An exposition on Friedmann Cosmology with Negative Energy Densities

How would negative energy density affect a classic Friedmann cosmology? Although never measured and possibly unphysical, certain realizations of quantum field theories leaves the door open for such a possibility. In this paper we analyze the evolution of a universe comprising varying amounts of negative energy forms. Negative energy components have negative normalized energy densities, $\Omega < 0$. They include negative phantom energy with an equation of state parameter $w<-1$, negative cosmological constant: $w=-1$, negative domain walls: $w=-2/3$, negative cosmic strings: $w=-1/3$, negative mass: $w=0$, negative radiation: $w=1/3$ and negative ultralight: $w > 1/3$. Assuming that such energy forms generate pressure like perfect fluids, the attractive or repulsive nature of negative energy components are reviewed. The Friedmann equation is satisfied only when negative energy forms are coupled to a greater magnitude of positive energy forms or positive curvature. We show that the solutions exhibit cyclic evolution with bounces and turnovers.The future and fate of such universes in terms of curvature, temperature, acceleration, and energy density are reviewed. The end states are dubbed Big Crunch, Big Void, or Big Rip and further qualified as "Warped", "Curved", or "Flat", "Hot" versus "Cold", "Accelerating" versus "Decelerating" versus "Coasting". A universe that ends by contracting to zero energy density is termed "Big Poof." Which contracting universes "bounce" in expansion and which expanding universes "turnover" into contraction are also reviewed.Comment: Abridged version with minor correction

Flux Enhancement of Slow-moving Particles by Sun or Jupiter: Can they be Detected on Earth?

Slow-moving particles capable of interacting solely with gravity might be detected on Earth as a result of the gravitational lensing induced focusing action of the Sun. The deflection experienced by these particles are inversely proportional to the square of their velocities and as a result their focal lengths will be shorter. We investigate the velocity dispersion of these slow-moving particles, originating from distant point-like sources, for imposing upper and lower bounds on the velocities of such particles in order for them to be focused onto Earth. We find that fluxes of such slow-moving and non-interacting particles must have speeds between ~0.01 and ~0.14 times the speed of light, $c$. Particles with speeds less than ~0.01 c will undergo way too much deflection to be focused, although such individual particles could be detected. At the caustics, the magnification factor could be as high as ~10E+6. We impose lensing constraints on the mass of these particles in order for them to be detected with large flux enhancements to be greater than E-9 eV. An approximate mass density profile for Jupiter is used to constrain particle velocities for lensing by Jupiter. We show that Jupiter could potentially focus particles with speeds as low as ~0.001c, which the Sun cannot. As a special case, the perfect alignment of the planet Jupiter with the Sun is also considered.Comment: 20 Pages, 5 figure

Gravitational Lensing Characteristics of the Transparent Sun

The transparent Sun is modeled as a spherically symmetric and centrally condensed gravitational lens using recent Standard Solar Model (SSM) data. The Sun's minimum focal length is computed to a refined accuracy of 23.5 +/- 0.1 AU, just beyond the orbit of Uranus. The Sun creates a single image of a distant point source visible to observers inside this minimum focal length and to observers sufficiently removed from the line connecting the source through the Sun's center. Regions of space are mapped where three images of a distant point source are created, along with their associated magnifications. Solar caustics, critical curves, and Einstein rings are computed and discussed. Extremely high gravitational lens magnifications exist for observers situated so that an angularly small, unlensed source appears near a three-image caustic. Types of radiations that might undergo significant solar lens magnifications as they can traverse the core of the Sun, including neutrinos and gravitational radiation, are discussed

Weak Equivalence Principle Test on a Sounding Rocket

SR-POEM, our principle of equivalence measurement on a sounding rocket, will compare the free fall rate of two substances yielding an uncertainty of E-16 in the estimate of \eta. During the past two years, the design concept has matured and we have been working on the required technology, including a laser gauge that is self aligning and able to reach 0.1 pm per root hertz for periods up to 40 s. We describe the status and plans for this project.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations

The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of its gravitational pressure to density ratio $w$. These energy forms include phantom energy ($w<-1$), cosmological constant ($w=-1$), domain walls ($w = -2/3$), cosmic strings ($w = -1/3$), normal matter ($w = 0$), radiation and relativistic matter ($w = 1/3$), and a previously little-discussed form of energy called "ultralight" ($w>1/3$). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.Comment: 32 pages, 4 tables; modified version accepted for publication in the American Journal of Physic