Abstract:
The Current Standard Model of the Universe asserts that the universe is generated from a single Big Bang event followed by inflation. There is no center to this universe, hence, no preferential reference frame to describe the motions of celestial objects. We propose a new, Shell Model of the Universe, which contends that the universe is created from multiple, concentric big bangs. Accordingly, that origin presents itself as a unique, preferential reference frame, which furnishes the simplest description of the motions of galaxies in the cosmos. This is similar in manner to how planetary motion is more straightforwardly described via a sun-centered Solar System rather than an earth-centered one. The appeal of the Shell Model of the Universe lies in its simplistic ability to resolve the paradox of quasars, explain the variability in Hubble’s Constant, and solve the problematic accelerated expansion of the universe.

Abstract:
Fundamental units of measurements are kilograms, meters, and seconds—in regards to mass length, and time. All other measurements in mechanical quantities including kinetic quantities and dynamic quantities are called derived units. These derived units can be expressed in terms of fundamental units, such as acceleration, area, energy, force, power, velocity and volume. Derived quantities will be referred to as time, length, and mass. In order to explain that fundamental units are not equivalent with fundamental quantities, we need to understand the contraction of time and length in Special Relativity. If we choose the velocity of light as fundamental quantity and length and time as derived quantities, then we are able to construct three-dimensional space-time frames. Three-dimensional space-time frames representing time with polar coordination, time contraction and length contraction can be shown graphically.

Abstract:
In classical physics, time and space are absolute and independent, so time and space can be treated separately. However, in modern physics, time and space are relative and dependent: time and space must be treated together. In 4-d s-t frames, we treat time and space independently, then add a constraint to link them together. In teaching, there is a big gap between classical and modern physics. We hope that we are able to find a frame connecting them to make learning simpler. 3-d s-t frame is the best candidate to serve this purpose: time and space are able to be treated dependently by defining the unit of time as T and the unit of space as λ in this frame. Furthermore, the ratio, λ/T, is the velocity, c, of the medium. This paper shows the equivalence between a 4-d s-t frame and a 3-d s-t frame by properly converting coordinates of two frames.

Abstract:
In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.

Abstract:
We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general $f(\phi, R)$ term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum and a new consistency relation of the model are calculated. We discuss in detail the issues of how to diagonize the coupled perturbation equations, how to deal with an entropy-like source, and how to determine the initial condition by quantization. By studying some explicit models, we find that rich phenomena such as a blue scalar power spectrum, a large running of the spectral index, and a blue tensor mode spectrum can be obtained.

Abstract:
Motivated by the idea of alpha-vacua in Schwarzschild spacetime, we studied the deformed spectrum of Hawking radiation. Such a deformation would leave signatures on the small black hole evaporation in LHC because their vacuum deviates from the Unruh state.

Abstract:
The past and recent data analyses gave some hints of steps in dark energy. Considering the dark energy as a dynamical scalar field, we investigate several models with various steps: a step in the scalar potential, a step in the kinetic term, a step in the energy density and a step in the equation-of-state parameter w. These toy models provide a workable mechanism to generate steps and features of dark energy. Remarkably, a single real scalar can cross w=-1 dynamically with a step in the kinetic term.

Abstract:
Two-field slow-roll inflation is the most conservative modification of a single-field model. The main motivations to study it are its entropic mode and non-Gaussianity. Several years ago, for a two-field model with additive separable potentials, Vernizzi and Wands invented an analytic method to estimate its non-Gaussianities. Later on, Choi et al. applied this method to the model with multiplicative separable potentials. In this note, we design a larger class of models whose non-Gaussianity can be estimated by the same method. Under some simplistic assumptions, roughly these models are unlikely able to generate a large non-Gaussianity. We look over some specific models of this class by scanning the full parameter space, but still no large non-Gaussianity appears in the slow-roll region. These models and scanning techniques would be useful for future model hunt if observational evidence shows up for two-field inflation.

Abstract:
The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of f(T) models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.

Abstract:
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the energy-momentum conservation law and cosmological equations are investigated. The covariant conservation law of energy-momentum tensor severely constrains viable modifications of entropic gravity. A discrepancy arises when two independent methods are applied to the homogeneous isotropic universe, posing a serious challenge to modified models of entropic gravity.