Andrei Linde

Superconformal symmetry, supergravity and cosmology

We introduce the general N = 1 gauge theory superconformally coupled to supergravity. The theory has local SU(2,2|1) symmetry and no dimensional parameters. The superconformal origin of the Fayet-Iliopoulos (FI) terms is clarified. The phase of this theory with spontaneously broken conformal symmetry gives various formulations of N = 1 supergravity interacting with matter, depending on the choice of the R-symmetry fixing. We have found that the locally superconformal theory is useful for describing the physics of the early universe with a conformally flat FRW metric. Few applications of superconformal theory to cosmology include the study of (a) particle production after inflation, particularly the nonconformal helicity-±½ states of gravitino, (b) the super-Higgs effect in cosmology and the derivation of the equations for the gravitino interacting with any number of chiral and vector multiplets in the gravitational background with varying scalar fields, (c) the weak-coupling limit of supergravity MP→∞ and gravitino-goldstino equivalence. This explains why gravitino production in the early universe is not suppressed in the limit of weak gravitational coupling. We discuss the possible existence of an unbroken phase of the superconformal theories, interpreted as a strong-coupling limit of supergravity MP→0.

Supersymmetry and the brane world

We investigate the possibility of gravity localization on the brane in the context of supersymmetric theories. To realize this scenario one needs to find a theory with the supersymmetric flow stable in IR at two critical points, one with positive and the other with negative values of the superpotential. We perform a general study of the supersymmetric flow equations of gauged massless supergravity interacting with arbitrary number of vector multiplets and demonstrate that localization of gravity does not occur. The same conclusion remains true when tensor multiplets are included. We analyze all recent attempts to find a BPS brane-world and conclude that localization of gravity on the brane in supersymmetric theories remains a challenging but unsolved problem.

Extended chaotic inflation and spatial variations of the gravitational constant

Abstract An extended chaotic inflation scenario is proposed. In this scenario the values of the effective gravitational constant in different parts of the universe may differ from each other. Depending on the choice of a particular model, the value of the gravitational constant in our part of the universe either can be expressed through other coupling constants in the theory or can be determined with the help of anthropic considerations. In some models the weakness of the gravitational interactions may be related to the duration of inflation.

Eternal extended inflation and graceful exit from old inflation without Jordan-Brans-Dicke

Abstract Recently a possible solution to the graceful exit problem of the old inflation was proposed in the context of the Jordan-Brans-Dicke theory (extended inflation). In this paper we will argue that inflation in this theory occurs in a most natural way if it starts near the Planck density, as in the standard version of chaotic inflation. With most natural initial conditions, the inflationary universe in the JBD theory enters the stage of permanent reproduction of new inflationary domains (eternal extended inflation). In order to realize the extended inflation scenario at least two classical scalar fields driving inflation are necessary, as distinct from the simplest versions of new and chaotic inflation. It is shown that in the theory of two scalar fields one can solve the graceful exit problem even without modifying the Einstein gravity theory, due to the possibility that the decay rate of the false rate vacuum in old inflation depends on the value of the second scalar field and hence on time.

Axionic domain wall production during inflation

Abstract It is shown that quantum fluctuations of the axion field produced during inflation may lead to formation of exponentially big axionic domain walls even in the simplest (N = 1) axion models. Unlike the axionic walls previously discussed in the literature, the walls produced during inflation are exponentially (or even infinitely) large. Similar walls appear also in other theories of pseudo-Goldstone bosons. Possible cosmological consequences of our results are discussed.

Supersymmetric multiple basin attractors

We explain that supersymmetric attractors in general have several critical points due to the algebraic nature of the stabilization equations. We show that the critical values of the cosmological constant of the AdS5 vacua are given by the topological (moduli independent) formulae analogous to the entropy of the d = 5 supersymmetric black holes. We present conditions under which more than one critical point is available (for black hole entropy as well as to the cosmological constant) so that the system tends to its own locally stable attractor point. We have found several families of 2-symmetric critical points where the central charge has equal absolute values but opposite signs in two attractor points. We present examples of interpolating solutions and discuss their generic features.

Inflation after preheating

Preheating after inflation may lead to non-thermal phase transitions with symmetry restoration. These phase transitions may occur even if the total energy density of fluctuations produced during reheating is relatively small as compared with the vacuum energy in the state with restored symmetry. As a result, in some inflationary models one encounters a secondary, non-thermal stage of inflation due to symmetry restoration after preheating. We review the theory of non-thermal phase transitions and make a prediction about the expansion factor during the secondary inflationary stage. We then present the results of lattice simulations which verify these predictions, and discuss possible implications of our results for the theory of formation of topological defects during non-thermal phase transitions.

Vacuum stability, wormholes, cosmic rays and the cosmological bounds on mt and mH

Abstract In the standard model, if the top quark mass m t is larger than some critical value depending on the Higgs mass m H , then we live in an unstable vacuum state corresponding to a local minimum of the effective potential. An experimental discovery of the top quark with m t above this critical value would invalidate the standard version of the wormhole theory, according to which the vacuum energy should be zero at the absolute minimum of the effective potential. However, unless the top quark is much heavier than this, the lifetime is much heavier than this, the lifetime of the unstable vacuum state is greater than the age of our part of the universe. In this paper we develop a stochastic approach to tunneling and apply it to examine the possibility that cosmic ray collisions may trigger vacuum decay and derive improved cosmological bounds on m H and m t .

Life after inflation and the cosmological constant problem

Abstract It is argued that if the present vacuum energy density ϱv exceeds some extremely small critical value ϱc (ϱcR∼10−107g cm−3 for chaotic inflation in the theory 1 2 m 2 φ 2 ), then the lifetime of mankind in the inflationary universe should be finite, even though the universe as a whole will exist without end. A possible way to justify the anthropic principle in the context of the baby universe theory and to apply it to the evaluation of masses of elementary particles, of their coupling constants and of the vacuum energy density is also discussed.