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Condensation of a Classical Scalar Field After Inflation and Dark Energy
Abstract
In cosmological context, classical scalar fields are important ingredients for inflation models, many candidate models of dark energy, symmetry breaking and phase transition epochs, and their consequences such as baryo and lepto-genesis. We investigate the formation of these fields by studying the production of a light quantum scalar field during the decay of a heavy particle. For simplicity it is assumed to be a scalar too. We discuss the effects of the decay mode, the thermodynamical state of the decaying field, boundary conditions, and related physical parameters on the production and evolution of a condensate. For a simplified version of this model we calculate the asymptotic behaviour of the condensate and conditions for its contribution to the dark energy with an equation of state close to a cosmological constant. We also discus the role of the back-reaction from interactions with other fields and expansion of the Universe on the evolution of the condensate. Comment: 19 pages, no figures,v2: a reference is added,v3: text improved
Recent data and new data analysis methods show that most probably the
parameter w in the equation of state of the dark energy is smaller than
-1 at low redshifts. We briefly review some of the models with such a
property and without violating null energy condition. We investigate the
difference between the observables and predictions of these models, and
how they can be explored to single out or constrain the origin of dark
energy and its properties.
We present a nonparametric method to determine the sign of w+1 in the equation of state of dark energy. It is based on geometrical behaviour and is more tolerant to uncertainties of other cosmological parameters than fitting methods. It permits to distinguish between different classes of dark energy models even with relatively low precision data. We apply this method to SNLS supernovae and to gold sample of re-analyzed supernovae data from Riess et.al. 2004. Both data sets show strong indication of . If this result is confirmed by more extended and precise data available in near future, many of dark energy models, including simple cosmological constant, standard quintessence models without interaction between quintessence scalar field(s) and matter, and scaling models are ruled out.
Possible effects due to nonequilibrium dynamics in the Affleck-Dine mechanism of baryogenesis are examined. Using the closed-time-path formalism, the quantum fluctuation and the backreaction of the Affleck-Dine scalar field are incorporated self-consistently into the dynamical equations of the system by invoking a nonperturbative Hartree approximation. It is found that such nonequilibrium effects can significantly affect the amount of baryon asymmetry that can be generated. In particular, it is possible to generate the observed baryon asymmetry with suitable initial conditions. The methodology described in this paper as well as some of the results obtained are quite general, and can be applied to any complex scalar field in a cosmological background.
Cosmological scaling solutions are particularly important in solving the coincidence problem of dark energy. We derive the equations of sub-Hubble linear matter perturbations for a general scalar-field Lagrangian—including quintessence, tachyon, dilatonic ghost condensate and k-essence—and solve them analytically for scaling solutions. We find that matter perturbations are always damped if a phantom field is coupled to dark matter and identify the cases in which the gravitational potential is constant. This provides an interesting possibility to place stringent observational constraints on scaling dark energy models.
We review the closed time path formalism of Schwinger using a path integral approach. We apply this formalism to the study of pair production from strong external fields as well as the time evolution of a nonequilibrium chiral phase transition.
We present a consistent low energy effective field theory framework for parameterizing the effects of novel short distance physics in inflation, and their possible observational signatures in the Cosmic Microwave Background. We consider the class of general homogeneous, isotropic initial states for quantum scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor which couples to gravity. In the functional Schr\"odinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuum at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and stress tensor expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Due to the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result. Comment: 83 pages, 2 figures, minor changes in content and style
Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we examine the renormalization of a scalar theory with nontrivial initial conditions in the simpler setting of flat space. The renormalization of the bulk theory proceeds exactly as for the standard vacuum state. However, the short distance features of the initial conditions can introduce new divergences which are confined to the surface on which the initial conditions are imposed. We show how the addition of boundary counterterms removes these divergences and induces a renormalization group flow in the space of initial conditions. Comment: 22 pages, 4 eps figures, uses RevTeX
In light of the recent work by Sen and Gibbons, we present a phase-plane analysis on the cosmology containing a rolling tachyon field in a potential resulted from string theory. We show that there is no stable point on the phase-plane, which indicated that there is a coincidence problem if one consider tachyon as a candidate of quintessence. Furthermore, we also analyze the phase-plane of the cosmology containing a rolling tachyon field for an exactly solvable toy potential in which the critical point is stable. Therefore, it is possible for rolling tachyon to be quintessence if one give up the strict constraint on the potential or find a more appropriate effective potential for the tachyon from M/string theory. Comment: typos corrected, references added and a brief discussion concerning the recent progress added to the introduction
We examine the nonequilibrium dynamics of a self-interacting scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and , the effective equation of motion describing the approach to equilibrium. We present a detailed analysis of the approximations used in order to obtain a Langevin-like equation of motion, in which the noise and dissipation terms associated with quantum fluctuations obey a fluctuation-dissipation relation. We show that, in general, the noise is colored (time-dependent) and multiplicative (couples nonlinearly to the field), even though it is still Gaussian distributed. The noise becomes white in the infinite temperature limit. We also address the effect of couplings to other fields, which we assume play the r\^ole of the thermal bath, in the effective equation of motion for . In particular, we obtain the fluctuation and noise terms due to a quadratic coupling to another scalar field. Comment: 30 pages, LaTex (uses RevTex 3.0), DART-HEP-93/06
We consider supersymmetric models with right-handed neutrinos where neutrino masses are purely Dirac-type. In this model, right-handed sneutrino can be the lightest supersymmetric particle and can be a viable candidate of cold dark matter of the universe. Right-handed sneutrinos are never thermalized in the early universe because of weakness of Yukawa interaction, but are effectively produced by decays of various superparticles. We show that the present mass density of right-handed sneutrino can be consistent with the observed dark matter density. Comment: 4 pages, 1 figure
Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered both in the Heisenberg and the Schr\"odinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter ) decaying mode is neglected. In the quasi-classical limit , the perturbation mode functions can be made real by a time-independent phase rotation, this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the rigid sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space. Comment: Revised version to appear in Class. Quantum Grav. All prior conclusions hold. This version contains in particular a Wigner function calculation
There are many reasons to believe the present mass density of the
universe is dominated by a weakly interacting massive particle (WIMP), a
fossil relic of the early universe. Theoretical ideas and experimental
efforts have focused mostly on production and detection of thermal
relics, with mass typically in the range a few GeV to a hundred GeV.
Here, I will review scenarios for production of nonthermal dark matter.
Since the masses of the nonthermal WIMPS are in the range 10^{12} to
10^{16} GeV, much larger than the mass of thermal wimpy WIMPS, they may
be referred to as WIMPZILLAS. In searches for dark matter it may be well
to remember that ``size does matter.''
We show that an interaction between dark matter and dark energy generically results in an effective dark-energy equation of state of w<-1. This arises because the interaction alters the redshift dependence of the matter density. An observer who fits the data treating the dark matter as noninteracting will infer an effective dark-energy fluid with w<-1. We argue that the model is consistent with all current observations, the tightest constraint coming from estimates of the matter density at different redshifts. Comparing the luminosity and angular-diameter distance relations with ΛCDM and phantom models, we find that the three models are degenerate within current uncertainties but likely distinguishable by the next generation of dark-energy experiments.
The observation that all objects in our universe interact with each other to a greater or lesser degree seems rather trivial at first sight. The strength, and thereby the consequences, of interactions vary enormously, depending on the situation considered. Sometimes, even in the framework of classical physics, surprising results have been found. A prominent example, already mentioned in Sect. 2.3, is the influence of a small mass of a few grams, as far away as the star Sirius, on the trajectories of air molecules here on earth (Borel 1914a, Brillouin 1964) . This example demonstrates that even a coupling which is considered as weak (as gravity certainly is over such distances) can have a great influence on systems that are sensitive enough to this kind of interaction, “The representation of gaseous matter... composed of molecules with positions and velocities which are rigorously determined at a given instant is therefore a pure abstract fiction;... as soon as one supposes the indeterminacy of the external forces, the effect of collisions will very rapidly disperse the trajectory bundles which are supposed to be infinitely narrow, and the problem of the subsequent movement of the molecules becomes, within a few seconds, very indeterminate, in the sense that an enormously large number of different possibilities are a priori equally probable.”1 (Borel 1914b)
Recent cosmological observations suggest the presence of small but nonzero cosmological constant . It is an intriguing possibility that such a small cosmological constant is supplied by the potential energy density of an ultralight axion-like field (called as quintessence axion). If this axion couples to the electroweak gauge fields, its potential may be generated by the electroweak instanton effects. We calculate the axion potential assuming the supersymmetric standard model and obtain a surprising result that the induced energy density of the quintessence axion field is very close to the value suggested from the observations.
In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (CGEA)) and ideas (scaling, coarse-graining and backreaction) behind the treatment of quantum processes in dynamical background spacetimes and fields. We show how they are useful for the construction of renormalization group (RG) theories for studying these nonequilibrium processes and discuss the underlying issues. Examples are drawn from quantum field processes in an inflationary universe, semiclassical cosmology and stochastic gravity. In Part I (Sections 2, 3) we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) can be treated as static critical phenomena, while a ‘slow-roll’ or power-law inflation can be treated as dynamical critical phenomena. In Part II (Sections 4, 5) we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger–DeWitt) CGEA devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III (Sections 6–8) we present the CTP (in–in, or Schwinger–Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be usefully applied. This is followed by an introduction to the influence functional in the (Feynman–Vernon) formulation of quantum open systems, illustrated by the quantum Brownian motion models. We show its relation to the CTP CGEA, and indicate how to identify the noise and dissipation kernels therein. We derive the master and Langevin equations for interacting quantum fields, represented in the works of Lombardo and Mazzitelli and indicate how they can be applied to the problem of coarse-graining, decoherence and structure formation in de Sitter universe. We perform a nonperturbative evaluation of the CTP CGEA and show how to derive the renormalization group equations under an adiabatic approximation adopted for the modes by Dalvit and Mazzitelli. We assert that this approximation is incomplete as the effect of noise is suppressed. We then discuss why noise is expected in the RG equations for nonequilibrium processes. In Part IV (Sections 9, 10), following Lombardo and Mazzitelli, we use the RG equations to derive the Einstein–Langevin equation in stochastic semiclassical gravity. As an example, we calculate the quantum correction to the Newtonian potential. We end with a discussion on why a stochastic component of RG equations is expected for nonequilibrium processes.
If CDM particles decay and their lifetime is comparable to the age of the Universe, they can modify its equation of state. By comparing the results of numerical simulations with high redshift SN-Ia observations we show that this hypothesis is consistent with present data. Fitting the simplest quintessence models with constant to data leads to . We show that a universe with a cosmological constant or quintessence matter with and a decaying Dark Matter has an effective and fits SN data better than stable CDM or quintessence models with .
Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are included. We apply these observations to the quantum state of the inflaton, and find that, at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy. Comment: 31 pages, 4 figures
In the one-loop approximation we derive the equation of motion for a classical scalar field \phi_c (t) with the back reaction of particle production included. Renormalization of mass and couplings of \phi_c is done explicitly. The equation is non-local in time, but can easily be treated perturbatively or numerically. For the weak trilinear coupling of the external field to the produced particles, the new equation gives the same solution as the familiar one with the \Gamma \phi_c term. For a stronger coupling and other types of couplings the results are significantly different. The equation can be applied to the universe heating by the inflaton decay and to spontaneous baryogenesis. Comment: 29 pages, 16 figures, subm to NPB
The connection between the axion and right-handed neutrinos
is explored in the framework of the minimal SUSY SO(10) model. The
former is related to the Peccei-Quinn (PQ) solution to the strong CP
problem and the latter is to the light Majorana neutrinos through the
see-saw mechanism. In this model, a relative phase between (10,1,3) (≡R)⊂
and (,1,3) (≡ΔR)⊂126 multiplets of SU(4) × SU(2)L× SU(2)R⊂SO(10) becomes a physical degree of freedom
identified with the axion. Then, the PQ symmetry breaking scale
(ΛPQ) and the B−L symmetry breaking scale
(ΛB−L) coincide through the VEV of R. The scalar partner of the lightest right-handed
neutrino is regarded as the inflaton, which gives a consistent density
fluctuation for the CMB.
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van-Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given. Comment: 22 pages, 3 eps figures. Version to appear in Physical Review C
We investigate the possibility of replacing the cosmological constant with gradual condensation of a scalar field produced during the decay of a superheavy dark matter. The advantage of this class of models to the ordinary quintessence is that the evolution of the dark energy and the dark energy are correlated and cosmological coincidence problem is solved. This model does not need a special form for the quitessence potential and even a simple theory or an axion like scalar is enough to explain the existence of the Dark Energy. We show that the model has an intrinsic feedback between energy density of the dark matter and the scalar field such that for a large volume of the parameter space the equation of state of the scalar field from very early in the history of the Universe is very close to a cosmological constant. Other aspects of this model are consistent with recent CMB and LSS observations. Comment: 14 pages, 4 figures
We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe. Comment: harvmac, 38 pages. V5: One error corrected in section 3.1
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