This paper reviews particle-theory models of inflation and their predictions for the primordial density perturbation, which is thought to be the origin of structure in the Universe. It includes mini-reviews of observational cosmology, elementary field theory, and supersymmetry. The spectral index $ n(k) $, specifying the scale dependence of the curvature perturbation spectrum, will be a powerful discriminator between models when measured by Planck with accuracy $ \Delta n \sim 0.01 $. The usual formula for $ n $ is derived, as well as its extension to multi-component inflatons. Primordial gravitational waves will be a more powerful discriminator if observed, as most inflation models predict they are negligible. The paper focuses on new models rooted in modern particle theory with supersymmetry as a key ingredient. It is addressed to both astrophysicists and particle physicists, with each section homogeneous in assumed background knowledge. The paper discusses the slow-roll paradigm, which describes the slow evolution of the inflaton field. The slow-roll predictions include the spectrum $ \mathcal{P}_{\mathcal{R}}(k) $, the spectral index $ n(k) $, and error estimates. The number of e-folds of slow-roll inflation and the generation of gravitational waves are also discussed. The curvature perturbation generated by inflation is calculated, with the spectrum and spectral index derived. The paper also covers field theory and the potential, including renormalizable and non-renormalizable theories, internal symmetry, and supersymmetry. It reviews various inflation models, including single-field and hybrid inflation, and discusses the role of supersymmetry in inflation. The paper concludes with a discussion of the spectral index as a discriminator and the importance of supersymmetry in inflationary models.This paper reviews particle-theory models of inflation and their predictions for the primordial density perturbation, which is thought to be the origin of structure in the Universe. It includes mini-reviews of observational cosmology, elementary field theory, and supersymmetry. The spectral index $ n(k) $, specifying the scale dependence of the curvature perturbation spectrum, will be a powerful discriminator between models when measured by Planck with accuracy $ \Delta n \sim 0.01 $. The usual formula for $ n $ is derived, as well as its extension to multi-component inflatons. Primordial gravitational waves will be a more powerful discriminator if observed, as most inflation models predict they are negligible. The paper focuses on new models rooted in modern particle theory with supersymmetry as a key ingredient. It is addressed to both astrophysicists and particle physicists, with each section homogeneous in assumed background knowledge. The paper discusses the slow-roll paradigm, which describes the slow evolution of the inflaton field. The slow-roll predictions include the spectrum $ \mathcal{P}_{\mathcal{R}}(k) $, the spectral index $ n(k) $, and error estimates. The number of e-folds of slow-roll inflation and the generation of gravitational waves are also discussed. The curvature perturbation generated by inflation is calculated, with the spectrum and spectral index derived. The paper also covers field theory and the potential, including renormalizable and non-renormalizable theories, internal symmetry, and supersymmetry. It reviews various inflation models, including single-field and hybrid inflation, and discusses the role of supersymmetry in inflation. The paper concludes with a discussion of the spectral index as a discriminator and the importance of supersymmetry in inflationary models.