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SuperCosmology

Renata Kallosh, Sergey Prokushkin

TL;DR

SuperCosmology provides a Mathematica toolkit for analyzing cosmologies derived from N=1 supergravity and string compactifications. It combines symbolic computation of the scalar potential via V = V_F + V_D, with explicit forms V_F = e^K[(D_i W) g^{ij} (D_j W^*) - 3 W W^*] and V_D = (1/2)(Re f)^{-1} P^2, and a numerical solver for multi-field FRW dynamics with noncanonical kinetic terms in a Hamiltonian first-order formulation. The paper demonstrates new models including a shift-symmetric inflation scenario with a mobile D3 brane and a KKLT-based dark-energy model driven by the axion of the volume modulus. By providing Part I (potential computation) and Part II (FRW evolution), the work enables systematic exploration of moduli stabilization, inflationary trajectories, and late-time acceleration in string-inspired cosmologies.

Abstract

We present a Mathematica package for performing algebraic and numerical computations in cosmological models based on supersymmetric theories. The programs allow for (I) evaluation and study of the properties of a scalar potential in a large class of supergravity models with any number of moduli and arbitrary superpotential, Kahler potential, and D-term; (II) numerical solution of a system of scalar and Friedmann equations for the flat FRW universe, with any number of scalar moduli and arbitrary moduli space metric. We are using here a simple set of first order differential equations which we derived in a Hamiltonian framework. Using our programs we present some new results: (I) a shift-symmetric potential of the inflationary model with a mobile D3 brane in an internal space with stabilized volume; (II) a KKLT-based dark energy model with the acceleration of the universe due to the evolution of the axion partner of the volume modulus. The gzipped package can be downloaded from http://www.stanford.edu/~prok/SuperCosmology/ or from http://www.stanford.edu/~rkallosh/SuperCosmology/

SuperCosmology

TL;DR

SuperCosmology provides a Mathematica toolkit for analyzing cosmologies derived from N=1 supergravity and string compactifications. It combines symbolic computation of the scalar potential via V = V_F + V_D, with explicit forms V_F = e^K[(D_i W) g^{ij} (D_j W^*) - 3 W W^*] and V_D = (1/2)(Re f)^{-1} P^2, and a numerical solver for multi-field FRW dynamics with noncanonical kinetic terms in a Hamiltonian first-order formulation. The paper demonstrates new models including a shift-symmetric inflation scenario with a mobile D3 brane and a KKLT-based dark-energy model driven by the axion of the volume modulus. By providing Part I (potential computation) and Part II (FRW evolution), the work enables systematic exploration of moduli stabilization, inflationary trajectories, and late-time acceleration in string-inspired cosmologies.

Abstract

We present a Mathematica package for performing algebraic and numerical computations in cosmological models based on supersymmetric theories. The programs allow for (I) evaluation and study of the properties of a scalar potential in a large class of supergravity models with any number of moduli and arbitrary superpotential, Kahler potential, and D-term; (II) numerical solution of a system of scalar and Friedmann equations for the flat FRW universe, with any number of scalar moduli and arbitrary moduli space metric. We are using here a simple set of first order differential equations which we derived in a Hamiltonian framework. Using our programs we present some new results: (I) a shift-symmetric potential of the inflationary model with a mobile D3 brane in an internal space with stabilized volume; (II) a KKLT-based dark energy model with the acceleration of the universe due to the evolution of the axion partner of the volume modulus. The gzipped package can be downloaded from http://www.stanford.edu/~prok/SuperCosmology/ or from http://www.stanford.edu/~rkallosh/SuperCosmology/

Paper Structure

This paper contains 6 sections, 29 equations, 6 figures.

Table of Contents

  1. Introduction
  2. N=1 supergravity potentials fixing the moduli
  3. Solving Friedmann equations in supergravity-based models of dark energy
  4. First order Friedmann equations
  5. A KKLT-based toy model of dark energy
  6. Discussion

Figures (6)

  • Figure 1: Potential of the KKLT model depending on the volume $\sigma$ and the axion $\alpha$
  • Figure 2: Contour plot in the $(\sigma, \alpha)$ plane
  • Figure 3: Volume as a function of time
  • Figure 4: Axion as a function of time
  • Figure 5: $\Omega_D$ growth towards $\sim 0.72$
  • ...and 1 more figures