A pr 2 00 3 Introductory Review of Cosmic Inflation

These lecture notes provide an introduction to cosmic inflation. In particular I will review the basic concepts of inflation, generation of density perturbations, and reheating after inflation. email: shinji@resceu.s. u-tokyo.ac. jp, shinji@gravity.phys.waseda.ac. jp 1 Preface These lecture notes are based on invited lectures at The Second Tah Poe School on Cosmology “Modern Cosmology”, Naresuan University, Phitsanulok, Thailand, April 17 -25, 2003. See the web page http://www.tech.port.ac. uk/staffweb/gumjudpb/TPC2FIRSTpage.html for the details of this school and conference. 2 Introduction The proposal of General Relativity by Einstein in 1915 made it possible to discuss the structure of spacetime and the evolution of the universe in terms of physical laws. In 1922 Friedmann found the existence of expanding/collapsing cosmological solutions by solving the Einstein field equations. In 1929 Hubble discovered the expansion of the universe by the observations in the redshift of galaxies, as the Einstein theory predicts. In 1946 Gamov and his collaborators showed that the universe must begin in a very hot and dense state from the theory of nucleosynthesis. They also predicted that the present universe should be filled with the microwaves with black body radiations. In 1965 Penzias and Wilson discovered microwave background radiations which coincide well with theoretical predictions by Gamov et al. These strong observational evidences have made people believe that the universe started out from a hot and dense state, which is called as the standard big-bang model. In standard big-bang cosmology the state of the universe is characterized by the radiationdominated or the matter-dominated stage. These correspond to the decelerated expansion of the universe where the second derivative of the scale factor is negative. Meanwhile this decelerated expansion is not sufficient to solve a number of cosmological problems such as flatness and horizon problems which plagues in the standard big-bang scenario2. In order to overcome these fundamental problems, it is required to consider an epoch of accelerated expansion in the early universe, i.e., inflation. The basic ideas of inflation were originally proposed by Guth [1] and Sato [2] independently in 1981, which is now termed as old inflation3. This corresponds to the de-Sitter inflation which makes use of the first-order transition to true vacuum. However, it has a serious shortcoming that the universe becomes inhomogeneous by the bubble collision soon after the inflation ends. The revised version was proposed by Linde [4], and Albrecht and Steinhardt [5] in 1982, which is dubbed as new inflation. This corresponds to the slow-roll inflation with the second-order transition to true vacuum. Unfortunately this scenario also suffers from a fine-tuning problem of spending enough time in false vacuum to lead to sufficient amount of inflation. In 1983 Linde [6] considered the variant version of the slow-roll inflation called chaotic inflation, in which initial conditions of scalar fields are chaotic. According to this model, our homogeneous and isotropic universe may be produced in the regions where inflation occurs sufficiently. While old and new inflation models are based on the assumption that the universe was in a state of thermal equilibrium from the beginning, chaotic inflation can occur even without such an assumption. In addition chaotic inflation can start out in the regime close to Planck density, thereby solving the problem of initial conditions. In the next section I will explain how inflation solves these problems. Note that a specific version of the inflationary scenario–so called R inflation– was proposed by Starobinsky one year earlier [3]. Nevertheless this did not explicitly point out the virtue of inflation as in the paper of Guth.