D. Boyanovsky

PHASE TRANSITIONS IN THE EARLY AND PRESENT UNIVERSE

▪ Abstract The evolution of the universe is the ultimate laboratory for studying fundamental physics across energy scales that span approximately 25 orders of magnitude. The standard models of cosmology and particle physics provide the basic understanding of the early and present universe and predict a series of phase transitions that occurred in succession during the universes expansion and cooling history. We survey these phase transitions, highlighting the equilibrium and nonequilibrium effects as well as their observational and cosmological consequences. We discuss the current theoretical and experimental programs studying phase transitions in QCD and nuclear matter in accelerators. A critical assessment of similarities and differences between the conditions in the early universe and those in ultrarelativistic heavy ion collisions is presented. Cosmological observations and accelerator experiments are converging toward an unprecedented understanding of the early and present universe.

Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations

Abstract Precise cosmological data from WMAP and forthcoming cosmic microwave background experiments motivate the study of the quantum corrections to the slow roll inflationary parameters. We find the quantum (loop) corrections to the equations of motion of the classical inflaton, to those for the fluctuations and to the Friedmann equation in general single field slow roll inflation. We implement a renormalized effective field theory (EFT) approach based on an expansion in ( H / M Pl ) 2 and slow roll parameters ϵ V , η V , σ V , ξ V . We find that the leading order quantum corrections to the inflaton effective potential and its equation of motion are determined by the power spectrum of scalar fluctuations. Its near scale invariance introduces a strong infrared behavior naturally regularized by the slow roll parameter Δ = η V − ϵ V = 1 2 ( n s − 1 ) + r / 8 . To leading order in the (EFT) and slow roll expansions we find V eff ( Φ 0 ) = V R ( Φ 0 ) [ 1 + Δ T 2 32 n s − 1 + 3 8 r n s − 1 + 1 4 r + higher orders ] where n s and r = Δ T 2 / Δ R 2 are the CMB observables that depend implicitly on Φ 0 and V R ( Φ 0 ) is the renormalized classical inflaton potential. This effective potential during slow roll inflation is strikingly different from the usual Minkowski space–time result. We also obtain the quantum corrections to the slow roll parameters in leading order. Superhorizon scalar field fluctuations grow for late times η → 0 − as | η | − 1 + Δ − d − where d − is a novel quantum correction to the scaling exponent related to the self-decay of superhorizon inflaton fluctuations φ → φ φ and η is the conformal time. We find to leading order − d − = Δ R 2 σ V ( η V − ϵ V ) + 6 ξ V 2 4 ( η V − ϵ V ) 2 in terms of the CMB observables. These results are generalized to the case of the inflaton interacting with a light scalar field σ and we obtain the decay rate Γ φ → σ σ . These quantum corrections arising from interactions will compete with higher order slow-roll corrections in the Gaussian approximation and must be taken into account for the precision determination of inflationary parameters extracted from CMB observations.

Linear versus nonlinear relaxation: Consequences for reheating and thermalization

We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and the study the relaxation of the inflaton via particle production in both the linear and non-linear regimes. This has an immediate application to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and ther-malization. We find that particle production when the inflaton starts in the non-linear region is typically a far more efficient way of transfering energy out of the inflaton zero mode and into the quanta of the lighter scalar than single particle decay. For the non-linear regime we take into account self-consistently the evolution of the expectation value of the inflaton field coupled to the evolution of the quantum fluctuations. An exhaustive numerical analysis reveals that the distribution of produced particles is far from thermal and the effect of open channels. In the fermionic case, Pauli blocking begins to hinder the transfer of energy into the fermion modes very early on in the evolution of the inflaton. We examine the implications of our results to the question of how to calculate the reheating temperature of the universe after inflation.

Dynamical renormalization group approach to relaxation in quantum field theory

Abstract The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms , namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch–Nordsieck but directly in real time and that goes beyond the scope of Bloch–Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.

Quantum corrections to the inflaton potential and the power spectra from superhorizon modes and trace anomalies

We obtain the effective inflaton potential during slow roll inflation by including the one loop quantum corrections to the energy momentum tensor from scalar curvature and tensor perturbations as well as quantum fluctuations from light scalars and light Dirac fermions generically coupled to the inflaton. During slow roll inflation there is a clean and unambiguous separation between superhorizon and subhorizon contributions to the energy momentum tensor. The superhorizon part is determined by the curvature perturbations and scalar field fluctuations: both feature infrared enhancements as the inverse of a combination of slow roll parameters which measure the departure from scale invariance in each case.Fermions and gravitons do not exhibit infrared divergences. The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. The one-loop quantum corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow-roll and in the (H/M_PL)^2 expansion. This study provides a complete assessment of the backreaction problem up to one loop including bosonic and fermionic degrees of freedom. The result validates the effective field theory description of inflation and confirms the robustness of the inflationary paradigm to quantum fluctuations. Quantum corrections to the power spectra are expressed in terms of the CMB observables:n_s, r and dn_s/dln k. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations.

Particle decay during inflation: Self-decay of inflaton quantum fluctuations during slow roll

Particle decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small Delta expansion. Delta measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow roll inflation, Delta is a simple function of the slow roll parameters epsilon_V, eta_V.We find that quantum fluctuations can self-decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-decay of the inflaton quantum fluctuations during slow roll inflation.For wavelengths deep inside the Hubble radius the decay is enhanced by the emission of ultrasoft collinear quanta, i.e. bremsstrahlung radiation of superhorizon quanta which becomes the leading decay channel for physical wavelengths H 3.6 10^{-9}.

Particle decay in inflationary cosmology

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.

Scalar field dynamics in Friedmann-Robertson-Walker spacetimes

We study the nonlinear dynamics of quantum fields in matter- and radiation-dominated universes, using the nonequilibrium field theory approach combined with the nonperturbative Hartree and the large N approximations. We examine the phenomenon of explosive particle production due to spinodal instabilities and parametric amplification in expanding universes with and without symmetry breaking. For a variety of initial conditions, we compute the evolution of the inflaton, its quantum fluctuations, and the equation of state. We find explosive growth of quantum fluctuations, although particle production is somewhat sensitive to the expansion of the universe. In the large N limit for symmetry-breaking scenarios, we determine generic late time solutions for any flat Friedmann-Robertson-Walker (FRW) cosmology. We also present a complete and numerically implementable renormalization scheme for the equation of motion and the energy momentum tensor in flat FRW cosmologies. In this scheme the renormalization constants are independent of time and of the initial conditions. {copyright} {ital 1997} {ital The American Physical Society}

Can disoriented chiral condensates form? A dynamical perspective.

We address the issue of whether a region of disoriented chiral condensate (DCC), in which the chiral condensate has components along the pion directions, can form. We consider a system going through the chiral phase transition via a quench, in which relaxation of the high temperature phase to the low temperature one occurs rapidly (within a time scale of order [similar to]1 fm/[ital c]). We use a density matrix based formalism that takes both thermal and quantum fluctuations into account nonperturbatively to argue that if the O(4) linear [sigma] model is the correct way to model the situation in QCD, then it is very unlikely, at least in the Hartree approximation, that a large ([gt]10 fm) DCC region will form. Typical sizes of such regions are [similar to]1--2 fm and the density of pions in such regions is at most of order [similar to]0.2/fm[sup 3]. We end with some speculations on how large DCC regions may be formed.

The Physics of the Chiral Schwinger Model: Taming an Anomalous Theory

Abstract We study the physical aspects of the chiral Schwinger model, comparing the content of this theory to that of the vector-like case. The theory is analyzed by bosonization with special attention to charged sectors and aspects of symmetry breaking. A generalized model with different left and right couplings is analyzed and the currents coupled to the gauge fields are shown to be conserved by using the equations of motion. The effects of the anomaly are studied and the mechanisms by which a new massless particle is introduced in the physical spectrum of the chiral model are clarified. We find that the longitudinal mode of the gauge field, acquiring dynamics because of the anomaly, is responsible for restoring the cluster property of chirality-carrying operators. The physics of the Wess-Zumino term is clarified and the equivalence between the theories with and without the Wess-Zumino term is spelled out. We construct the Hilbert spaces of the theories with and without the W-Z term and the physical subspaces are shown to be the same, with positive definite metric in both cases. The Ward identity Z 2 = Z 1 is shown to hold in the theory (without the W-Z term) despite its lack of local gauge invariance.