Inflation with Ω≠1\Omega \not = 1

We discuss various models of inflationary universe with $\Omega \not = 1$. A homogeneous universe with $\Omega > 1$ may appear due to creation of the universe "from nothing" in the theories where the effective potential becomes very steep at large $\phi$, or in the theories where the inflaton field $\phi$ nonminimally couples to gravity. Inflation with $\Omega < 1$ generally requires intermediate first order phase transition with the bubble formation, and with a second stage of inflation inside the bubble. It is possible to realize this scenario in the context of a theory of one scalar field, but typically it requires artificially bent effective potentials and/or nonminimal kinetic terms. It is much easier to obtain an open universe in the models involving two scalar fields. However, these models have their own specific problems. We propose three different models of this type which can describe an open homogeneous inflationary universe.Comment: 29 pages, LaTeX, parameters of one of the models are slightly modifie

Particle Production and Gravitino Abundance after Inflation

Thermal history after inflation is studied in a chaotic inflation model with supersymmetric couplings of the inflaton to matter fields. Time evolution equation is solved in a formalism that incorporates both the back reaction of particle production and the cosmological expansion. The effect of the parametric resonance gives rise to a rapid initial phase of the inflaton decay followed by a slow stage of the Born term decay. Thermalization takes place immediately after the first explosive stage for a medium strength of the coupling among created particles. As an application we calculate time evolution of the gravitino abundance that is produced by ordinary particles directly created from the inflaton decay, which typically results in much more enhanced yield than what a naive estimate based on the Born term would suggest.Comment: 23 pages + 13 figure

Two Photon Radiation in W and Z Boson Production at the Tevatron Collider

We present a calculation of two photon radiation in W and Z boson production in hadronic collisions, based on the complete matrix elements for the processes q\bar q'\to\ell^\pm\nu\gamma\gamma and q\bar q\to\ell^+\ell^-\gamma\gamma, including finite charged lepton masses. In order to achieve stable numerical results over the full phase space, multiconfiguration Monte Carlo techniques are used to map the peaks in the differential cross section. Numerical results are presented for the Fermilab Tevatron.Comment: Revtex, 28 pages, 3 figure

TASI Lectures on the Cosmological Constant

The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.Comment: 39 pages, 3 figure

Inflation with a constant ratio of scalar and tensor perturbation amplitudes

The single scalar field inflationary models that lead to scalar and tensor perturbation spectra with amplitudes varying in direct proportion to one another are reconstructed by solving the Stewart-Lyth inverse problem to next-to-leading order in the slow-roll approximation. The potentials asymptote at high energies to an exponential form, corresponding to power law inflation, but diverge from this model at low energies, indicating that power law inflation is a repellor in this case. This feature implies that a fine-tuning of initial conditions is required if such models are to reproduce the observations. The required initial conditions might be set through the eternal inflation mechanism. If this is the case, it will imply that the spectral indices must be nearly constant, making the underlying model observationally indistinguishable from power law inflation.Comment: 20 pages, 7 figures. Major changes to the Introduction following referee's comments. One figure added. Some other minor changes. No conclusion was modifie

The non-forward BFKL amplitude and rapidity gap physics

We discuss the BFKL approach to processes with large momentum transferred through a rapidity gap. The Mueller and Tang scheme to the BFKL non-forward parton-parton elastic scattering amplitude at large $t$, is extended to include higher conformal spins. The new contributions are found to decrease with increasing energy, as follows from the gluon reggeisation phenomenon, and to vanish for asymptotically high energies. However, at moderate energies and high $|t|$, the higher conformal spins dominate the amplitude. We illustrate the effects by studying the production of two high $E_T$ jets separated by a rapidity gap at HERA energies. In a simplified framework, we find excellent agreement with the HERA photoproduction data once we incorporate the rapidity gap survival probability against soft rescattering effects. We emphasize that measurements of the analogous process in electroproduction may probe different summations over conformal spins.Comment: Latex, 14 pages, 3 figures; the final version to appear in Phys. Lett. B; a short discussion of the Tevatron data added; a previously missing factor of i^n introduced in eq. (13

Dynamical model of sequential spatial memory: winnerless competition of patterns

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns.Comment: 4 pages, submitted to PR

Dynamics of tachyonic preheating after hybrid inflation

We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to local symmetry restoration and faster thermalization. We believe this explains why tachyonic preheating is so effective in transferring energy away from the inflaton zero mode.Comment: 12 pages, 10 figures, REVTeX. Minor changes, some references added. To appear in PR

Is nonperturbative inflatino production during preheating a real threat to cosmology?

We discuss toy models where supersymmetry is broken due to non-vanishing time-varying vacuum expectation value of the inflaton field during preheating. We discuss the production of inflatino the superpartner of inflaton due to vacuum fluctuations and then we argue that they do not survive until nucleosynthesis and decay along with the inflaton to produce a thermal bath after preheating. Thus the only relevant remnant is the helicity \pm 3/2 gravitinos which can genuinely cause problem to nucleosynthesis.Comment: 10 pages, Updates to match the accepted version in Phys. Rev.

Leptoquark Contribution to the Higgs Boson Production at the LHC Collider

In this report we study how a light-scalar leptoquark could affect the Higgs boson production cross-section at the LHC collider. We construct the most general renormalizable and gauge invariant effective Lagrangian involving the standard model particles and a scalar, isoscalar leptoquark, \eta. The total cross-section for pp -> H+X is then calculated for different values of the unknown parameters \lambda_eta, m_eta and m_H.(Here \lambda_eta is the coupling associated with the Higgs-leptoquark interaction.) We find that if \lambda_eta is moderately large and m_eta is around a few hundred GeV, then the cross-section is significantly larger than the standard model value.Comment: 9 pages, 4 postscript figure