Inflation and Eternal Inflation

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed.Comment: 27 pages, including 5 figures, LaTeX (elsart macros for Physics Reports, included). To be published in the David Schramm Memorial Volume of Physics Report

Day-Night and Energy Dependence of MSW Solar Neutrinos for Maximal Mixing

It has been stated in the literature that the case of maximal mixing angle for \nu_e leads to no day-night effect for solar neutrinos and an energy independent flux suppression of 1/2. While the case of maximal mixing angle and \Delta m^2 in the MSW range does lead to suppression of the electron neutrinos reaching the earth from the sun by P_S=1/2, the situation is different for neutrinos that have passed through the earth. We make the pedagogical point that, just as with smaller mixing angles, the earth regenerates the |\nu_1> state from the predominantly |\nu_2 > state reaching the earth, leading to coherent interference effects. This regeneration can lead to a day-night effect and an energy dependence of the suppression of solar electron neutrinos, even for the case of maximal mixing. For large mixing angles, the energy dependence of the day-night asymmetry depends heavily on Delta m^2. With a sufficiently sensitive measurement of the day-night effect, this energy dependence could be used to distinguish among the large mixing angle solutions of the solar neutrino problem.Comment: JHEP style, 22 pages, 7 figures. References added, and minor rewordin

A New Redshift Interpretation

A nonhomogeneous universe with vacuum energy, but without spacetime expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7K Cosmic Blackbody Radiation.Comment: 9 pages LaTeX, no figure

Inflationary paradigm after Planck 2013

Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter ($\Omega_k = 1 - \Omega$) and the spectral tilt of primordial curvature perturbations ($n_s - 1 = d \ln {\cal P}_{\cal R} / d \ln k$), among others---predictions that match the latest observations from the {\it Planck} satellite to very good precision. In the light of data from {\it Planck} as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.Comment: 11 pages, no figures; added references, and brief additions to Footnote 1, Section VI, and the Acknowledgment