SciPost Phys. 14, 109 (2023) ·
published 12 May 2023

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Nontrivial inflaton selfinteractions can yield calculable signatures of primordial nonGaussianity that are measurable in cosmic surveys. We calculate the nonGaussian corrections to Stochastic Inflation within the framework of Soft de Sitter Effective Theory, from which we derive the associated probability distribution for the scalar fluctuations. As a consequence of this new result, we show that the phase transition to slowroll eternal inflation is often incalculable in these models. Instead, this transition is sensitive to the nonGaussian tail of the distribution of scalar fluctuations, which probes physics inside the horizon, potentially beyond the cutoff scale of the Effective Field Theory of Inflation. We delineate the parameter space consistent with current observations and weak coupling at horizon crossing in which the large fluctuations relevant for eternal inflation can only be determined by appealing to a UV completion. We also argue that this breakdown of the perturbative description is required for the de Sitter entropy to reflect the number of de Sitter microstates.
Timothy Cohen, Kara Farnsworth, Rachel Houtz, Markus A. Luty
SciPost Phys. 13, 011 (2022) ·
published 4 August 2022

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Hamiltonian truncation is a nonperturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finitedimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finitedimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective Hamiltonian is nonlocal, with the nonlocality controlled in an expansion in powers of $H_0/E_\text{max}$. The effective Hamiltonian is also nonHermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda \phi^4$ theory, and compute the the leading $1/E_\text{max}^2$ corrections to the effective Hamiltonian. We show that these corrections nontrivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_\text{max}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda \phi^4$ theory and perform calculations that demonstrate the separation of scales in this theory.
SciPost Phys. 10, 098 (2021) ·
published 3 May 2021

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This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in arXiv:2011.02484 . The code and an example notebook are available at https://www.github.com/EFTMatching/STrEAM .
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