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Paul H. Frampton

Publications and source records attributed to Paul H. Frampton.

At least 127 records · Page 7Linked to original sources

Cyclic Universe and Infinite Past

We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde-Guth-Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.

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Did time begin? Will time end?

Did time begin at a Big Bang? Will the present expansion of the universe last for a finite or infinite time? These questions sound philosophical but are becoming, now in the twenty-first century, central to the scientific study of cosmology. The answers, which should become clarified in the next decade or two, could have profound implications for how we see our own role in the universe. Since the original publication of Stephen Hawking's {\it A Brief History of Time} in 1988, the answers to these questions have progressed as a result of research by the community of active theoretical physicists including myself. To present the underlying ideas requires discussion of a wide range of topics in cosmology, especially the make up of the energy content of the universe. A brief summary of my conclusions, that of three different possibilities concerning the history and future of time, the least likely is the conventional wisdom (time began and will never end) and most likely is a cyclic model (time never begins or ends), is in the short final Chapter which could be read first. To understand the reasoning leading to my conclusions could encourage reading of my entire book. My hope in writing this, my first popular book, is that it will engender reflection about time. Many a non-scientist may already hold a philosophical opinion about whether time begins and ends. This book's aim is to present some recently discovered scientific facts which can focus the reader's consideration of the two short questions in my title.

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Group Theoretic Bases for Tribimaximal Mixing

Present data on neutrino masses and mixing favor the highly symmetric tribimaximal neutrino mixing matrix which suggests an underlying flavor symmetry. A systematic study of non-abelian finite groups of order $g \leq 31$ reveals that tribimaximal mixing can be derived not only from the well known flavor symmetry $T \equiv A_4$, the tetrahedral group, but also by using the alternative flavor symmetry X(24) $\equiv SL_2(F_3) \equiv Q_4 \tilde{\times} Z_3$. X(24) does not contain the tetrahedral group as a subgroup, and has the advantage over it as a flavor symmetry that it can not only underwrite bitrimaximal mixing for neutrinos, equally as well, but also provide a first step to understanding the quark mass hierarchy.

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Entropy of Contracting Universe in Cyclic Cosmology

Following up a recent proposal \cite{BF} for a cyclic model based on phantom dark energy, we examine the content of the contracting universe (cu) and its entropy $S_{cu}$. We find that beyond dark energy the universe contains on average zero or at most a single photon which if present immediately after turnaround has infinitesimally energy which subsequently blue shifts to produce $e^+e^-$ pairs. These statements are independent of the equation of state $ω= p/ρ$ of dark energy provided $ω< -1$. Thus $S_{cu} = 0$ and if observations confirm $ω< -1$ the entropy problem is solved. We discuss the absence of a theoretical lower bound on $ϕ= |ω+ 1|$, then describe an anthropic fine tuning argument that renders unlikely extremely small $ϕ$. The present bound $ϕ\lesssim 0.1$ already implies a time until turnaround of $(t_T - t_0) \gtrsim 100$ Gy.

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Turnaround in Cyclic Cosmology

It is speculated how dark energy in a brane world can help reconcile an infinitely cyclic cosmology with the second law of thermodynamics. A cyclic cosmology is described, in which dark energy leads to a turnaround at a time, extremely shortly before the would-be Big Rip, at which both volume and entropy of our universe decrease by a gigantic factor, while very many independent similarly small contracting universes are spawned. The entropy of our universe decreases almost to zero at turnaround but increases for the remainder of the cycle by a vanishingly small amount during contraction, empty of matter, then by a large factor during inflationary expansion.

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Deflation at Turnaround for Oscillatory Cosmology

It is suggested that dark energy in a brane world can help reconcile an infinitely cyclic cosmology with the second law of thermodynamics. A cyclic cosmology is described, in which dark energy with constant equation of state leads to a turnaround at finite future time, when entropy is decreased by a huge factor equal to the inverse of its enhancement during the initial inflation. Thermodynamic consistency of cyclicity requires the arrow of time to reverse during contraction. Entropy reduction in the contracting phase is infinitesimally smaller than entropy increase during expansion.

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Darwin and Phenomenology Beyond the Standard Model

After preamble about Darwin, my talk described the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics included quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation of quadratic divergences, cancellation of U(1) anomalies, and a dark matter candidate.

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Phenomenology Beyond the Standard Model

My talk described the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics included quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation of quadratic divergences, cancellation of U(1) anomalies, and a dark matter candidate.

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Anomaly Cancellation and Conformality in Quiver Gauge Theories

Abelian quiver gauge theories provide nonsupersymmetric candidates for the conformality approach to physics beyond the standard model. Written as ${\cal N}=0$, $U(N)^n$ gauge theories, however, they have mixed $U(1)_p U(1)_q^2$ and $U(1)_p SU(N)_q^2$ triangle anomalies. It is shown how to construct explicitly a compensatory term $Δ{\cal L}_{comp}$ which restores gauge invariance of ${\cal L}_{eff} = {\cal L} + Δ{\cal L}_{comp}$ under $U(N)^n$. It can lead to a negative contribution to the U(1) $β$-function and hence to one-loop conformality at high energy for all dimensionless couplings.

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Suggestion of Explicit Field Transformations underlying Misaligned Supersymmetry

In order that nonsupersymmetric quiver gauge theories can satisfy naturalness requirements to all orders of perturbation theory, one expects a global symmetry similar to, but different from, supersymmetry. Consistent with the generalized no-go theorem published by Haag {\it et al} in 1975, we suggest a generalization of supersymmetry to a misaligned supersymmetry where fermionic generators do not commute with gauge transformations. An explicit form for the corresponding field transformations is suggested.

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Conformal Transformations and Accelerated Cosmologies

A cosmological theory that predicts a late-time accelerated attractor with a constant dark matter to dark energy ratio can be said to solve the Coincidence Problem. Such cosmologies are naturally generated in the context of non-standard gravity theories under conformal transformation because of the resulting couplings between scalar fields and matter. The present work examines four classes of these transformed theories and finds that only a small subset--those with a single scalar field--are capable of solving the Coincidence Problem.

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Ultra High Energy Cosmic Rays from Sequestered X Bursts

Assuming that there is no GZK (Greisen-Zatsepin-Kuzmin) cut-off and that super-GZK cosmic rays correlate with AGN (Active Galactic Nuclei) at cosmological distances, it is speculated that a relic superheavy particle (X) has its lifetime enhanced by sequestration in an extra dimension. This sequestration is assumed to be partially liberated by proximity of merging supermassive black holes in an AGN, temporarily but drastically reducing the lifetime, thus stimulating an X burst. Based on sequestration of the decay products of X, a speculative explanation of the observed $γ/N$ ratio is proposed.

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Testable and Untestable Aspects of Dark Energy

It has been suggested that dark energy will lead to a frequency cut-off in an experiment involving a Josephson junction. Here we show that were such a cut-off detected, it would have dramatic consequences including the possible demise of the string landscape.

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Conformality Emergent In String Phenomenology

Use of the AdS/CFT correspondence to arrive at phenomenological gauge field theories is discussed, focusing on the orbifolded case without supersymmetry. An abelian orbifold with the finite group Z_p can give rise to a G = U(N)^p gauge group with chiral fermions and complex scalars in different bi-fundamental representations of G. The naturalness issue is discussed, particularly the absence of quadratic divergences in the scalar propagator at one loop. This requires that the scalars all be in bi-fundamentals with no adjoints, coincident with the necessary and sufficient condition for presence of chiral fermions. Speculations are made concerning new gauge and matter particles expected soon to be pursued experimentally at the LHC.

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Introduction to Dark Energy and Dark Matter

In an introductory manner, the nature of dark energy is addressed, how it is observed and what further tests are needed to reconstruct its properties. Several theoretical approaches to dark energy will be discussed. Finally, the dark matter, especially WIMPs, is introduced.

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Primordial Black Holes, Hawking Radiation and the Early Universe

The 511 keV gamma emission from the galactic core may originate from a high concentration ($\sim 10^{22}$) of primordial black holes (PBHs) in the core each of whose Hawking radiation includes $\sim 10^{21}$ positrons per second. The PBHs we consider are taken as near the lightest with longevity greater than the age of the universe (mass $\sim 10^{12}$ kg; Schwarzschild radius $\sim 1$ fm). These PBHs contribute only a small fraction of cold dark matter, $Ω_{PBH} \sim 10^{-8}$. This speculative hypothesis, if confirmed implies the simultaneous discovery of Hawking radiation and an early universe phase transition.

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Chiral Fermions and Quadratic Divergences

In an approach towards naturalness without supersymmetry, renormalization properties of nonsupersymmetric abelian quiver gauge theories are studied. In the construction based on cyclic groups Z_p the gauge group is U(N)^p, the fermions are all in bifundamentals and the construction allows scalars in adjoints and bifundamentals. Only models without adjoint scalars, however, exhibit both chiral fermions and the absence of one-loop quadratic divergences in the scalar propagator.

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Dark Energy - a Pedagogic Review

In an introductory manner, the nature of dark energy is addressed, how it is observed and what further tests are needed to reconstruct its properties. Several theoretical approaches to dark energy will be discussed.

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