polychord: nested sampling for cosmology Handley, W. J; Hobson, M. P; Lasenby, A. N
Monthly notices of the Royal Astronomical Society. Letters,
06/2015, Letnik:
450, Številka:
1
Journal Article
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Odprti dostop
polychord is a novel nested sampling algorithm tailored for high-dimensional parameter spaces. In addition, it can fully exploit a hierarchy of parameter speeds such as is found in cosmomc and camb. ...It utilizes slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently and is parallelized using openmpi. polychord is available for download at http://ccpforge.cse.rl.ac.uk/gf/project/polychord/.
polychord: next-generation nested sampling Handley, W. J; Hobson, M. P; Lasenby, A. N
Monthly notices of the Royal Astronomical Society,
11/2015, Letnik:
453, Številka:
4
Journal Article
Recenzirano
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polychord is a novel nested sampling algorithm tailored for high-dimensional parameter spaces. This paper coincides with the release of polychord v1.6, and provides an extensive account of the ...algorithm. polychord utilizes slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently, and is parallelized using openmpi. It is capable of exploiting a hierarchy of parameter speeds such as those present in cosmomc and camb, and is now in use in the cosmochord and modechord codes. polychord is available for download from http://ccpforge.cse.rl.ac.uk/gf/project/polychord/.
We develop a novel technique for numerically computing the primordial power spectra of comoving curvature perturbations. By finding suitable analytic approximations for different regions of the mode ...equations and stitching them together, we reduce the solution of a differential equation to repeated matrix multiplication. This results in a wave-number-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wave numbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance. We further generalize to a novel class of frozen initial conditions which prove capable of emulating a quantized primordial power spectrum.
We theoretically and observationally investigate different choices of initial conditions for the primordial mode function that are imposed during an epoch preceding inflation. By deriving predictions ...for the observables resulting from several alternate quantum vacuum prescriptions we show some choices of vacua are theoretically observationally distinguishable from others. Comparing these predictions to the Planck 2018 observations via a Bayesian analysis shows no significant evidence to favor any of the quantum vacuum prescriptions over the others. In addition we consider frozen initial conditions, representing a white-noise initial state at the big-bang singularity. Under certain assumptions the cosmological concordance model and frozen initial conditions are found to produce identical predictions for the cosmic microwave background anisotropies. Frozen initial conditions may thus provide an alternative theoretic paradigm to explain observations that were previously understood in terms of the inflation of a quantum vacuum.
Abstract
Data-driven model-independent reconstructions of the dark energy equation of state w(z) are presented using Planck 2015 era cosmic microwave background, baryonic acoustic oscillations (BAO), ...Type Ia supernova (SNIa) and Lyman α (Lyα) data. These reconstructions identify the w(z) behaviour supported by the data and show a bifurcation of the equation of state posterior in the range 1.5 < z < 3. Although the concordance Λ cold dark matter (ΛCDM) model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other, a supernegative equation of state (also known as ‘phantom dark energy’) is identified within the 1.5σ confidence intervals of the posterior distribution. To identify the power of different data sets in constraining the dark energy equation of state, we use a novel formulation of the Kullback–Leibler divergence. This formalism quantifies the information the data add when moving from priors to posteriors for each possible data set combination. The SNIa and BAO data sets are shown to provide much more constraining power in comparison to the Lyα data sets. Further, SNIa and BAO constrain most strongly around redshift range 0.1–0.5, whilst the Lyα data constrain weakly over a broader range. We do not attribute the supernegative favouring to any particular data set, and note that the ΛCDM model was favoured at more than 2 log-units in Bayes factors over all the models tested despite the weakly preferred w(z) structure in the data.
Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. ...The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.
We review the effect that the choice of a uniform or logarithmic prior has on the Bayesian evidence and hence on Bayesian model comparisons when data provide only a one-sided bound on a parameter. We ...investigate two particular examples: the tensor-to-scalar ratio r of primordial perturbations and the mass of individual neutrinos mν, using the cosmic microwave background temperature and polarization data from Planck 2018 and the NuFIT 5.0 data from neutrino oscillation experiments. We argue that the Kullback–Leibler divergence, also called the relative entropy, mathematically quantifies the Occam penalty. We further show how the Bayesian evidence stays invariant upon changing the lower prior bound of an upper constrained parameter. While a uniform prior on the tensor-to-scalar ratio disfavors the r extension compared to the base ΛCDM model with odds of about 1∶20, switching to a logarithmic prior renders both models essentially equally likely. ΛCDM with a single massive neutrino is favored over an extension with variable neutrino masses with odds of 20∶1 in case of a uniform prior on the lightest neutrino mass, which decreases to roughly 2∶1 for a logarithmic prior. For both prior options we get only a very slight preference for the normal over the inverted neutrino hierarchy with Bayesian odds of about 3∶2 at most.
ABSTRACT
Emulation of the Global (sky-averaged) 21-cm signal with neural networks has been shown to be an essential tool for physical signal modelling. In this paper, we present globalemu, a Global ...21-cm signal emulator that uses redshift as a character-defining variable alongside a set of astrophysical parameters to estimate the signal brightness temperature. Combined with physically motivated data pre-processing, this makes for a reliable and fast emulator that is relatively insensitive to the network design. globalemu can emulate a high-resolution signal in 1.3 ms in comparison to 133 ms, a factor of 102 improvement, when using the existing public state-of-the-art 21cmGEM. We illustrate, with the standard astrophysical models used to train 21cmGEM, that globalemu is almost twice as accurate and for a test set of ≈1700 signals we achieve a mean root mean squared error of 2.52 mK across the band z = 7–28 ≈10 per cent the expected noise of the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). The models are parametrized by the star formation efficiency, f*, minimum virial circular velocity, Vc, X-ray efficiency, fX, cosmic microwave background optical depth, τ, the slope and low energy cut-off of the X-ray spectral energy density, α and νmin, respectively, and the mean free path of ionizing photons, Rmfp. globalemu provides a flexible framework for easily emulating updated simulations of the Global signal and in addition the neutral fraction history. The emulator is pip installable and available at https://github.com/htjb/globalemu. globalemu will be used extensively by the REACH collaboration.
We present cosmological constraints from Planck 2015 data for a Universe that is kinetically dominated at very early times. We perform a Markov chain Monte Carlo analysis to estimate parameters and ...use nested sampling to determine the evidence for a model comparison of the single-field quadratic and Starobinsky inflationary models with the standard ΛCDM cosmology. In particular we investigate how different amounts of inflation before and after horizon exit affect the primordial power spectrum and subsequently the power spectrum of the cosmic microwave background. We find that the model using kinetically dominated initial conditions for inflation performs similarly well in terms of Bayesian evidence as a model directly starting out in the slow-roll phase, despite having an additional parameter. The data show a slight preference for a cutoff at large scales in the primordial and temperature power spectra.
We propose a one-parameter extension to Λ CDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early Universe redshifts away as hot dark matter, then ...quintessence, tracking the dominant equation-of-state parameter and leaving a falsifiable torsion field in the current epoch. This picture results from a new Poincaré gauge theory (PGT), one of the most promising among the latest batch of 58 PGTs found to be both power-counting renormalizable and free from ghosts and tachyons. We systematically categorize the cosmologies of 33 of these PGTs, as special cases of the most general parity-preserving, Ostrogradsky-stable PGT with a purely Yang-Mills action. The theory we consider contains two propagating massless gravitons, which may be JP = 2+ (long-range gravitation and gravitational waves). A conspiracy among the coupling constants eliminates the spatial curvature k ∈ {±1, 0} from the field equations. We show that this " k-screening" is not restricted to conformal gravity theories. The flat Friedmann equations are then emergent, with potentially tension-resolving freedom at the early scale-invariant epoch that reliably gives way to an attractorlike state of modern Λ CDM evolution. We compare with related theories and promising special cases, such as k -screened theories with negative-definite effective k , and more traditional theories with effective Λ and a JP = 0− massive graviton (dark matter candidate). As a bonus, we analyze similarly constrained actions in the new extended Weyl gauge theory (eWGT). We show that in cosmology, PGT and eWGT span exactly the same classical phenomenology up to a linear map between their coupling constants, hinting at a deeper relationship between the two.
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