arXiv subjects

M. Douspis

Publications and source records attributed to M. Douspis.

295 records · Page 17Linked to original sources

arXiv2001

Cosmological Constraints from the Cosmic Microwave Background

Using an approximate likelihood method adapted to band--power estimates, we analyze the ensemble of first generation cosmic microwave background anisotropy experiments to deduce constraints over a six--dimensional parameter space describing Inflation--generated adiabatic, scalar fluctuations. The basic preferences of simple Inflation scenarios are consistent with the data set: flat geometries $(\OmT \equiv 1-\Omk \sim 1)$ and a scale--invariant primeval spectrum ($n\sim 1$) are favored. Models with significant negative curvature ($\OmT < 0.7$) are eliminated, while constraints on postive curvature are less stringent. Degeneracies among the parameters prevent independent determinations of the matter density $\OmM$ and the cosmological constant $Λ$, and the Hubble constant $\Ho$ remains relatively unconstrained. We also find that the height of the first Doppler peak relative to the amplitude suggested by data at larger $l$ indicates a high baryon content ($\Omb h^2$), almost independently of the other parameters. Besides the overall qualitative advance expected of the next generation experiments, their improved dipole calibrations will be particularly useful for constraining the peak height. Our analysis includes a {\em Goodness--of--Fit} statistic applicable to power estimates and which indicates that the maximum likelihood model provides an acceptable fit to the data set.

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arXiv2001

Concerning Parameter Estimation Using the Cosmic Microwave Background

Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on pixel values. With the specific goal of testing this kind of approach, we have performed a complete (un-approximated) likelihood analysis combining the COBE, Saskatoon and MAX data sets. We examine in detail the ability of certain approximate techniques based on band-power estimates to recover the full likelihood constraints. The traditional $χ^2$-method does not always find the same best-fit model as the likelihood analysis (a bias), due mainly to the false assumption of Gaussian likelihoods that makes the method overly sensitive to data outliers. Although an improvement, other approaches employing non-Gaussian flat-band likelihoods do not always faithfully reproduce the complete likelihood constraints either; not even when using the exact flat-band likelihood curves. We trace this to the neglect of spectral information by simple flat band-power estimates. A straightforward extension incorporating a local effective slope (of the power spectrum, $C_l$) provides a faithful representation of the likelihood surfaces without significantly increasing computing cost. Finally, we also demonstrate that the best-fit model to this particular data set is a {\em good fit}, or that the observations are consistent with Gaussian sky fluctuations, according to our statistic.

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arXiv2001

An Approximation to the Likelihood Function for Band-Power Estimates of CMB Anisotropies

Band-power estimates of cosmic microwave background fluctuations are now routinely used to place constraints on cosmological parameters. For this to be done in a rigorous fashion, the full likelihood function of band-power estimates must be employed. Even for Gaussian theories, this likelihood function is not itself Gaussian, for the simple reason that band-powers measure the {\em variance} of the random sky fluctuations. In the context of Gaussian sky fluctuations, we use an ideal situation to motivate a general form for the full likelihood function from a given experiment. This form contains only two free parameters, which can be determined if the 68% and 95% confidence intervals of the true likelihood function are known. The ansatz works remarkably well when compared to the complete likelihood function for a number of experiments. For application of this kind of approach, we suggest that in the future both 68% and 95% (and perhaps also the 99.7%) confidence intervals be given when reporting experimental results.

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arXiv2000

CMB Cosmological Parameter Estimation: Methods and Current Results

The majority of present efforts to constrain cosmological parameters with cosmic microwave background (CMB) anisotropy data employ approximate likelihood functions, the time consuming nature of a complete analysis being a major obstacle. We have performed a full (unapproximated) likelihood analysis on several experiments that allows us to examine the various assumptions made in these approximate methods and to evaluate their performance. Our results indicate that care should be taken when using such approaches. With an improved approximate method, we present some constraints on cosmological parameters using the entire present CMB data set.

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arXiv1998

Approximating the Likelihood Function of CMB Experiments

We discuss the problem of constraining cosmological parameters with cosmic microwave background band--power estimates. Because these latter are variances, they do not have gaussian distribution functions and, hence, the standard $χ^2$--approach is not strictly applicable. A general purpose approximation to experimental band--power likelihood functions is proposed, which requires only limited experimental details. Comparison with the full likelihood function calculated for several experiments shows that the approximation works well.

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arXiv1998

Constraints on Cosmological Parameters from Current CMB Data

We discuss the constraints one can place on cosmological parameters using current cosmic microwave background data. A standard $χ^2$--minimization over band--power estimates is first presented, followed by a discussion of the more correct likelihood approach. We propose an approximation to the complete likelihood function of an arbitrary experiment requiring only limited and easily found information about the observations. Examination of both open models -- $(Ω,h,Q,n)$ -- and flat models ($Ω+Ω_Λ=1$) -- $(Ω,Ω_b,h,Q,n)$ -- leaves one rather robust result: models with small curvature are favored.

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arXiv1998

Constraints on Cosmological Parameters from Existing CMB Data

We use current cosmic microwave background data to constrain cosmological parameters. The results are presented as confidence regions in the ($Ω$--$H_o$) -- plane for both open and flat geometries, and are based on a $χ^2$ minimization to the power spectrum. Although such an approach does not strictly apply to power spectrum estimates, the results should nonetheless be indicative. We find that purely open, low--$Ω$ models are strongly disfavored, due to the position of the ``Doppler Peak'' at high $l$; flat models are less strongly constrained. The parameter space explored is the largest to date, covering $Ω$, $H_o$, $n$, $Q$ and $Ω_B h^2$.

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