How many cosmological parameters

By Andrew R. Liddle. 2004

409 citations recorded by the source corpus.

Constraints on cosmological parameters depend on the set of parameters chosen to define the model that is compared with observational data. I use the Akaike and Bayesian information criteria to carry out cosmological model selection, in order to determine the parameter set providing the preferred fit to the data. Applying the information criteria to the current cosmological data sets indicates, for example, that spatially flat models are statistically preferred to closed models, and that possible running of the spectral index has lower significance than inferred from its confidence limits. I also discuss some problems of statistical assessment arising from there being a large number of 'candidate' cosmological parameters that can be investigated for possible cosmological implications, and argue that 95 per cent confidence is too low a threshold to identify robustly the need for new parameters in model fitting. The best present description of cosmological data uses a scale-invariant (n = 1) spectrum of Gaussian adiabatic perturbations in a spatially flat Universe, with the cosmological model requiring only five fundamental parameters to specify it fully.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4083571709dba96b9ec50d731e72bacb35ed983e

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Citations in the corpus

A remarkably flat relationship between the average star formation rate and AGN luminosity for distant X-ray AGN. (2015, methodology): “If BIC ≤ 2 then both models are considered equally valid (e.g. Liddle 2004).”
Issues in the Philosophy of Cosmology (2006, background): “ matter clustering [48] together with observations of gravitational lensing and large-scale motions of matter [203]. This model is characterized by speciﬁc values for a set of cosmological parameters [139], in particular Ω cdm0 ≃ 0.3, ΩΛ0 ≃ 0.7, T cbr0 = 2.75K, H0 ≃ 65km/sec/mpc, t0 ≃ 1.4×1010years.”
Confronting Lemaitre–Tolman–Bondi models with observational cosmology (2008, background): “cosmological model, within some given priors, both theoretical and observational, see e.g. Refs. [ 52 , 53, 54, 55].”
Information criteria for astrophysical model selection (2007, methodology): “In Liddle (2004), I described two such statistics, the AIC and BIC, which have subsequently been quite widely applied to astrophysics problems.”
SN 2008S: An electron-capture SN from a super-AGB progenitor? (2009, methodology): “To test further that the data are better represented by a temporally declining EW, rather than a fixed value, we exploited the Bayesian information criterion (BIC), which give an approximation for the Bayes factor (see Liddle 2004, and references therein).”
The Axis of Evil revisited (2006, background): “This matter is behind the “Occam’s razor” rationale (Magueijo & Sorkin 2006), and the information criteria (Liddle 2004).”
RECONSTRUCTING DARK ENERGY (2006, neutral): “A.R.Liddle,2004,M on.”
Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes (2007, background): “Liddle (2004) examines the use of information criteria in the context of cosmological observations and we follow his prescription here.”
A kinematical approach to dark energy studies (2006, background): “∆BIC between 2 and 6 indicates ‘positive evidence’ for an improvement, and values greater than 6 signify ‘strong evidence’ for the model with the higher BIC (Jeffreys 1961; Kass & Raftery 1995; Mukherjee et al. 1998; Liddle 2004).”
THE EFFECT OF HOST GALAXIES ON TYPE Ia SUPERNOVAE IN THE SDSS-II SUPERNOVA SURVEY (2010, methodology): “1 and 2 respectively) to the full SN sample, regardless of host galaxy type, using the Bayesian Information Criteria (BIC; Liddle 2004).”
General Relativity and Cosmology: Unsolved Questions and Future Directions (2016, neutral): “Should we include a cosmological constant in General Relativity? Or should we include dynamical dark energy parameter? Although current data are consistent with the six-parameter ΛCDM model based on GR, there are more than twenty candidate parameters which might be required by future data (see [516]”
A Nested Sampling Algorithm for Cosmological Model Selection (2005, result): “Hence we do not find any indication of a need to introduce parameters be- yond the base set of 5, in agreement with the conclusions of Liddle (2004) and Trotta (2005).”
Conditions for Reionizing the Universe with a Low Galaxy Ionizing Photon Escape Fraction (2019, neutral): “This is similar to the Bayesian information criteria (Liddle 2004) in that it takes into account both the number of data points and the number of free parameters.”