Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization

We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.Comment: 15 pages, two figures, to appear in JHE

Detection of Galactic Center source G2 at 3.8 μ\mum during periapse passage

We report new observations of the Galactic Center source G2 from the W. M. Keck Observatory. G2 is a dusty red object associated with gas that shows tidal interactions as it nears closest approach with the Galaxy's central black hole. Our observations, conducted as G2 passed through periapse, were designed to test the proposal that G2 is a 3 earth mass gas cloud. Such a cloud should be tidally disrupted during periapse passage. The data were obtained using the Keck II laser guide star adaptive optics system (LGSAO) and the facility near-infrared camera (NIRC2) through the K' [2.1 $\mu$m] and L' [3.8 $\mu$m] broadband filters. Several results emerge from these observations: 1) G2 has survived its closest approach to the black hole as a compact, unresolved source at L'; 2) G2's L' brightness measurements are consistent with those over the last decade; 3) G2's motion continues to be consistent with a Keplerian model. These results rule out G2 as a pure gas cloud and imply that G2 has a central star. This star has a luminosity of $\sim$30 $L_{\odot}$ and is surrounded by a large ($\sim$2.6 AU) optically thick dust shell. The differences between the L' and Br-$\gamma$ observations can be understood with a model in which L' and Br-$\gamma$ emission arises primarily from internal and external heating, respectively. We suggest that G2 is a binary star merger product and will ultimately appear similar to the B-stars that are tightly clustered around the black hole (the so-called S-star cluster).Comment: Accepted by ApJ Letters, 2014 October 1

Classical Stabilization of Homogeneous Extra Dimensions

If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general relativity, it is highly nontrivial to obtain solutions where the extra dimensions are static and are dynamically stable to small perturbations. We also illustrate that intuition on equilibrium and stability built up from non-gravitational physics can be highly misleading. For all static, homogeneous solutions satisfying the null energy condition, we show that the Ricci curvature of space must be nonnegative in all directions. Much of our analysis focuses on a class of spacetime models where space consists of a product of homogeneous and isotropic geometries. A dimensional reduction of these models is performed, and their stability to perturbations that preserve the spatial symmetries is analyzed. We conclude that the only physically realistic examples of classically stabilized large extra dimensions are those in which the extra-dimensional manifold is positively curved.Comment: 25 pages; minor changes, improved reference

Spheres, Deficit Angles and the Cosmological Constant

We consider compactifications of six dimensional gravity in four dimensional Minkowski or de Sitter space times a two dimensional sphere, S^2. As has been recently pointed out, it is possible to introduce 3-branes in these backgrounds with arbitrary tension without affecting the effective four dimensional cosmological constant, since its only effect is to induce a deficit angle in the sphere. We show that if a monopole like configuration of a 6D U(1) gauge field is used to produce the spontaneous compactification of the two extra dimensions in a sphere a fine tuning between brane and bulk parameters is reintroduced once the quantization condition for the gauge field is taken into account, so the 4D cosmological constant depends on the brane tension. This problem is absent if instead of the monopole we consider a four form field strength in the bulk to obtain the required energy-momentum tensor. Also, making use of the four form field, we generalize the solution to an arbitrary number of dimensions (\ge 6), keeping always four noncompact dimensions and compactifying the rest in a n-dimensional sphere. We show that a (n+1)-brane with arbitrary tension can be introduced in this background without affecting the effective 4D cosmological constant.Comment: 14 pages, LaTe

Modeling instrumental field-dependent aberrations in the NIRC2 instrument on the Keck II telescope

We present a model of field-dependent aberrations arising in the NIRC2 instrument on the W. M. Keck II telescope. We use high signal-to-noise phase diversity data employing a source in the Nasmyth focal plane to construct a model of the optical path difference as a function of field position and wavelength. With a differential wavefront error of up to 190 nm, this effect is one of the main sources of astrometric and photometric measurement uncertainties. Our tests of temporal stability show sufficient reliability for our measurements over a 20-month period at the field extrema. Additionally, while chromaticity exists, applying a correction for field-dependent aberrations provides overall improvement compared to the existing aberrations present across the field of view

Cosmology of codimension-two braneworlds

We present a comprehensive study of the cosmological solutions of 6D braneworld models with azimuthal symmetry in the extra dimensions, moduli stabilization by flux or a bulk scalar field, and which contain at least one 3-brane that could be identified with our world. We emphasize an unusual property of these models: their expansion rate depends on the 3-brane tension either not at all, or in a nonstandard way, at odds with the naive expected dimensional reduction of these systems to 4D general relativity at low energies. Unlike other braneworld attempts to find a self-tuning solution to the cosmological constant problem, the apparent failure of decoupling in these models is not associated with the presence of unstabilized moduli; rather it is due to automatic cancellation of the brane tension by the curvature induced by the brane. This provides some corroboration for the hope that these models provide a distinctive step toward understanding the smallness of the observed cosmological constant. However, we point out some challenges for obtaining realistic cosmology within this framework.Comment: 30 pages, 4 figures; generalized result for nonconventional Friedmann equation, added referenc

Cosmological Effects of Radion Oscillations

We show that the redshift of pressureless matter density due to the expansion of the universe generically induces small oscillations in the stabilized radius of extra dimensions (the radion field). The frequency of these oscillations is proportional to the mass of the radion and can have interesting cosmological consequences. For very low radion masses $m_b$ ($m_b\sim10-100 H_0\simeq10^{-32} eV$) these low frequency oscillations lead to oscillations in the expansion rate of the universe. The occurrence of acceleration periods could naturally lead to a resolution of the coincidence problem, without need of dark energy. Even though this scenario for low radion mass is consistent with several observational tests it has difficulty to meet fifth force constraints. If viewed as an effective Brans-Dicke theory it predicts $\omega=-1+\frac{1}{D}$ ($D$ is the number of extra dimensions), while experiments on scales larger than $1mm$ imply $\omega>2500$. By deriving the generalized Newtonian potential corresponding to a massive toroidally compact radion we demonstrate that Newtonian gravity is modified only on scales smaller than $m_b^{-1}$. Thus, these constraints do not apply for $m_b>10^{-3} eV$ (high frequency oscillations) corresponding to scales less than the current experiments ($0.3mm$). Even though these high frequency oscillations can not resolve the coincidence problem they provide a natural mechanism for dark matter generation. This type of dark matter has many similarities with the axion.Comment: Accepted in Phys. Rev. D. Clarifying comments added in the text and some additional references include

Cosmology of Brane Models with Radion Stabilization

We analyze the cosmology of the Randall-Sundrum model and that of compact brane models in general in the presence of a radius stabilization mechanism. We find that the expansion of our universe is generically in agreement with the expected effective four dimensional description. The constraint (which is responsible for the appearance of non-conventional cosmologies in these models) that must be imposed on the matter densities on the two branes in the theory without a stabilized radius is a consequence of requiring a static solution even in the absence of stabilization. Such constraints disappear in the presence of a stablizing potential, and the ordinary FRW (Friedmann-Robertson-Walker) equations are reproduced, with the expansion driven by the sum of the physical values of the energy densities on the two branes and in the bulk. For the case of the Randall-Sundrum model we examine the kinematics of the radion field, and find that corrections to the standard FRW equations are small for temperatures below the weak scale. We find that the radion field has renormalizable and unsuppressed couplings to Standard Model particles after electroweak symmetry breaking. These couplings may have important implications for collider searches. We comment on the possibility that matter off the TeV brane could serve as a dark matter candidate.Comment: 35 pages, Late