Curvature Constraints from the Causal Entropic Principle

Current cosmological observations indicate a preference for a cosmological constant that is drastically smaller than what can be explained by conventional particle physics. The Causal Entropic Principle (Bousso, {\it et al}.) provides an alternative approach to anthropic attempts to predict our observed value of the cosmological constant by calculating the entropy created within a causal diamond. We have extended this work to use the Causal Entropic Principle to predict the preferred curvature within the "multiverse". We have found that values larger than $\rho_k = 40\rho_m$ are disfavored by more than 99.99% and a peak value at $\rho_{\Lambda} = 7.9 \times 10^{-123}$ and $\rho_k =4.3 \rho_m$ for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work.Comment: 5 pages, 3 Figure

Spectroscopy of the 1S0−3P0^1S_0-{}^3P_0 Clock Transition of 87^{87}Sr in an Optical Lattice

We report on the spectroscopy of the $5s^2 {}^1S_0 (F=9/2) \to 5s5p {}^3P_0 (F=9/2)$ clock transition of ${}^{87}{\rm Sr}$ atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be $813.5\pm0.9$ nm.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett. (09/May/2003

Linearized self-forces for branes

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu--Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.Comment: 15 page

The flatness problem and Λ\Lambda

By way of a complete integration of the Friedmann equations, in terms of observables, it is shown that for the cosmological constant $\Lambda > 0$ there exist non-flat FLRW models for which the total density parameter $\Omega$ remains $\sim 1$ throughout the entire history of the universe. Further, it is shown that in a precise quantitative sense these models are not finely tuned. When observations are brought to bear on the theory, and in particular the WMAP observations, they confirm that we live in just such a universe. The conclusion holds when the classical notion of $\Lambda$ is extended to dark energy.Comment: Final form to appear in Physical Review Letters. Further information at http://grtensor.org/Robertson

How (Not) to Palatini

We revisit the problem of defining non-minimal gravity in the first order formalism. Specializing to scalar-tensor theories, which may be disguised as `higher-derivative' models with the gravitational Lagrangians that depend only on the Ricci scalar, we show how to recast these theories as Palatini-like gravities. The correct formulation utilizes the Lagrange multiplier method, which preserves the canonical structure of the theory, and yields the conventional metric scalar-tensor gravity. We explain the discrepancies between the na\"ive Palatini and the Lagrange multiplier approach, showing that the na\"ive Palatini approach really swaps the theory for another. The differences disappear only in the limit of ordinary General Relativity, where an accidental redundancy ensures that the na\"ive Palatini works there. We outline the correct decoupling limits and the strong coupling regimes. As a corollary we find that the so-called `Modified Source Gravity' models suffer from strong coupling problems at very low scales, and hence cannot be a realistic approximation of our universe. We also comment on a method to decouple the extra scalar using the chameleon mechanism.Comment: 18 pages, LaTeX; added references and minor improvements in sec

Optically controlled spin-glasses in multi-qubit cavity systems

Recent advances in nanostructure fabrication and optical control, suggest that it will soon be possible to prepare collections of interacting two-level systems (i.e. qubits) within an optical cavity. Here we show theoretically that such systems could exhibit novel phase transition phenomena involving spin-glass phases. By contrast with traditional realizations using magnetic solids, these phase transition phenomena are associated with both matter and radiation subsystems. Moreover the various phase transitions should be tunable simply by varying the matter-radiation coupling strength.Comment: 4 pages, 3 figure

Drastic effects of damping mechanisms on the third-order optical nonlinearity

We have investigated the optical response of superradiant atoms, which undergoes three different damping mechanisms: radiative dissipation ($\gamma_r$), dephasing ($\gamma_d$), and nonradiative dissipation ($\gamma_n$). Whereas the roles of $\gamma_d$ and $\gamma_n$ are equivalent in the linear susceptibility, the third-order nonlinear susceptibility drastically depends on the ratio of $\gamma_d$ and $\gamma_n$: When $\gamma_d \ll \gamma_n$, the third-order susceptibility is essentially that of a single atom. Contrarily, in the opposite case of $\gamma_d \gg \gamma_n$, the third-order susceptibility suffers the size-enhancement effect and becomes proportional to the system size.Comment: 5pages, 2figure

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.Comment: 9 pages, no figure

Generation of scalar-tensor gravity effects in equilibrium state boson stars

Boson stars in zero-, one-, and two-node equilibrium states are modeled numerically within the framework of Scalar-Tensor Gravity. The complex scalar field is taken to be both massive and self-interacting. Configurations are formed in the case of a linear gravitational scalar coupling (the Brans-Dicke case) and a quadratic coupling which has been used previously in a cosmological context. The coupling parameters and asymptotic value for the gravitational scalar field are chosen so that the known observational constraints on Scalar-Tensor Gravity are satisfied. It is found that the constraints are so restrictive that the field equations of General Relativity and Scalar-Tensor gravity yield virtually identical solutions. We then use catastrophe theory to determine the dynamically stable configurations. It is found that the maximum mass allowed for a stable state in Scalar-Tensor gravity in the present cosmological era is essentially unchanged from that of General Relativity. We also construct boson star configurations appropriate to earlier cosmological eras and find that the maximum mass for stable states is smaller than that predicted by General Relativity, and the more so for earlier eras. However, our results also show that if the cosmological era is early enough then only states with positive binding energy can be constructed.Comment: 20 pages, RevTeX, 11 figures, to appear in Class. Quantum Grav., comments added, refs update