Supersymmetry and Inflation

A variant of hybrid inflation which is applicable in a wide class of supersymmetric grand unified models and reproduces the observed temperature perturbations of cosmic background radiation with natural values of the parameters is presented. The theory is consistent with the unification of the minimal supersymmetric standard model gauge couplings as measured at LEP. The termination of inflation is smooth and does not produce any topological defects. Numerical investigation of the cosmological evolution of the system shows that for almost all initial values of the fields we do get an adequate amount of inflation. Finally, the "reheating" process following inflation and the production of the baryon asymmetry of the universe via a primordial lepton asymmetry are briefly discussed and some important implications for right handed neutrino Majorana masses are investigated.Comment: 5 pages LaTeX 1 eps figure. Talk presented at SUSY 96,Maryland,May 1996. Published in Nuclear Physics B(Proc.Suppl.) 52A(1997)242-24

Comments on the Electroweak Phase Transition

We report on an investigation of various problems related to the theory of the electroweak phase transition. This includes a determination of the nature of the phase transition, a discussion of the possible role of higher order radiative corrections and the theory of the formation and evolution of the bubbles of the new phase. We find in particular that no dangerous linear terms appear in the effective potential. However, the strength of the first order phase transition is 2/3 times less than what follows from the one-loop approximation. This rules out baryogenesis in the minimal version of the electroweak theory.Comment: 14 pages, 2 figures (not included

Initial Conditions for Supersymmetric Inflation

We perform a numerical investigation of the fields evolution in the supersymmetric inflationary model based on radiative corrections. Supergravity corrections are also included. We find that, out of all the examined initial data, only about 10% give an adequate amount of inflation and can be considered as ''natural''. Moreover, these successful initial conditions appear scattered and more or less isolated.Comment: 15 pages RevTeX 4 eps figure

Inflation with Ω≠1\Omega \not = 1

We discuss various models of inflationary universe with $\Omega \not = 1$. A homogeneous universe with $\Omega > 1$ may appear due to creation of the universe "from nothing" in the theories where the effective potential becomes very steep at large $\phi$, or in the theories where the inflaton field $\phi$ nonminimally couples to gravity. Inflation with $\Omega < 1$ generally requires intermediate first order phase transition with the bubble formation, and with a second stage of inflation inside the bubble. It is possible to realize this scenario in the context of a theory of one scalar field, but typically it requires artificially bent effective potentials and/or nonminimal kinetic terms. It is much easier to obtain an open universe in the models involving two scalar fields. However, these models have their own specific problems. We propose three different models of this type which can describe an open homogeneous inflationary universe.Comment: 29 pages, LaTeX, parameters of one of the models are slightly modifie

Towards the Theory of Cosmological Phase Transitions

We discuss recent progress (and controversies) in the theory of finite temperature phase transitions. This includes the structure of the effective potential at a finite temperature, the infrared problem in quantum statistics of gauge fields, the theory of formation of critical and subcritical bubbles and the theory of bubble wall propagation.Comment: 50 p

Pre-Big-Bang Requires the Universe to be Exponentially Large From the Very Beginning

We show that in a generic case of the pre-big-bang scenario, inflation will solve cosmological problems only if the universe at the onset of inflation is extremely large and homogeneous from the very beginning. The size of a homogeneous part of the universe at the beginning of the stage of pre-big-bang (PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the stringy length. The total mass of an inflationary domain must be greater than $10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially radiation dominated, then its total entropy at that time must be greater than $10^{68}$. If the universe is closed, then at the moment of its formation it must be uniform over $10^{24}$ causally disconnected domains. The natural duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the initial state of the open PBB universe could not be homogeneous because of quantum fluctuations. Independently of the issue of homogeneity, one must introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B > 10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime of eternal inflation does not occur in the PBB scenario. This should be compared with the simplest versions of the chaotic inflation scenario, where the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$ with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy O(1). We conclude that the current version of the PBB scenario cannot replace usual inflation even if one solves the graceful exit problem in this scenario.Comment: 14 pages, a discussion of the flatness problem in the PBB cosmology is adde

Inflation and Large Internal Dimensions

We consider some aspects of inflation in models with large internal dimensions. If inflation occurs on a 3D wall after the stabilization of internal dimensions in the models with low unification scale (M ~ 1 TeV), the inflaton field must be extremely light. This problem may disappear In models with intermediate (M ~10^{11} GeV) to high (M ~ 10^{16} GeV) unification scale. However, in all of these cases the wall inflation does not provide a complete solution to the horizon and flatness problems. To solve them, there must be a stage of inflation in the bulk before the compactification of internal dimensions.Comment: 4 pages, revtex, minor modification

Dynamical renormalization group methods in theory of eternal inflation

Dynamics of eternal inflation on the landscape admits description in terms of the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one correspondence with vacuum dynamics equations. On those sectors of the landscape, where transport properties of the probability measure for eternal inflation are important, renormalization group fixed points of the MSR effective action determine late time behavior of the probability measure. I argue that these RG fixed points may be relevant for the solution of the gauge invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos

Living with ghosts in Lorentz invariant theories

We argue that theories with ghosts may have a long lived vacuum state even if all interactions are Lorentz preserving. In space-time dimension D = 2, we consider the tree level decay rate of the vacuum into ghosts and ordinary particles mediated by non-derivative interactions, showing that this is finite and logarithmically growing in time. For D > 2, the decay rate is divergent unless we assume that the interaction between ordinary matter and the ghost sector is soft in the UV, so that it can be described in terms of non-local form factors rather than point-like vertices. We provide an example of a nonlocal gravitational-strength interaction between the two sectors, which appears to satisfy all observational constraints.Comment: 17 pages, comments and references adde

Stationarity of Inflation and Predictions of Quantum Cosmology

We describe several different regimes which are possible in inflationary cosmology. The simplest one is inflation without self-reproduction of the universe. In this scenario the universe is not stationary. The second regime, which exists in a broad class of inflationary models, is eternal inflation with the self-reproduction of inflationary domains. In this regime local properties of domains with a given density and given values of fields do not depend on the time when these domains were produced. The probability distribution to find a domain with given properties in a self-reproducing universe may or may not be stationary, depending on the choice of an inflationary model. We give examples of models where each of these possibilities can be realized, and discuss some implications of our results for quantum cosmology. In particular, we propose a new mechanism which may help solving the cosmological constant problem.Comment: 30 pages, Stanford preprint SU-ITP-94-24, LaTe