14 exponential growth. This follows since the entropy fluc- tuations act as a source for ζ - the equation (72) gets replaced by can fragment to form non-topological solitons [110], since the fragmentation of the inflaton condensate is inhomo- geneous and anisotropic, it leads to large production of gravity waves as shown in [111]. This resonant growth of entropy fluctuations only is important in models in which the entropy fluctuations are not suppressed during inflation. Some recent examples were studied in [100, 101]. The source for this instability need not be the oscillations of the inflaton field. In SUSY models, the decay of flat directions can also induce this instability [102]. We have presented an overview of theory and appli- cation of reheating in inflationary cosmology. Particular emphasis has been on the preheating mechanisms which in many models leads to rapid energy transfer between the inflaton and regular matter. Our discussion of applications of reheating has been superficial due to lack of space. We have in fact not discussed a number of issues such as topological defect production during preheating [112–114], magnetic field generation [115, 116], induced non-Gaussianities (see e.g. [117–120]), preheating in theories with non-Standard ki- netic terms (see e.g. [121] or extra dimensions (possible excitation of Kaluza-Klein modes), applications to multi- field inflation models [122] and to reheating in brane in- flation models [123], and effects of noise on reheating [124, 125] (leading to a new proof [126] of Anderson lo- calization). It is important to point out that resonant phenomena which are important in reheating can also play a role in other areas of cosmology where there are oscillating scalar fields. One example is in the context of the MSSM where oscillating moduli fields can lead to resonances [102, 127]. The study of resonant effects in early universe cosmology is a rich area of research which has of now barely been touched. Many of the lessons learned in the context of inflationary reheating have more general applicability. The equation of motion for gravitational waves is sim- ilar to that of scalar metric fluctuations (70) except that there is no coupling between the oscillating scalar field and the wave amplitude. Hence, there is no direct pre- heating of gravitational waves. Nevertheless, gravitational waves can be produced by secondary processes. As analyzed in [103], gravitational waves can be produced from the interaction of the classi- cal matter waves produced during preheating. This is a re-scattering effect. The induced gravitational wave spec- trum is not scale-invariant but has a pronounced peak whose frequency is determined by the scale of inflation. For an inflation energy scale of 10 $^{15}$GeV, the peak of the spectrum is at about 10 $^{8}$Hz. In hybrid inflation models, the scale of the peak can be in the kHz range relevant for Advanced LIGO [104]. The amplitude of the peak is a couple of orders of magnitude higher than the scale- invariant background of gravity waves produced directly during inflation. Recently, several groups [105–108] have performed im- proved analyses of gravitational wave production during preheating. The formalism of [105, 107, 108] are quite general and were applied e.g. to a λφ 4 model of infla- tion [108]. In [109], the formalism for the generation of gravitational waves was applied to hybrid inflation, and [106] considered mostly gravitational wave production by the collision of bubbles formed during the tachyonic reso- nance in hybrid inflation models. The tachyonic instabil- ity leads to the formation of bubbles, and the collision of the bubbles is the primary source of gravitational waves. In presence of fermionic couplings, see Eq. 65, the inflaton This work is supported in part (RB) by a NSERC Dis- covery Grant, and by funds from the Canada Research Chairs Program. RB also acknowledges support from a Killam Research Fellowship. FYCR is recipient of a NSERC CGS D scholarship. AM is partly supported by the Marie Curie Research and Training Network #8220, UniverseNet #8221, MRTN-CT-2006-035863. We wish to thank Juan Garcia-Bellido, J. Serreau, A. Tranberg and M. Trodden for comments on the draft. Acknowledgments (1981)]. VII. DISCUSSION AND CONCLUSIONS 2. Gravity waves: ˙ ζ = ˙ p p + ρ δS . (73) [1] Guth AH, “The Inflationary Universe: A Possible So- lution To The Horizon And Flatness Problems,” Phys. Rev. D 23 , 347 (1981). [2] Mukhanov VF, Chibisov GV, “Quantum Fluctuation And Nonsingular Universe. (In Russian),” JETP Lett. 33 , 532 (1981) [Pisma Zh. Eksp. Teor. Fiz. 33 , 549 [3] Abbott LF, Farhi E, Wise, MB. “Particle Production In The New Inflationary Cosmology,” Phys. Lett. B 117 , 29 (1982); Dolgov AD, Linde AD “Baryon Asym- metry In Inflationary Universe,” Phys. Lett. B 116 , 329 (1982); Albrecht AJ, Steinhardt PJ, Turner MS,