Bayesian parameter inference is an essential tool in modern cosmology, and typically requires the calculation of 105–106 theoretical models for each inference of model parameters for a given dataset combination. Computing these models by solving the linearised Einstein-Boltzmann system usually takes tens of CPU core-seconds per model, making the entire process very computationally expensive. In this paper we present connect, a neural network framework emulating class computations as an easy-to-use plug-in for the popular sampler MontePython. connect uses an iteratively trained neural network which emulates the observables usually computed by class. The training data is generated using class, but using a novel algorithm for generating favourable points in parameter space for training data, the required number of class-evaluations can be reduced by two orders of magnitude compared to a traditional inference run. Once connect has been trained for a given model, no additional training is required for different dataset combinations, making connect many orders of magnitude faster than class (and making the inference process entirely dominated by the speed of the likelihood calculation). For the models investigated in this paper we find that cosmological parameter inference run with connect produces posteriors which differ from the posteriors derived using class by typically less than 0.01–0.1 standard deviations for all parameters. We also stress that the training data can be produced in parallel, making efficient use of all available compute resources. The connect code is publicly available for download on GitHub (https://github.com/AarhusCosmology/connect_public).

Bayesian parameter inference is an essential tool in modern cosmology, and typically requires the calculation of 10 5 -10 6 theoretical models for each inference of model parameters for a given dataset combination. Computing these models by solving the linearised Einstein-Boltzmann system usually takes tens of CPU core-seconds per model, making the entire process very computationally expensive.In this paper we present connect, a neural network framework emulating class computations as an easy-to-use plug-in for the popular sampler MontePython. connect uses an iteratively trained neural network which emulates the observables usually computed by class. The training data is generated using class, but using a novel algorithm for generating favourable points in parameter space for training data, the required number of class-evaluations can be reduced by two orders of magnitude compared to a traditional inference run. Once connect has been trained for a given model, no additional training is required for different dataset combinations, making connect many orders of magnitude faster than class (and making the inference process entirely dominated by the speed of the likelihood calculation).For the models investigated in this paper we find that cosmological parameter inference run with connect produces posteriors which differ from the posteriors derived using class by typically less than 0.01-0.1 standard deviations for all parameters. We also stress that the training data can be produced in parallel, making efficient use of all available compute resources. The connect code is publicly available for download at https://github.com/ AarhusCosmology.

Recent interest in new early dark energy (NEDE), a cosmological model with a vacuum energy component decaying in a triggered phase transition around recombination, has been sparked by its impact on the Hubble tension. Previous constraints on the model parameters were derived in a Bayesian framework with Markov-chain Monte Carlo (MCMC) methods. In this work, we instead perform a frequentist analysis using the profile likelihood in order to assess the impact of prior volume effects on the constraints. We constrain the maximal fraction of NEDE f NEDE , finding f NEDE ¼ 0.076 þ0.040 −0.035 at 68% CL with our baseline dataset and similar constraints using either data from SPT-3G, ACT or full-shape large-scale structure, showing a preference over ΛCDM even in the absence of a SH0ES prior on H 0 . While this is stronger evidence for NEDE than obtained with the corresponding Bayesian analysis, our constraints broadly match those obtained by fixing the NEDE trigger mass. Including the SH0ES prior on H 0 , we obtain f NEDE ¼ 0.136 þ0.024 −0.026 at 68% CL. Furthermore, we compare NEDE with the early dark energy (EDE) model, finding similar constraints on the maximal energy density fractions and H 0 in the two models. At 68% CL in the NEDE model, we find H 0 ¼ 69.56 þ1.16 −1.29 km s −1 Mpc −1 with our baseline and H 0 ¼ 71.62 þ0.78 −0.76 km s −1 Mpc −1 when including the SH0ES measurement of H 0 , thus corroborating previous conclusions that the NEDE model provides a considerable alleviation of the H 0 tension.

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