties of P_{in}(k) are retained. The reconstruction also suffers much less from the correlated errors of binning methods. The shape of the primordial power spectrum, as reconstructed in detail here, reveals an interesting new feature at 0.001 \la k/{Mpc}^{-1} \la 0.005. It will be interesting to see if this feature is confirmed by future data. The reconstructed and denoised P_{in}(k) is favored over the scale-invariant and power-law forms at \ga 1σ.

astro-ph↗

arXiv2003

Model-Independent Reconstruction of the Primordial Power Spectrum from WMAP Data

Reconstructing the shape of the primordial power spectrum in a model independent way from cosmological data is a useful consistency check on what is usually assumed regarding early universe physics. It is also our primary window to unknown physics during the inflationary era. Using a power-law form for the primordial power spectrum $P_{in}(k)$ and constraining the scalar spectral index and its running, \cite{Peiris03} found that the first year WMAP data seem to indicate a preferred scale in $P_{in}(k)$. We use two complementary methods: the wavelet band powers method of \cite{pia1}, and the top-hat binning method of \cite{Wang99} to reconstruct $P_{in}(k)$ as a free function from CMB data alone (WMAP, CBI, and ACBAR), or from CMB data together with large scale structure data (2dFGRS and PCSZ). The shape of the reconstructed $P_{in}(k)$ is consistent with scale-invariance, although it allows some indication of a preferred scale at $k \sim 0.01$Mpc$^{-1}$. While consistent with the possible evidence for a running of the scalar spectral index found by the WMAP team, our results highlight the need of more stringent and independent constraints on cosmological parameters (the Hubble constant in particular) in order to more definitively constrain deviations of $P_{in}(k)$ from scale-invariance without making assumptions about the inflationary model.

astro-ph↗

arXiv2003

Galactic Foreground Constraints from the Python V Cosmic Microwave Background Anisotropy Data

We constrain Galactic foreground contamination of the Python V cosmic microwave background anisotropy data by cross correlating it with foreground contaminant emission templates. To model foreground emission we use 100 and 12 $μ$m dust emission templates and two point source templates based on the PMN survey. The analysis takes account of inter-modulation correlations in 8 modulations of the data that are sensitive to a large range of angular scales and also densely sample a large area of sky. As a consequence the analysis here is highly constraining. We find little evidence for foreground contamination in an analysis of the whole data set. However, there is indication that foregrounds are present in the data from the larger-angular-scale modulations of those Python V fields that overlap the region scanned earlier by the UCSB South Pole 1994 experiment. This is an independent consistency cross-check of findings from the South Pole 1994 data.

astro-ph↗

arXiv2003

Wavelet Band Powers of the Primordial Power Spectrum from CMB Data

Measuring the primordial matter power spectrum is our primary means of probing unknown physics in the very early universe. We allow the primordial power spectrum to be an arbitrary function, and parametrize it in terms of wavelet band powers. Current cosmological data correspond to 11 such wavelet bands. We derive constraints on these band powers as well as $H_0$, $Ω_b h^2$ and $Ω_m h^2$ from current Cosmic Microwave Background Anisotropy (CMB) data using the Markov Chain Monte Carlo (MCMC) technique. Our results indicate a feature in the primordial power spectrum at $ 0.008 \la k/(h {Mpc}^{-1}) \la 0.1$. MAP and Planck data should allow us to put tighter constraints on the primordial power spectrum.

astro-ph↗

arXiv2002

CMB Anisotropy Constraints on Flat-Lambda and Open CDM Cosmogonies from DMR, UCSB South Pole, Python, ARGO, MAX, White Dish, OVRO, and SuZIE Data

We use joint likelihood analyses of combinations of fifteen cosmic microwave background (CMB) anisotropy data sets from the DMR, UCSB South Pole 1994, Python I--III, ARGO, MAX 4 and 5, White Dish, OVRO, and SuZIE experiments to constrain cosmogonies. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with nonrelativistic-mass density parameter Omega_0 in the range 0.1--1, baryonic-mass density parameter Omega_B in the range (0.005--0.029) h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the data favor Omega_0 \simeq 0.9--1 (0.4--0.6) flat-Lambda (open) models. The range in deduced Omega_0 values is partially a consequence of the different combinations of smaller-angular-scale CMB anisotropy data sets used in the analyses, but more significantly a consequence of whether the DMR quadrupole moment is accounted for or ignored in the analysis. For both flat-Lambda and open models, after marginalizing over all other parameters, a lower Omega_B h^2 \simeq 0.005--0.009 is favored. This is also marginally at odds with estimates from more recent CMB anisotropy data and some estimates from standard nucleosynthesis theory and observed light element abundances. For both sets of models a younger universe with t_0 \simeq 12--15 Gyr is favored, consistent with other recent non-CMB indicators. We emphasize that since we consider only a small number of data sets, these results are tentative. More importantly, the analyses here do not rule out the currently favored flat-Lambda model with Omega_0 \sim 0.3, nor the larger Omega_B h^2 values favored by some other data.

astro-ph↗

arXiv2002

OVRO CMB Anisotropy Measurement Constraints on Flat-Lambda and Open CDM Cosmogonies

We use Owens Valley Radio Observatory (OVRO) cosmic microwave background (CMB) anisotropy data to constrain cosmological parameters. We account for the OVRO beamwidth and calibration uncertainties, as well as the uncertainty induced by the removal of non-CMB foreground contamination. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with nonrelativistic-mass density parameter Omega_0 in the range 0.1--1, baryonic-mass density parameter Omega_B in the range (0.005--0.029)h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the OVRO data favors an open (spatially-flat-Lambda) model with Omega_0 ~= 0.33 (0.1). At the 2 sigma confidence level model normalizations deduced from the OVRO data are mostly consistent with those deduced from the DMR, UCSB South Pole 1994, Python I-III, ARGO, MAX 4 and 5, White Dish, and SuZIE data sets.

astro-ph↗

arXiv2002

Galactic Foregrounds in OVRO and UCSB South Pole 1994 Cosmic Microwave Background Anisotropy Data

We study Galactic emission foreground contamination of the OVRO and UCSB South Pole 1994 cosmic microwave background (CMB) anisotropy data by cross-correlating with templates of infrared dust emission and new high resolution $H_α$ data. $H_α$ data provide rough upper limits on the level of free-free emission in the data sets. The cross-correlation analysis does not contradict a two component foreground emission hypothesis, with the two dust-correlated components being free-free emission and spinning dust emission.

astro-ph↗