We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action ("Lefschetz thimble"). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). We exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.

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We present a new public Python package, DarkHistory, for computing the effects of dark matter annihilation and decay on the temperature and ionization history of the early universe. DarkHistory simultaneously solves for the evolution of the free electron fraction and gas temperature, and for the cooling of annihilation/decay products and the secondary particles produced in the process. Consequently, we can self-consistently include the effects of both astrophysical and exotic sources of heating and ionization, and automatically take into account backreaction, where modifications to the ionization/temperature history in turn modify the energy-loss processes for injected particles. We present a number of worked examples, demonstrating how to use the code in a range of different configurations, in particular for arbitrary dark matter masses and annihilation/decay final states. Possible applications of DarkHistory include mapping out the effects of dark matter annihilation/decay on the global 21cm signal and the epoch of reionization, as well as the effects of exotic energy injections other than dark matter annihilation/decay. The code is available at https://github.com/hongwanliu/DarkHistory with documentation at https://darkhistory.readthedocs.io. Data files required to run the code can be downloaded at https://doi.org/10.7910/DVN/DUOUWA. arXiv:1904.09296v1 [astro-ph.CO] 19 Apr 2019 1 We follow the standard astrophysical convention in which H and H + are denoted HI and HII, while He, He + and He 2+ are denoted HeI, HeII and HeIII respectively. 2 The value of β H used in DarkHistory includes the constant and gaussian fudge factors used by version 1.5.2 of RECFAST.

We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz thimble method.

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A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V 3 ), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V ). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N 3 ) to less than O(N 2 ). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar φ 4 theory with weak and strong couplings.

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