Abstract
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
Highlights
Theory on torus and orbifold compactifications at the tree level is invariant under the Tduality
Since the modular invariance is a striking symmetry in string theory, taking it for granted, in this paper, we study a phenomenological consequence, in case the modular invariance is preserved in the 4D low energy effective field theory, in particular, by considering the period of the cosmological inflation
We show that an inflationary solution which successfully ends can be accommodated in the low energy effective field theory with the modular invariance
Summary
We consider a modulus field which remains invariant under the modular transformation in the 4D low-energy effective action of superstring theory. (See for a review, e.g. Ref. [4].) For a notational brevity, we express chiral superfields and their. We consider a modulus field which remains invariant under the modular transformation in the 4D low-energy effective action of superstring theory. [4].) For a notational brevity, we express chiral superfields and their. 2 = 8πG = 1, lowest components by the same letters. We omit the Planck mass, setting Mpl unless necessary
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