Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction

We construct an inflationary model in 6D supergravity that is based on explicit time-dependent solutions to the full higher-dimensional field equations, back-reacting to the presence of a 4D inflaton rolling on a space-filling codimension-2 source brane. Fluxes in the bulk stabilize all moduli except the `breathing' modulus (that is generically present in higher-dimensional supergravities). Back-reaction to the inflaton roll causes the 4D Einstein-frame on-brane geometry to expand, a(t) ~ t^p, as well as exciting the breathing mode and causing the two off-brane dimensions to expand, r(t) ~ t^q. The model evades the general no-go theorems precluding 4D de Sitter solutions, since adjustments to the brane-localized inflaton potential allow the power p to be dialed to be arbitrarily large, with the 4D geometry becoming de Sitter in the limit p -> infinity (in which case q = 0). Slow-roll solutions give accelerated expansion with p large but finite, and q = 1/2. Because the extra dimensions expand during inflation, the present-day 6D gravity scale can be much smaller than it was when primordial fluctuations were generated - potentially allowing TeV gravity now to be consistent with the much higher gravity scale required at horizon-exit for observable primordial gravity waves. Because p >> q, the 4 on-brane dimensions expand more quickly than the 2 off-brane ones, providing a framework for understanding why the observed four dimensions are presently so much larger than the internal two. If uplifted to a 10D framework with 4 dimensions stabilized, the 6D evolution described here could describe how two of the six extra dimensions evolve to become much larger than the others, as a consequence of the enormous expansion of the 4 large dimensions we can see.Comment: 27 pages + appendices, 2 figure

The Hamilton-Waterloo Problem with even cycle lengths

The Hamilton-Waterloo Problem HWP$(v;m,n;\alpha,\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\alpha$ $C_m$-factors and $\beta$ $C_n$-factors, where $3 \leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \in \{\alpha,\beta\}$ or when $\alpha$ and $\beta$ are both odd, in which case necessarily $v \equiv 2 \pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certain conditions. This construction enables us to show that there is a solution to HWP$(v;2m,2n;\alpha,\beta)$ for odd $\alpha$ and $\beta$ whenever the obvious necessary conditions hold, except possibly if $\beta=1$; $\beta=3$ and $\gcd(m,n)=1$; $\alpha=1$; or $v=2mn/\gcd(m,n)$. This result almost completely settles the existence problem for even cycles, other than the possible exceptions noted above

Brane Gases on K3 and Calabi-Yau Manifolds

We initiate the study of Brane Gas Cosmology (BGC) on manifolds with non-trivial holonomy. Such compactifications are required within the context of superstring theory in order to make connections with realistic particle physics. We study the dynamics of brane gases constructed from various string theories on background spaces having a K3 submanifold. The K3 compactifications provide a stepping stone for generalising the model to the case of a full Calabi-Yau three-fold. Duality symmetries are discussed within a cosmological context. Using a duality, we arrive at an N=2 theory in four-dimensions compactified on a Calabi-Yau manifold with SU(3) holonomy. We argue that the Brane Gas model compactified on such spaces maintains the successes of the trivial toroidal compactification while greatly enhancing its connection to particle physics. The initial state of the universe is taken to be a small, hot and dense gas of p-branes near thermal equilibrium. The universe has no initial singularity and the dynamics of string winding modes allow three spatial dimensions to grow large, providing a possible solution to the dimensionality problem of string theory.Comment: 26 pages; Significant revisions: review material truncated; presentation improve

Study of space cabin atmospheres Status report, Jul. 1 - Dec. 31, 1967

Calibration of hot-wire detector for particle concentration and size distribution in closed spacecraft cabin atmosphere

Study of Space Cabin Atmospheres Status Report, 1 Jan. - 30 Jun. 1966

Performance characteristics of aerosol generator, and distribution sampling errors of electrostatic precipitator sampling device for space cabin atmospher

Running with Rugby Balls: Bulk Renormalization of Codimension-2 Branes

We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D-2 dimensions, although our explicit formulae do not capture all divergences when D>6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.Comment: 42 pages + appendices. This is the final version which appears in JHE