Inflationary Reheating in Grand Unified Theories

Abstract

Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) what is the nature of chaotic reheating after inflation, and (2) how is reheating sensitive to the mass spectrum of these theories ? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances non-thermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which non-thermal destabilsation of discrete symmetries occurs at reheating. An ideal inflationary scenario should arise naturally from within supergravity or a Grand Unified Theory (GUT) without fine-tuning. It should solve the plethora of problems of standard cosmology while simultaneously diltuting the monopoles inevitably produced due to the homotopic content π 2 (G/U (1)) ≃ π 1 (U (1)) ≃ Z of the standard model. Significant progress has been made within GUT's and supersymmetric theories towards this utopic vision [1,2]. However, the issue of reheating after inflation in these theories, where the universe is revived, phoenix-like, from the frozen vacuum state, has remained relatively unexplored [3]. This is precisely one area where the full symmetry and particle content of the underlying theory is likely to be crucial. SISSA-42Indeed reheating poses a severe threat to the simple ideal presented above since non-perturbative effects are typically dominant [4][5][6][7]. Reheating is therefore not a minor phase at the end of inflation, of little dynamical interest. The large quantum fluctuations allow for GUT baryogenesis [8,5] and, as pointed out by Kofman et al [4], may cause the monopole and domain wall problems to reappear due to non-thermal symmetry restoration. This last possibility is actually rather difficult in simple models of reheating with only two fields [6]. As we shall show, however, this situation changes dramatically in the case of multiple fields, relevant for GUT models.The main motivation of this work then is to understand what new effects multiple fields have on reheating. This issue encompasses two particularly interesting unknowns. (i) The nature of reheating at strong coupling when the fields evolve chaotically. This is relevant for GUT's with divergent UV fixed points [9,10] and models such as softly broken Seiberg-Witten inflation [11] where reheating occurs in the strongly coupled, confining, regime. Setting aside the subtle issue of the quantum behaviour of gauge theories at strong coupling [12], in the two and three scalar-field cases studied so far, (classical) chaotic motion has been typical [13], especially at reheating. This chaotic evolution parallels results in the Einstein-Yang-Mills equations [14], semi-classical QCD and lattice gauge theory [15]. Thus a natural question is "what is the nature of chaotic reheating ?"The second issue is (ii) the sensitivity of reheating to the mass spectrum ...

Preheating afterN-flation

“…In particular, we considered only one matter field coupled to the whole spectrum of axion fields with the same coupling strength g. Although we believe this choice to be reasonable and the model to be rather generic, dropping some of the assumptions might change the scenario. For instance, it is argued in [33,38] that the oscillations of multiple inflatons (with irrational mass ratios) can enhance drastically the decay rate (Cantor preheating). This argument is based on two pillars: first, theorems in spectral theory indicate that stability bands vanish [33,34,38] in the case of more fields whose masses are not related by rational numbers.…”

“…For instance, it is argued in [33,38] that the oscillations of multiple inflatons (with irrational mass ratios) can enhance drastically the decay rate (Cantor preheating). This argument is based on two pillars: first, theorems in spectral theory indicate that stability bands vanish [33,34,38] in the case of more fields whose masses are not related by rational numbers. Second, numerical evidence in two field models indicate a slight enhancement of particle production for well chosen parameters [38].…”

“…This argument is based on two pillars: first, theorems in spectral theory indicate that stability bands vanish [33,34,38] in the case of more fields whose masses are not related by rational numbers. Second, numerical evidence in two field models indicate a slight enhancement of particle production for well chosen parameters [38]. In the latter study of Cantor preheating, dephasing of fields is unimportant since only two fields are considered.…”

“…Here, a non-periodic variation of the matter field's effective mass leads to the dissolution of the stability bands and a possible parametric amplification of almost all Fourier modes. This expectation is based on spectral theory [34,35,36,37], but a quantitative study about the magnitude of the amplification with more than two fields is missing [38]. Owing to the possible dissolution of the stability bands, one might expect that the collective behavior of the fields gives rise to efficient particle production after N -flation.…”

Floquet analysis of two-dimensional perturbed Keplerian flows in cataclysmic variables

“…Floquet analysis is also used in a wide range of physical scenarios such as the Bloch wave formalism for the study of crystal lattices, Anderson localization, condensed matter physics and cosmology (see e.g. Bassett & Tamburini 1998). This analysis characterizes the behavior of a system in terms of resonance bands present in the space of the parameters describing the dynamics.…”