Effects of Cosmological Moduli Fields on Cosmic Microwave Background

We discuss effects of cosmological moduli fields on the cosmic microwave background (CMB). If a modulus field φ once dominates the universe, the CMB we observe today is from the decay of φ and its anisotropy is affected by the primordial fluctuation in the amplitude of the modulus field. Consequently, constraints on the inflaton potential from the CMB anisotropy can be relaxed. In particular, the scale of the inflation may be significantly lowered. In addition, with the cosmological moduli fields, correlated mixture of adiabatic and isocurvature fluctuations may be generated, which results in enhanced CMB angular power spectrum at higher multipoles relative to that of lower ones. Such an enhancement can be an evidence of the cosmological moduli fields, and may be observed in future satellite experiments. In superstring theory [1], it is well known that there are various flat directions parameterized by scalar fields. (Hereafter, we call these fields as “moduli” fields.) Since their potential is usually generated by effects of supersymmetry (SUSY) breaking, their masses are expected to be of the order of the gravitino mass. Although masses of the moduli fields can be as light as (or even lighter than) the electroweak scale, moduli fields do not affect collider experiments since their interactions are suppressed by inverse powers of the gravitational scale. Cosmologically, however, they may cause serious problems [2]. Since the modulus field φ is a scalar field, its primordial amplitude may be displaced from the minimum of the potential, and this is naturally the case unless the minimum of the potential is protected by some symmetry [3]. If such a displacement exists, then the modulus field starts to oscillate at later stage of the universe and dominates the energy density of the universe. Since the interaction of the modulus field is expected to be suppressed by inverse powers of the gravitational scale, its decay width is at most Γφ ∼ 1 4π mφ M2 ∗ , (1) where mφ is the mass of the modulus field and M∗ ≃ 2.4×10 18 GeV is the reduced Planck scale. Using Eq. (1), φ decays before the present epoch if mφ > ∼O(100 MeV). In this case, the reheating temperature is estimated as [4]