arXiv subjects

Pia Mukherjee

Publications and source records attributed to Pia Mukherjee.

At least 19 recordsLinked to original sources

arXiv2013

General CMB bispectrum analysis using wavelets and separable modes

In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. This will be particularly important for upcoming surveys such as \emph{Planck}. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding $\fnllocal=38.4\pm 23.6$ and $\fnlequil=-119.2\pm123.6$.

astro-ph.CO↗

arXiv2012

Effects of cosmological model assumptions on galaxy redshift survey measurements

The clustering of galaxies observed in future redshift surveys will provide a wealth of cosmological information. Matching the signal at different redshifts constrains the dark energy driving the acceleration of the expansion of the Universe. In tandem with these geometrical constraints, redshift-space distortions (RSD) depend on the build up of large-scale structure. As pointed out by many authors measurements of these effects are intrinsically coupled. We investigate this link, and argue that it strongly depends on the cosmological assumptions adopted when analysing data. Using representative assumptions for the parameters of the Euclid survey in order to provide a baseline future experiment, we show how the derived constraints change due to different model assumptions. We argue that even the assumption of a Friedman-Robertson-Walker (FRW) space-time is sufficient to reduce the importance of the coupling to a significant degree. Taking this idea further, we consider how the data would actually be analysed and argue that we should not expect to be able to simultaneously constrain multiple deviations from the standard $Λ$CDM model. We therefore consider different possible ways in which the Universe could deviate from the $Λ$CDM model, and show how the coupling between geometrical constraints and structure growth affects the measurement of such deviations.

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arXiv2012

A Comparative Study of Dark Energy Constraints from Current Observational Data

We examine how dark energy constraints from current observational data depend on the analysis methods used: the analysis of Type Ia supernovae (SNe Ia), and that of galaxy clustering data. We generalize the flux-averaging analysis method of SNe Ia to allow correlated errors of SNe Ia, in order to reduce the systematic bias due to weak lensing of SNe Ia. We find that flux-averaging leads to larger errors on dark energy and cosmological parameters if only SN Ia data are used. When SN Ia data (the latest compilation by the SNLS team) are combined with WMAP 7 year results (in terms of our Gaussian fits to the probability distributions of the CMB shift parameters), the latest Hubble constant (H_0) measurement using the Hubble Space Telescope (HST), and gamma ray burst (GRB) data, flux-averaging of SNe Ia increases the concordance with other data, and leads to significantly tighter constraints on the dark energy density at z=1, and the cosmic curvature Ω_k. The galaxy clustering measurements of H(z=0.35)r_s(z_d) and r_s(z_d)/D_A(z=0.35) (where H(z) is the Hubble parameter, D_A(z) is the angular diameter distance, and r_s(z_d) is the sound horizon at the drag epoch) by Chuang & Wang (2011) are consistent with SN Ia data, given the same pirors (CMB+H_0+GRB), and lead to significantly improved dark energy constraints when combined. Current data are fully consistent with a cosmological constant and a flat universe.

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arXiv2011

Optimizing future dark energy surveys for model selection goals

We demonstrate a methodology for optimizing the ability of future dark energy surveys to answer model selection questions, such as `Is acceleration due to a cosmological constant or a dynamical dark energy model?'. Model selection Figures of Merit are defined, exploiting the Bayes factor, and surveys optimized over their design parameter space via a Monte Carlo method. As a specific example we apply our methods to generic multi-fibre baryon acoustic oscillation spectroscopic surveys, comparable to that proposed for SuMIRe PFS, and present implementations based on the Savage-Dickey Density Ratio that are both accurate and practical for use in optimization. It is shown that whilst the optimal surveys using model selection agree with those found using the Dark Energy Task Force (DETF) Figure of Merit, they provide better informed flexibility of survey configuration and an absolute scale for performance; for example, we find survey configurations with close to optimal model selection performance despite their corresponding DETF Figure of Merit being at only 50% of its maximum. This Bayes factor approach allows us to interpret the survey configurations that will be good enough for the task at hand, vital especially when wanting to add extra science goals and in dealing with time restrictions or multiple probes within the same project.

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arXiv2010

Detecting and distinguishing topological defects in future data from the CMBPol satellite

The proposed CMBPol mission will be able to detect the imprint of topological defects on the cosmic microwave background (CMB) provided the contribution is sufficiently strong. We quantify the detection threshold for cosmic strings and for textures, and analyse the satellite's ability to distinguish between these different types of defects. We also assess the level of danger of misidentification of a defect signature as from the wrong defect type or as an effect of primordial gravitational waves. A 0.002 fractional contribution of cosmic strings to the CMB temperature spectrum at multipole ten, and similarly a 0.001 fractional contribution of textures, can be detected and correctly identified at the 3σ level. We also confirm that a tensor contribution of r = 0.0018 can be detected at over 3σ, in agreement with the CMBpol mission concept study. These results are supported by a model selection analysis.

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arXiv2010

Designing a space-based galaxy redshift survey to probe dark energy

A space-based galaxy redshift survey would have enormous power in constraining dark energy and testing general relativity, provided that its parameters are suitably optimized. We study viable space-based galaxy redshift surveys, exploring the dependence of the Dark Energy Task Force (DETF) figure-of-merit (FoM) on redshift accuracy, redshift range, survey area, target selection, and forecast method. Fitting formulae are provided for convenience. We also consider the dependence on the information used: the full galaxy power spectrum P(k, P(k) marginalized over its shape, or just the Baryon Acoustic Oscillations (BAO). We find that the inclusion of growth rate information (extracted using redshift space distortion and galaxy clustering amplitude measurements) leads to a factor of ~ 3 improvement in the FoM, assuming general relativity is not modified. This inclusion partially compensates for the loss of information when only the BAO are used to give geometrical constraints, rather than using the full P(k) as a standard ruler. We find that a space-based galaxy redshift survey covering ~20,000 deg^2 over 0.5< z < 2 with σ_z/(1+z)<= 0.001 exploits a redshift range that is only easily accessible from space, extends to sufficiently low redshifts to allow both a vast 3-D map of the universe using a single tracer population, and overlaps with ground-based surveys to enable robust modeling of systematic effects. We argue that these parameters are close to their optimal values given current instrumental and practical constraints.

astro-ph.CO↗

arXiv2008

Planck and reionization history: a model selection view

We use Bayesian model selection tools to forecast the Planck satellite's ability to distinguish between different models for the reionization history of the Universe, using the large angular scale signal in the cosmic microwave background polarization spectrum. We find that Planck is not expected to be able to distinguish between an instantaneous reionization model and a two-parameter smooth reionization model, except for extreme values of the additional reionization parameter. If it cannot, then it will be unable to distinguish between different two-parameter models either. However, Bayesian model averaging will be needed to obtain unbiased estimates of the optical depth to reionization. We also generalize our results to a hypothetical future cosmic variance limited microwave anisotropy survey, where the outlook is more optimistic.

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arXiv2008

On the degeneracy between primordial tensor modes and cosmic strings in future CMB data from Planck

While observations indicate that the predominant source of cosmic inhomogeneities are adiabatic perturbations, there are a variety of candidates to provide auxiliary trace effects, including inflation-generated primordial tensors and cosmic defects which both produce B-mode cosmic microwave background (CMB) polarization. We investigate whether future experiments may suffer confusion as to the true origin of such effects, focusing on the ability of Planck to distinguish tensors from cosmic strings, and show that there is no significant degeneracy.

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arXiv2008

Planck priors for dark energy surveys

Although cosmic microwave background (CMB) anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. However computing a full CMB power spectrum with a Boltzmann code is quite slow; for instance if we want to work with many dark energy and/or modified gravity models, or would like to optimize experiments where many different configurations need to be tested, it is possible to adopt a quicker and more efficient approach. In this paper we consider the compression of the projected Planck CMB data into four parameters, R (scaled distance to last scattering surface), l_a (angular scale of sound horizon at last scattering), Omega_b h^2 (baryon density fraction) and n_s (powerlaw index of primordial matter power spectrum), all of which can be computed quickly. We show that, although this compression loses information compared to the full likelihood, such information loss becomes negligible when more data is added. We also demonstrate that the method can be used for scalar field dark energy independently of the parametrisation of the equation of state, and discuss how this method should be used for other kinds of dark energy models.

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arXiv2007

Observational Constraints on Dark Energy and Cosmic Curvature

Current observational bounds on dark energy depend on assumptions about the curvature of the universe. We present a simple and efficient method for incorporating constraints from CMB anisotropy data, and use it to derive constraints on cosmic curvature and dark energy density as a free function of cosmic time using current data. We show that there are two CMB shift parameters, R=sqrt{Ω_m H_0^2} r(z_{CMB}) (scaled distance to recombination) and l_a=πr(z_{CMB})/r_s(z_{CMB})(angular scale of the sound horizon at recombination), with measured values that are nearly uncorrelated with each other. Allowing nonzero cosmic curvature, the three-year WMAP data give R =1.71 +/- 0.03, l_a =302.5 +/- 1.2, and Ω_b h^2 = 0.02173 +/- 0.00082, independent of the dark energy model. The corresponding bounds for a flat universe are R =1.70 +/- 0.03, l_a =302.2 +/- 1.2, and Ω_b h^2 = 0.022 +/- 0.00082. We give the covariance matrix of (R, l_a, Ω_b h^2) from the three-year WMAP data. We find that (R, l_a, Ω_b h^2) provide an efficient and intuitive summary of CMB data as far as dark energy constraints are concerned. Using current CMB, SN Ia, and BAO data, we find that dark energy density is consistent with a constant in cosmic time, with marginal deviations from a cosmological constant that may reflect current systematic uncertainties or true evolution in dark energy. A flat universe is allowed by current data: Ω_k=-0.006_{-0.012}^{+0.013}_{-0.025}^{+0.025} for w_X(z)=const., and Ω_k=-0.002_{-0.018}^{+0.018}_{-0.032}^{+0.041} for w_X(z)=w_0+w_a(1-a)(68% and 95% C.L.). The bounds on cosmic curvature are less stringent if dark energy density is allowed to be a free function of cosmic time, and are also dependent on the assumption about the early time property of dark energy.

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arXiv2007

When can the Planck satellite measure spectral index running?

We use model selection forecasting to assess the ability of the Planck satellite to make a positive detection of spectral index running. We simulate Planck data for a range of assumed cosmological parameter values, and carry out a three-way Bayesian model comparison of a Harrison-Zel'dovich model, a power-law model, and a model including running. We find that Planck will be able to strongly support running only if its true value satisfies |dn/d ln k| > 0.02.

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arXiv2007

Observational Bounds on Modified Gravity Models

Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the Ricci and the Gauss-Bonnet scalars, both in the metric and in the Palatini formalisms. We do not use an explicit form for the functions, but a general form with a valid Taylor expansion up to second order about redshift zero in the Riemann-scalars. The coefficients of this expansion are then reconstructed via the cosmic expansion history measured using current cosmological observations. These are the quantities of interest for theoretical considerations relating to ghosts and instabilities. We find that current data provide interesting constraints on the coefficients. The next-generation dark energy surveys should shrink the allowed parameter space for modifed gravity models quite dramatically.

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arXiv2007

Nontrivial Geometries: Bounds on the Curvature of the Universe

Probing the geometry of the universe is one of the most important endevours in cosmology. Current observational data from the Cosmic Microwave Background anisotropy (CMB), galaxy surveys and type Ia supernovae (SNe Ia) strongly constrain the curvature of the universe to be close to zero for a universe dominated by a cosmological constant or dark energy with a constant equation of state. Here we investigate the role of cosmic priors on deriving these tight bounds on geometry, by considering a landscape motivated scenario with an oscillating curvature term. We perform a likelihood analysis of current data under such a model of non-trivial geometry and find that the uncertainties on curvature, and correspondingly on parameters of the matter and dark energy sectors, are larger. Future dark energy experiments together with CMB data from experiments like Planck could dramatically improve our ability to constrain cosmic curvature under such models enabling us to probe possible imprints of quantum gravity.

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arXiv2007

On what scale should inflationary observables be constrained?

We examine the choice of scale at which constraints on inflationary observables are presented. We describe an implementation of the hierarchy of inflationary consistency equations which ensures that they remain enforced on different scales, and then seek to optimize the scale for presentation of constraints on marginalized inflationary parameters from WMAP3 data. For models with spectral index running, we find a strong variation of the constraints through the range of observational scales available, and optimize by finding the scale which decorrelates constraints on the spectral index n_S and the running. This scale is k=0.017 Mpc^{-1}, and gives a reduction by a factor of more than four in the allowed parameter area in the n_S-r plane (r being the tensor-to-scalar ratio) relative to k=0.002 Mpc^{-1}. These optimized constraints are similar to those obtained in the no-running case. We also extend the analysis to a larger compilation of data, finding essentially the same conclusions.

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arXiv2007

Comment on `Tainted evidence: cosmological model selection versus fitting', by Eric V. Linder and Ramon Miquel (astro-ph/0702542v2)

In astro-ph/0702542v2, Linder and Miquel seek to criticize the use of Bayesian model selection for data analysis and for survey forecasting and design. Their discussion is based on three serious misunderstandings of the conceptual underpinnings and application of model-level Bayesian inference, which invalidate all their main conclusions. Their paper includes numerous further inaccuracies, including an erroneous calculation of the Bayesian Information Criterion. Here we seek to set the record straight.

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arXiv2006

Present and future evidence for evolving dark energy

We compute the Bayesian evidences for one- and two-parameter models of evolving dark energy, and compare them to the evidence for a cosmological constant, using current data from Type Ia supernova, baryon acoustic oscillations, and the cosmic microwave background. We use only distance information, ignoring dark energy perturbations. We find that, under various priors on the dark energy parameters, LambdaCDM is currently favoured as compared to the dark energy models. We consider the parameter constraints that arise under Bayesian model averaging, and discuss the implication of our results for future dark energy projects seeking to detect dark energy evolution. The model selection approach complements and extends the figure-of-merit approach of the Dark Energy Task Force in assessing future experiments, and suggests a significantly-modified interpretation of that statistic.

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arXiv2006

Cosmological model selection

Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require introduction of an additional parameter, describing a newly-discovered physical effect. We review several model selection statistics, and then focus on use of the Bayesian evidence, which implements the usual Bayesian analysis framework at the level of models rather than parameters. We describe our CosmoNest code, which is the first computationally-efficient implementation of Bayesian model selection in a cosmological context. We apply it to recent WMAP satellite data, examining the need for a perturbation spectral index differing from the scale-invariant (Harrison-Zel'dovich) case.

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arXiv2006

The WMAP normalization of inflationary cosmologies

We use the three-year WMAP observations to determine the normalization of the matter power spectrum in inflationary cosmologies. In this context, the quantity of interest is not the normalization marginalized over all parameters, but rather the normalization as a function of the inflationary parameters n and r with marginalization over the remaining cosmological parameters. We compute this normalization and provide an accurate fitting function. The statistical uncertainty in the normalization is 3 percent, roughly half that achieved by COBE. We use the k-l relation for the standard cosmological model to identify the pivot scale for the WMAP normalization. We also quote the inflationary energy scale corresponding to the WMAP normalization.

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