evolution and CMB signatures of meta-stable semi-local cosmic strings [493] as their forma- tion is very motivated from a particle physics point of view, especially at the end of F -term hybrid inflation [444] or D -term hybrid inflation (see Sec. IV F 4). Other very stringent constraints on the presence of cosmic strings in the universe comes from the amplitude of gravity wave background arises from the timing of the millisecond pulsar, which gives [480] Note that these constraints are more model-dependent than the CMB or lensing constraints. IV. MODELS OF INFLATION A. What is the inflaton ? Gµ < $_{10}$− 8 − $_{10}$− 9 . A detailed account on inflation model building can be found in many reviews [9, 10, 158, 494, 495]. In this chapter and the next, we will review some inflationary models 45 that are motivated or that originate from particle physics, and present their successes and their challenges. By no means this section is an exhaustive description of all the models, their number being huge and still growing gradually. There are two classes of models of inflation, which have been discussed extensively in the literature. In the first one, the inflaton field belongs to some hidden sector (not charged under the SM), such models will have at least one SM gauge singlet component, whose couplings to other fields and mass are chosen to match the CMB observations. This section will review some of the important ones. Models involving gauge invariant inflatons, charged under the SM gauge group or its extensions will be discussed in Sec. V. All the inflationary models are tested by the required amplitude of density perturba- tions for the observed large scale structures [12]. Therefore the predictions for the CMB 45 The very first attempt to build an inflation model was made in [2], where one-loop quantum correction to the energy momentum tensor due to the space-time curvature were taken into account, resulting in terms of higher order in curvature invariants. Such corrections to the Einstein equation admit a de Sitter solution [496], which was presented in [2, 497]. Inflation in Einstein gravity with an additional R 2 term was considered in [173]. A similar situation arises in theories with a variable Planck mass, i.e. in scalar tensor theories [498]. 76