Measuring spacetime: from the big bang to black holes

Landau–Lifshitz and Weinberg Energy Distributions for the Static Regular Simpson–Visser Space-Time Geometry

The symmetric Landau–Lifshitz and Weinberg energy–momentum complexes are utilized in order to determine the energy distribution in a four-dimensional, static and spherically symmetric regular Simpson–Visser space-time geometry. For different values of the metric parameter a, the static Simpson–Visser space-time geometry corresponds to the Schwarzschild black hole solution, to a regular black hole solution with a one-way spacelike throat, to a one-way wormhole solution with an extremal null throat, or to a traversable Morris–Thorne wormhole solution. Both symmetric prescriptions yield a zero momentum, while the energy distributions calculated have an expression dependent on the mass m, the radial coordinate r, and the metric parameter a. Some special limiting cases of the results derived are considered, while a possible astrophysical application to questions of gravitational lensing is indicated.

Zeta Functions and the Cosmos—A Basic Brief Review

This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown how these powerful methods are used for the regularization of physical quantities, such as quantum vacuum fluctuations in various contexts. In special, in Casimir effect setups, with a note on the dynamical Casimir effect, and mainly concerning its application in quantum theories in curved spaces, subsequently used in gravity theories and cosmology. The second part of this work starts with an essential introduction to large scale cosmology, in search of the observational foundations of the Friedmann-Lemaître-Robertson-Walker (FLRW) model, and the cosmological constant issue, with the very hard problems associated with it. In short, a concise summary of all these interrelated subjects and applications, involving zeta functions and the cosmos, and an updated list of the pioneering and more influential works (according to Google Scholar citation counts) published on all these matters to date, are provided.

Exploring the expansion history of the universe

Exploring the recent expansion history of the universe promises insights into the cosmological model, the nature of dark energy, and potentially clues to high energy physics theories and gravitation. We examine the extent to which precision distance-redshift observations can map out the history, including the acceleration-deceleration transition, and the components and equations of state of the energy density. We consider the ability to distinguish between various dynamical scalar field models for the dark energy, as well as higher dimension and alternate gravity theories. Finally, we present a new, advantageous parametrization for the study of dark energy.