Stephon Alexander

Brane gases in the early Universe

Over the past decade it has become clear that fundamental strings are not the only fundamental degrees of freedom in string theory. D-branes are also part of the spectrum of fundamental states. In this paper we explore some possible effects of D-branes on early Universe string cosmology, starting with two key assumptions: firstly that the initial state of the Universe corresponded to a dense, hot gas in which all degrees of freedom were in thermal equilibrium, and secondly that the topology of the background space admits one-cycles. We argue by t duality that in this context the cosmological singularities are not present. We derive the equation of state of the brane gases and apply the results to suggest that, in an expanding background, the winding modes of fundamental strings will play the most important role at late times. In particular, we argue that the string winding modes will only allow four space-time dimensions to become large. The presence of brane winding modes with p>1 may lead to a hierarchy in the sizes of the extra dimensions.

Chern-Simons Modified General Relativity

Abstract Chern–Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory. In this review, we begin by providing a pedagogical derivation of the three distinct ways such an extension arises: (1) in particle physics, (2) from string theory and (3) geometrically. We then review many exact and approximate vacuum solutions of the modified theory, and discuss possible matter couplings. Following this, we review the myriad astrophysical, solar system, gravitational wave and cosmological probes that bound Chern–Simons modified gravity, including discussions of cosmic baryon asymmetry and inflation. The review closes with a discussion of possible future directions in which to test and study gravitational parity violation.

Leptogenesis from gravity waves in models of inflation

We present a new mechanism for creating the observed cosmic matter-antimatter asymmetry which satisfies all three Sakharov conditions from one common thread, gravitational waves. We generate lepton number through the gravitational anomaly in the lepton number current. The source term comes from elliptically polarized gravity waves that are produced during inflation if the inflaton field contains a CP-odd component. The amount of matter asymmetry generated in our model can be of realistic size for the parameters within the range of some inflationary scenarios and grand unified theories.

Non-Commutative Inflation

We show how a radiation dominated universe subject to space-time quantization may give rise to inflation as the radiation temperature exceeds the Planck temperature. We consider dispersion relations with a maximal momentum (i.e. a mimimum Compton wavelength, or quantum of space), noting that some of these lead to a trans-Planckian branch where energy increases with decreasing momenta. This feature translates into negative radiation pressure and, in well-defined circumstances, into an inflationary equation of state. We thus realize the inflationary scenario without the aid of an inflaton field. As the radiation cools down below the Planck temperature, inflation gracefully exits into a standard Big Bang universe, dispensing with a period of reheating. Thermal fluctuations in the radiation bath will in this case generate curvature fluctuations on cosmological scales whose amplitude and spectrum can be tuned to agree with observations.

Birefringent Gravitational Waves and the Consistency Check of Inflation

In this work we show that the gravitational Chern-Simons term, aside from being a key ingredient in inflationary baryogenesis, modifies super-horizon gravitational waves produced during inflation. We compute the super-Hubble gravitational power spectrum in the slow-roll approximation and show that its overall amplitude is modified while its spectral index remains unchanged (at leading order in the slow-roll parameters). Then, we calculate the correction to the tensor to scalar ratio, T/S. We find a correction of T/S which is dependent on N (more precisely quadratic in N), the parameter characterizing the amplitude of the Chern-Simons terms. In a stringy embedding of the leptogenesis mechanism, N is the ratio between the Planck scale and the fundamental string scale. Thus, in principle, we provide a direct probe of leptogenesis due to stringy dynamics in the Cosmic Microwave Background (CMB). However, we demonstrate that the corresponding correction of T/S is in fact very small and not observable in the regime where our calculations are valid. To obtain a sizable effect, we argue that a non-linear calculation is necessary.

In the realm of the geometric transitions

Abstract We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kahler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kahler (both before and after the transition). On the other hand, the type I and heterotic backgrounds are non-Kahler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.

On the varying speed of light in a brane induced FRW universe

We investigate a string/M theoretic realization of the varying speed of light scenario. We consider a (3+1)-dimensional probe-brane universe in the background of a black hole in the bulk formed by a stack of branes, in the spirit of Kiritsis (hep-th/9906206). We generalize the dynamics of the system at hand by including rotation and Hubble damping of the bulk space-time and show that this may lead to a mechanism to stabilize the brane-universe and hence fix the speed of light at late times.

Brane Gas Cosmology, M-theory and Little String Theory

We generalize the Brane Gas Cosmological Scenario to M-theory degrees of freedom, namely M5 and M2 branes. Without brane intersections, the Brandenberger Vafa(BV) arguments applied to M-theory degrees of freedom generically predict a large 6 dimensional spacetime. We show that intersections of M5 and M2 branes can instead lead to a large 4 dimensional spacetime. One dimensional intersections in 11D is related to (2,0) little strings (LST) on NS5 branes in type IIA. The gas regime of membranes in M-theory corresponds to the thermodynamics of LST obtained from holography. We propose a mechanism whereby LST living on the worldvolume of NS5 (M5)-branes wrapping a five dimensional torus, annihilate most efficiently in 3+1 dimensions leading to a large 3+1 dimensional spacetime. We also show that this picture is consistent with the gas approximation in M-theory.

Thermal instability for positive brane cosmological constant in the Randall-Sundrum cosmologies

We describe a novel dynamical mechanism to radiate away a positive four dimensional cosmological constant, in the Randall-Sundrum cosmological scenario. We show that there are modes of the bulk gravitational field for which the brane is effectively a mirror. This will generally give rise to an emission of thermal radiation from the brane into the bulk. The temperature turns out to be nonvanishing only if the effective four dimensional cosmological constant is positive. In any theory where the four dimensional vacuum energy is a function of physical degrees of freedom, there is then a mechanism that radiates away any positive four dimensional cosmological constant.

Cosmological BCS mechanism and the big bang singularity

We provide a novel mechanism that resolves the big bang singularity present in Friedman-Lemaitre-Robertson-Walker space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in general relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter H to zero and results in a nonsingular bounce, at least in some special cases.