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The Standard Model of Elementary Particle Physics has global Family flavor symmetries corresponding to the 3 families in the Standard Model. It has been shown that the breaking of these symmetries at low energy produces Dark Energy which is the dominant component of the energy density of the Universe. It has also been shown that this model of Dark Energy not only explains the accelerated expansion of the universe but has additional observational consequences and makes verifiable predictions. This model allows a space-time dependent Dark Energy as indicated by recent observations. Further, the collapse of space dependent Dark Energy configurations leads to the formation of Dark Energy Black Holes resulting in verifiable predictions. We examine the implications of these symmetries at high energies and in the Early Universe. We consider what might happen if these global symmetries get gauged and that the global symmetries today are just a consequence of the gauge fields acquiring a constant vacuum expectation value below some energy scale v. Since, we have not yet seen signatures of such gauge fields at any of our particle accelerators, this would imply that v is greater than the electroweak scale. In the early Universe, when these gauge fields would be dynamical, the Higgs would not yet have acquired a non-zero vacuum expectation value and all Standard Model particles would be massless. The gauging of these global symmetries is desirable from a high energy and quantum gravity perspective. The chiral dynamics has a natural interpretation in terms of D Branes and our 4-dimensional Universe embedded in higher dimensions. Anomaly cancellation in this scenario results from the sum of the cubic terms vanishing. Finally, the analysis in this article can provide an explanation for one of the long standing mysteries of the natural world: the matter - antimatter asymmetry observed in our Universe.

Dark Energy is the largest fraction of the energy density of our Universe - yet it remains one of the enduring enigmas of our times. Here we show that Dark Energy can be used to solve 2 tantalizing mysteries of the observable universe. We build on existing models of Dark Energy linked to neutrino masses. In these models Dark Energy can undergo Phase Transitions and form Black Holes. Here we look at the implications of the family structure of neutrinos for the phase transitions in dark energy and associated peaks in black hole formation. It has been previously shown that one of these peaks in Black Hole formation is associated with the observed peak in Quasar formation. Here, we predict that there will also be an earlier peak in the Dark Energy Black Holes at high redshifts. These Dark Energy Black Holes formed at high redshifts are Intermediate Mass Black Holes (IMBHs).These Dark Energy Black Holes at large redshift can help explain both the EDGES observations and the observations of large Supermassive Black Holes (SMBHs) at redshifts $z \sim 7$. The existence of an earlier phase of Dark Energy Black Holes take care of some current challenges to theory implied by existing astronomical data and also helps us look for these Dark Energy Black Holes at high redshifts as predicted here through targeted searches for these Black Holes at the redshifts $z \sim 18$. There is a slight dependence of the location of the peak on the lightest neutrino mass - so the peak may be located at a slightly lower value of the redshift. This may actually enable a measurement of the lightest neutrino mass. Finding these Dark Energy Black Holes of Intermediate Mass should be within the reach of upcoming observations - particularly with the James Webb Space Telescope - but perhaps also through the use of other innovative techniques focusing specifically on the redshifts around $z \sim 18$., Comment: As embargo period is over - this version corresponds to the final published version

It is now a well established fact based on several observations that we live in a Universe dominated by dark energy. The most natural candidates for dark energy are fields in curved space-time. We develop the formalism to study the gravitational collapse of fields given any general potential. We apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting evolution equations which determine the time evolution of field configurations as well as the dynamics of spacetime.

We describe how a generalization of the original Gross-Neveu model from U(N) to O(N) flavor symmetry leads to the appearance of a pairing condensate at high density, in agreement with the conjectured phenomenon of color superconductivity in $(3+1)$-dimensional QCD. Moreover, the model displays a rich phase structure which closely resembles the one expected in two-flavor QCD., Comment: 11 pages, 1 fugure, Presented at TMU-Yale Symposium on Dynamics of Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec 1999

We study the dynamics of the chiral phase transition at finite chemical potential in the Gross-Neveu model in the leading order in large-N approximation. We consider evolutions starting in local thermal equilibrium in the massless unbroken phase for conditions pertaining to traversing a first or second order phase transition. We assume boost invariant kinematics and determine the evolution of the the order parameter $\sigma$, the energy density and pressure as well as the effective temperature, chemical potential and interpolating number densities as a function of $\tau$., Comment: 5 pages, Latex

We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved analytically in the large-N limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter $\delta$ that determines which of the condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For $\delta$ positive and sufficiently large, the phase diagram in the $\mu$-$T$ (chemical potential-temperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists low-$\mu$ chiral symmetry breaking and high-$\mu$ Cooper pair condensate regions which are separated by a first-order phase transition. At high $\mu$, when the temperature is raised, the system undergoes a second-order phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of $\delta$ the theory possesses a tricritical point ($\mu_{tc}$ and $T_{tc}$); for $\mu > \mu_{tc}$ ($\mu < \mu_{tc}$) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first-order (second-order). For the range of $\delta$ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars., Comment: 27 Pages, 7 embedded .eps figures, uses epsf

Starting from a Caldeira-Leggett model for the interaction of a system with an environment, Joichi, Matsumoto, and Yoshimura have reconsidered the derivation of the quantum Boltzmann equation. They find an extra term that accounts for the effects of virtual particles, and which drastically changes the results for relic densities of stable, weakly interacting massive particles (WIMPs), and for the decay products of unstable particles. We show, however, that this modified Boltzmann equation does not properly account for the interaction energy between the massive particles (which are decaying or annihilating) and the thermal bath of light particles. We argue that the conventional Boltzmann equation gives the correct result., Comment: 7 pages, no figures

We study the time evolution of the quantum fluctuations of the axion field for both the QCD axion as well as axions arising in the context of supergravity and string theories. We explicitly keep track not only of the coherently oscillating zero momentum mode of the axion but also of the higher non-zero momentum modes using the full axion potential. The full axion potential makes possible two kinds of instabilities: spinodal instabilities and parametric resonance instabilities. The presence of either of these instabilities can lead to a quasi-exponential increase in the occupation of non-zero momentum modes and the build-up of the quantum fluctuations of the axions. If either of these becomes a significant effect then axions would no longer be a suitable cold dark matter candidate. Our results confirm the conventional wisdom that these effects are not significant in the setting of an expanding FRW universe and hence axions are indeed cold dark matter candidates., Comment: Revtex, 15 pages including epsf figures, final version to appear in Phys. Rev. D: now contains a detailed discussion taking into account the time dependence of the axion mass; conclusions unchanged

Flat directions in the Minimal Supersymmetric Standard Model (MSSM) can become unstable due to radiative corrections, and the global minimum of the (zero temperature) potential can lie at large values of the squark and/or slepton fields. Here we show that, in inflationary models of early cosmology, the universe is very likely to be in the domain of attraction of this global minimum at the end of inflation. While the minimum at the origin of field space is global at sufficiently high temperatures, depending on details of the model, the universe may be trapped in the non-zero minimum until it becomes the global minimum at low temperatures. Parameter values leading to this scenario are therefore ruled out., Comment: 14 pages in LaTeX + 2 postscript figures, uses epsf.sty; revised version, effect of Yukawa couplings added, figure modified, one figure added, references altered

To optimally utilize all the exciting cosmological data coming in we need to sharpen also the theoretical tools available to cosmologists. One such indispensible tool to understand hot big bang cosmology is finite temperature field theory. We review and summarise the efforts made by us to use finite temperature field theory to address issues of current interest to cosmologists. An introduction to both the real time and the imaginary time formalisms is provided. The imaginary time formalism is illustrated by applying it to understand the interesting possibilty of Late Time Phase Transitions. Recent observations of the space distribution of quasars indicate a very notable peak in space density at a redshift of $2$ to $3$. It is pointed out that this may be the result of a phase transition which has a critical temperature of roughly a few meV (in the cosmological units, $~\hbar = c =k = 1$), which is natural in the context of massive neutrinos. In fact, the neutrino masses required for quasar production and those required to solve the solar neutrino problem by the MSW mechanism are consistent with each other. As a bonus, the cosmological constant implied by this model may also help resolve the discrepancy between the recently measured value of the Hubble Constant and the age of the universe. We illustrate the real time formalism by studying one of the most important time-dependent and non-equilibrium phenomena associated with phase transitions. The non-equilibrium dynamics of the first stage of the reheating process, that is dissipation via particle production is studied in scalar field theories. We show that a complete understanding of the mechanism of dissipation via particle production requires a non-perturbative resummation. We then study, Comment: 116 pages, LaTeX; 39 Figures available on request from watson@cmphys.phys.cmu.edu

Increasing improvements in the independent determinations of the Hubble constant and the age of the universe now seem to indicate that we need a small non-vanishing cosmological constant to make the two independent observations consistent with each other. The cosmological constant can be physically interpreted as due to the vacuum energy of quantized fields. To make the cosmological observations consistent with each other we would need a vacuum energy density, $ \rho_v \sim (10^{-3} eV)^4 $ today ( in the cosmological units $ \hbar=c=k=1 $ ). It is argued in this article that such a vacuum energy density is natural in the context of phase transitions linked to massive neutrinos. In fact, the neutrino masses required to provide the right vacuum energy scale to remove the age Vs Hubble constant discrepancy are consistent with those required to solve the solar neutrino problem by the MSW mechanism., Comment: 25 pages, latex, revised version to appear in Phys. Rev. D52 (1995): contains an expanded and clarified discussion of the particle physics model and connected issues

Recent observations of the space distribution of quasars indicate a very notable peak in space density at a redshift of $2$ to $3$.It is pointed out in this article that this may be the result of a phase transition which has a critical temperature of roughly a few meV (in the cosmological units h=c=k=1 ). It is further pointed out that such a phase transition is natural in the context of massive neutrinos. In fact,the neutrino masses required for quasar production and those required to solve the solar neutrino problem by the MSW mechanism are consistent with each other., Comment: 17 pages,DOE-ER-40682-26(Revised Version: To Appear in Phys. Rev. D)