The moduli problem at the perturbative level

M. Lemoine¹, J. Martin¹ and J. Yokoyama^2,3

¹  Institut d'Astrophysique de Paris, CNRS - UPMC - 98bis boulevard Arago, 75014 Paris, France, EU
²  Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo Tokyo, 113-0033, Japan
³  Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo Kashiwa, Chiba 277-8568, Japan

Corresponding authors: lemoine@iap.fr - jmartin@iap.fr - yokoyama@resceu.s.u-tokyo.ac.jp

Received: 14 October 2009
Accepted: 8 January 2010

Abstract

This paper demonstrates that existing upper bounds on the magnitude of cosmological dark matter and baryon isocurvature fluctuations can be translated into stringent constraints on the parameter space of moduli fields of supersymmetric theories, defined in terms of (modulus mass) and (modulus vacuum expectation value at the end of inflation). For the sake of concreteness, we assume here a quadractic modulus potential and we focus on high-scale inflationary models. These constraints are complementary to previously existing bounds from big-bang nucleosynthesis, therefore the moduli problem becomes worse at the level of cosmological perturbations. In particular, if the inflationary scale ~ 10¹³ GeV, particle physics scenarios which predict high moduli masses  ≳ 10–100 TeV are plagued by the perturbative moduli problem, even though they evade big-bang nucleosynthesis constraints. This perturbative moduli problem is somewhat relaxed if the modulus is made heavy during inflation, with effective mass ≳.