Research

My research concerns the interplay between gravity and particle physics in the very early universe. More precisely, I study the cosmological implications of quantum field theories, General Relativity, and superstring theories.

I am currently Principal Investigator on a grant from the National Science Foundation, and co-PI on a grant to support computing at Syracuse from the Department of Energy. I am also supported by a Cottrell Scholar Award

The descriptions below are less technical than the papers, but if you'd like to see a more general discussion you might find it in some of the media coverage of my research.

Dark Energy and Dark Matter
For decades, a central issue in cosmology was to figure out what would happen to the expansion of the universe as the universe aged. While the measurements were unclear as to whether the expansion would eventually stop and the universe recollapse, or whether the expansion would continue forever, it was clear that the expansion would always be slowing down. This is because gravity is attractive, and the mutual attraction between all the galaxies in the universe should act to slow the expansion. It was one of the most stunning realizations ever when, five years ago, observers of type Ia supernovae discovered the first evidence that the universe is actually speeding up or accelerating! This evidence has since become very firm and presents an immense challenge to theoretical particle cosmologists. What could be causing this?

With Sean Carroll, Michael Turner and Vikram Duvurri (U. Chicago) I showed

that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of General Relativity. This allowed us to eliminate the need for dark energy,replacing it with new gravitational physics.

In order to understand the detailed cosmological predictions of models like these, with Rachel Bean, David Bernat, Levon Pogosian and Alessandra Silvestri

I considered predictions for structure formation in these models. By considering the full evolution equations, we resolved perceived instabilities previously suggested, and found a suppression of perturbations, presenting significant challenges for agreement with current cosmological structure formation observations. Our results provide a powerful method to rule out a wide class of modified gravity models aimed at providing an alternative explanation to the dark energy problem.

In a later paper

we were joined by Antonio De Felice and Damien Easson in considering more general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature.

The techniques we developed in these papers turned out to be directly applicable to other modified gravity models. With Damien Easson, Frederic Schuller and Matias Wohlfarth

I investigated the cosmology of a proposed deformation of Einstein gravity, emerging from quantum gravity heuristics, identifying late-time power-law attractors, and demonstrated that it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology.

Many modified gravity models are plagued by ghosts. With Antonio De Felice and Mark Hindmarsh (U. Sussex)

I considered Modified Gravity models involving inverse powers of fourth-order curvature invariants and showed that the late-time attractor solutions are generically afflicted by superluminally propagating tensor or scalar modes.

The theoretical and observational obstacles to constructing a sensible infrared modification of General Relativity to explain cosmic acceleration arise because of the appearance of extra degrees of freedom. These may ruin the predictions of GR or be ghostlike, as I mentioned above. To avoid these problems, with Sean Carroll, Ignacy Sawicki and Alessandra Silvestri

I considered models with no new degrees of freedom, but with a modified dependence on the conventional energy-momentum tensor. These modified-source gravity theories offer an interesting testing ground for investigations of cosmological modified gravity. We studied the evolution of structure and showed that, in the linear regime, density perturbations exhibit scale dependent runaway growth at late times. We used this to describe how upcoming measurements may probe the differences between the modified theory and the standard Lambda-CDM model.

This is not the first time I've played with gravity. In much earlier papers, with Robert Brandenberger (Brown U.) and Slava Mukhanov (ETH Zurich), and with Richhild Moessner (Brown U.)

I considered how, in 2+1 dimensions, adding specific terms to the Einstein-Hilbert action can erase singularities in black holes and in FRW cosmologies


It is important to investigate all possible explanations for cosmic acceleration, since none of the existing models are particularly compelling. In an analysis of a number of cosmological datasets, Alessandro Melchiorri (then at Oxford), Laura Mersini (then my postdoc at Syracuse), Carolina Odman (then at Cambridge)and I showed

that, if we allow the equation of state parameter, w, of dark energy to take any values, then a significant amount of the allowed parameter space lies in the region w<-1. Cosmological models that achieve this value exist, but had not been analyzed from a particle physics perspective. Carroll, Mark Hoffmann (U. Chicago) and I performed

a particle physics analysis of the simplest phantom models and demonstrated that they exhibited an unacceptable decay rate into gravitons unless they existed as an effective theory in a dark sector with cutoff around an meV.

Of course, one does not measure the equation of state parameter of dark energy directly; rather one infers it from measurements of the Hubble parameter and its derivatives. If gravitational physics differs from General Relativity on cosmological scales, then the equations relating these measurements to the equation of state parameter will also change. This opens up the possibility that we might think w is less than -1, but that in fact it is not. Carroll, De Felice and I studied this

in the context of Brans-Dicke theories with a potential, and demonstrated that such theories are extremely finely-tuned.

Another class of exotic dark energy models are the so-called k-essence models, in which one relies on special kinetic energy functions (rather than special potentials) to obtain the requisite dynamics. With Ed Copeland, Andrew Liddle and Michael Malquarti (Sussex) I considered the use of field redefinitions to cast k-essence models in a more familiar form and showed that, in several cases, k-essence cannot be observationally distinguished from quintessence without studying small effects on the perturbation spectrum.

 

Although the universe is currently accelerating, inflation can take place in to the future only if vacuum-energy (or other sufficiently slowly redshifting source of energy density) dominates the energy density of a region of physical radius 1/H. With Glenn Starkman and Tanmay Vachaspati (Case Western), and then later with Starkman and Dragan Huterer (for general dark energy candidates),

I argued that for the best-fit values inferred from the supernovae data, one must confirm cosmic acceleration out to at least z~1.8 to infer that the universe is actually inflating.

Moving to the topic of the other dark side of cosmology - dark matter, Salah Nasri (then at Syracuse), Lawrence Krauss (Case Western) and I proposed a model for neutrino masses that simultaneously resulted in a new dark matter candidate, the right-handed neutrino.

We derived the dark matter abundance in this model, showed how the hierarchy of neutrino masses is obtained, and verified that the model is compatible with existing experimental results. The model provides an economical method of unifying two seemingly separate puzzles in contemporary particle physics and cosmology.

Extra Dimensions and Cosmology
Unification physics has traditionally been seen as the problem of reconciling wildly disparate mass scales, for example the weak scale (102 GeV) and the Planck scale (1019 GeV). This exponential hierarchy is technically unnatural in particle physics, since, in general, the effects of renormalization are to make the observable values of such scales much closer in size.

A fresh perspective on the problem of unification has recently been suggested. In this picture the hierarchy problem is no longer a disparity between mass scales, and instead becomes an issue of length scales. The new approach is a superstring-inspired modification of the Kaluza-Klein idea that the universe may have more spatial dimensions than the three that we observe. The general hypothesis is that the universe as a whole is 3+1+d dimensional, with gravity propagating in all dimensions, but the standard model fields confined to a 3+1 dimensional submanifold that comprises our observable universe.

As in traditional Kaluza-Klein theories, it is necessary that all dimensions other than those we observe be compactified, so that their existence does not conflict with experimental data. The difference in the new scenarios is that, since standard model fields do not propagate in the extra dimensions, it is only necessary to evade constraints on higher-dimensional gravity, and not, for example, on higher-dimensional electromagnetism. This is important, since electromagnetism is tested to great precision down to extremely small scales, whereas microscopic tests of gravity are far less precise.

Since constraints on the new scenarios are less stringent than those on ordinary Kaluza-Klein theories, the corresponding extra dimensions can be significantly larger, which translates into a much larger allowed volume for the extra dimensions. It is the spreading of gravitational flux into this large volume that allows gravity measured on our 3-brane to be so weak, parameterized by the Planck mass MP, while the fundamental scale of physics M* is parameterized by the weak scale, MW say. Thus, the problem of understanding the hierarchy between the Planck and weak scales now becomes that of understanding why extra dimensions are stabilized at a linear size (~0.1 mm, for example) large with respect to the fundamental length scale M*-1. This is the rephrasing of the hierarchy problem in these models.

With Nemanja Kaloper (then at Stanford), John March-Russell (then at CERN) and Glenn Starkman (Case Western Reserve)

we proposed a modification to the above picture, in which we argued that there exist attractive alternate choices of compactification.  These compactifications employ a topologically non-trivial internal space - a d-dimensional compact hyperbolic manifold. They also throw into a new light the problem of explaining the large Planck/Weak hierarchy, since even though the volume of these manifolds is large, their linear size L is only slightly larger than the new fundamental length scale (L ~ 30 M*-1 for example), thus only requiring numbers of  O(10). Following up on this work, Pedro Silva (postdoc), Starkman  and I performed a detailed examination of these compact hyperbolic cosmologies,

including methods of stabilizing the extra dimensions and relationships to M-theory and supergravity. In a related project, Starkman, Dejan Stojkovic (student, Case Western Reserve) and I studied how the problems of the standard cosmology appear, and may be reconciled, in new ways in extra dimensional models. 

To understand in detail the constraints on large extra dimension models, one must take into account not only that standard model particles can decay into Kaluza-Klein excitations, but also the effects of the decays of the KK modes themselves. With Cosmin Macesanu (postdoc, Syracuse), I reconsidered

cosmological constraints on extra dimension theories from the excess production of Kaluza-Klein gravitons. We pointed out that, if the normalcy temperature is above 1 GeV, then graviton states produced at this temperature decay early enough that they do not affect the present day dark matter density, or the diffuse gamma ray background. Taking into account these effects, we rederived the relevant cosmological constraints for this scenario.

Another class of extra-dimensional models rely on the warping of the extra dimensions in Anti de-Sitter (AdS) space to obtain the dilution of gravity. This was first proposed by Randall and Sundrum and in their original model the submanifold on which we live (our brane) must have negative tension. It is usually assumed that such a brane is stable because it sits at a point of special symmetry (an orbifold fixed point). However, in a much-simplified 2+1 dimensional model,

Don Marolf (then at Syracuse) and I proved that there is a non-perturbative instability of such configurations, ending in a space-like singularity.

The study of cosmology in such models requires a detailed understanding of GR in higher dimensional spaces. With Nicolas Chatillon and Cosmin Macesanu

I derived the effective cosmological equations for a non-Z_2 symmetric codimension one brane embedded in an arbitrary D-dimensional bulk spacetime, generalizing the $D=5,6$ cases much studied previously. As a particular case, this may be considered as a regularized codimension (D-4) brane avoiding the problem of curvature divergence on the brane. We applied our results to the case of spherical symmetry around the brane and to partly compactified AdS-Schwarzschild bulks.

Randall and Sundrum also showed that it is possible to take a limit of their theory in which the extra dimensions run over infinite values of the coordinates, but their volume is still finite. This model can be extended to a co-dimension 2 construction in which our 3-brane is localized at the intersection of two or more branes. With Sean Carroll and SImeon Helllerman (then UCSB) We considered models of scalar fields coupled to gravity which are higher-dimensional generalizations of four dimensional supergravity.

We used these models to describe domain wall junctions in an anti-de Sitter background and derived Bogomolnyi equations for the scalar fields from which the walls are constructed and for the metric. From these equations a BPS-like formula for the junction energy can be derived. We demonstrated that such junctions localize gravity in the presence of more than one uncompactified extra dimension.

Inflation
The scalar spectral index n is an important parameter describing the nature of primordial density perturbations. Recent data, including that from the WMAP satellite, shows some evidence that the index runs (changes as a function of the scale $k$ at which it is measured) from n>1 (blue) on long scales to n<1 (red) on short scales. With Daniel Chung and Gary Shiu (U. Wisconsin) I performed a careful technical investigation

of the extent to which inflationary models can accommodate such significant running of n. We presented several methods for constructing large classes of potentials which yield a running spectral index, and showed that within the slow-roll approximation, the fact that n - 1
changes sign from blue to red forces the slope of the potential to reach a minimum at a similar field location. We also briefly surveyed the running of the index in a wider class of inflationary models, including a subset of those with non-minimal kinetic terms.

 

An important question in inflation concerns the initial conditions. Tanmay Vachaspati and I made arguments resting purely on causality and general relativistic constraints on the structure of spacetime.

We argued, in the context of inflationary models with a pre-inflationary stage, in which the Einstein equations are obeyed, the weak energy condition is satisfied, and spacetime topology is trivial, that homogeneity on super-Hubble scales must be assumed as an initial condition. Models in which inflation arises from field dynamics in a Friedman-Robertson-Walker background fall into this class but models in which inflation originates at the Planck epoch, chaotic inflation, may evade this conclusion.

A novel way to make inflation begin is if it occurs for topological reasons in the core of a soliton. With Andrew de Laix and Vachaspati (Case Western) I studied the effects of multiple winding defects on this phenomenon, known as topological inflation

With Arvind Borde (Tufts & LIU), we later extended this work to consider whether collisions between superheavy magnetic monopoles of low winding, could lead to inflating monpoles of higher winding - in effect allowing the creation of baby universes in the laboratory.

We showed that the future evolution of initial data represented by the two incoming monopoles may contain a timelike singularity but this need not be the case. We also used these ideas to discuss the global structure of the spacetime associated with monopole collisions and also that of topological inflation. David Lowe and Gian Alberghi (Brown U.) and I later carried out a careful numerical analysis of related ideas in Anti de-Sitter space (AdS) and suggested how the AdS/CFT correspondence might help resolve the relevant singularities.

In addition to microphysical models for driving inflation, with Ademir Lima (University of Rio Grande do Norte, Brazil)I also studied a phenomenological approach to a decaying cosmological constant.

In our paper we extended some earlier work of Lima concerning decaying cosmological constants in flat universes to the general cases of closed and open universes.

 

Baryogenesis and Leptogenesis
 The symmetry between particles and antiparticles, firmly established in collider physics, naturally leads to the question of why the observed universe is composed almost entirely of matter with little or no primordial antimatter. 

The baryon number density does not remain constant during the evolution of the universe, instead scaling like the inverse cube of the cosmological scale factor. It is therefore convenient to define the baryon asymmetry of the universe in terms of the baryon to entropy ratio of the universe, which must lie in the range 3x10-10 - 10x10-10 to be consistent with primordial deuterium and 3He abundances. In the standard cosmological model there is no explanation for the value of this ratio. The generation of the observed value of is referred to as baryogenesis. 

My work has spanned a number of different aspects of the topic. Lawrence Krauss (Case Western Reserve) and I developed a new scenario which makes use of parametric resonance effects after low scale inflation to evade existing constraints.

Our low scale preheating model is fundamentally different from other implementations, is the first such mechanism to succeed at such a low temperature, and does not depend on details of the electroweak phase transition. In addition, our model has the added advantage of avoiding recently calculated gravitino and moduli bounds on the reheat temperature after inflation. More recently, in collaboration with Ed Copeland (Sussex), David Lyth (Lancaster) and Arttu Rajantie (DAMTP, Cambridge),

I investigated realistic particle physics implementations of this model

Antonio De Felice (Syracuse), Salah Nasri and I showed

that it was possible for the baryon asymmetry to be generated in models that unify inflation with the late-time acceleration of the universe. We named our scenario quintessential baryogenesis. With De Felice, I recently investigated

a related model in the context of hyperextended inflation.

With Robert Brandenberger (Brown) and Anne-Christine Davis (DAMTP, Cambridge) we developed an original scenario involving TeV scale topological defects. We also showed how our model found a natural home in certain particle  physics models. Later, with Tomislav Prokopec (Lausanne), we performed a detailed analysis of our defect-mediated electroweak baryogenesis scenarios and investigated spontaneous CPT-violation in these models.

 

With Krishna Rajagopal (then at Harvard) and Arthur Lue (then at MIT), we performed

a critical analysis of analytic approaches to local electroweak baryogenesis.

It is widely believed that, in the absence of exotic means for departing from equilibrium, a strongly first order phase transition is required for electroweak baryogenesis to occur. This is because for a weakly first order transition the traditional criterion that the transition be sufficiently strong provides a constraint that translates directly into a bound on the mass of the Higgs boson. In collaboration with Marcelo Gleiser (Dartmouth), I investigated an alternative scenario for baryogenesis in weakly first order phase transitions,

allowing for the fact that when transitions are weak, large-amplitude subcritical fluctuations between the symmetric and broken-symmetric phases cause the transition to begin by significant phase mixing and, after inter-phase fluctuations cease, to proceed by coarsening of the subsequent domain network. In this case the sphaleron washout temperature need not be the critical temperature, but the lower temperature when the large-amplitude fluctuations freeze out, the Ginzburg temperature, TG. Thus, fermion production and preservation may still be efficient in this picture, and possibly remain sufficient to account for the baryon asymmetry of the universe.

My interest in baryogenesis led to two widely-cited review articles, the first purely concerning the electroweak scenario, and the second, co-authored with Antonio Riotto (Pisa), of more general models.

Solitons in Particle Physics, Supersymmetry and Cosmology
With Sean Carroll I introduced a new class of topological defects in ordinary field theories.

These configurations consist of topological solitons which end on others of equal or higher dimension. In such models, the higher dimensional defect provides Dirichlet boundary conditions for the lower dimensional one. We therefore termed these configurations Dirichlet topological defects, since they are the field theory analogues of string theory D-branes. Later, with Mark Bowick (Syracuse) and Antonio De Felice, I investigated

the detailed shapes of these defects numerically.

Natural extensions of this work, with Carroll and Simeon Hellerman (then UCSB), led to a set of new ideas concerning the behavior of brane junctions in supersymmetric Yang-Mills theories.

In particular we proved that junctions of BPS domain walls preserve 1/4 of the supersymmetries of the underlying theory.

 

Anne-Christine Davis (DAMTP, Cambridge), Stephen Davis (Swansea) and I have investigated the particle physics and cosmological properties of topological defects in supersymmetic theories. Our first study,

dealing with abelian theories, demonstrated that all spontaneously broken abelian supersymmetric theories admit cosmic string solutions which are superconducting due to fermion zero modes. Further, by using supersymmetry transformations, we showed how to calculate the supercurrents in terms of the background String fields. The second paper

extended these results to nonabelian theories and investigated the effects of soft supersymmetry breaking. Such defects lead to strong cosmological constraints, and these techniques should prove powerful tools with which to constrain proposed particle physics models using cosmological arguments.

Indeed, whenever cosmic strings admit superconducting currents, they may lead to the stabilization of string loops, which, depending on the model, can be disastrous cosmologically and hence used to rule out the theory. In an early paper with Brandenberger, Davis and Andrew Matheson

we performed a general investigation of these constraints. It was later realized due to the work of Davis and Perkins, which I later followed up in

that there are more general ways in which strings may become superconducting. With Brandenberger, Davis and Brandon Carter (Meudon, Paris), I later performed the most general analysis of the wider class of theories admitting such defects, which are constrained by the production of these stable superconducting loops, or vortons

and with Brandenberger and Andrew Sornborger (then at Brown U.) I investigated

whether such superconducting cosmic strings could give rise to observable gamma-ray bursts.

There are also some interesting dynamics, particularly relating to topological inflation and its termination, that can occur due to phase transitions in the core of global embedded defects. I investigated this possibility

with Minos Axenides and Leandros Perivolaropoulos.

Given the significant, and sometimes dramatically constraining, particle physics and cosmological consequences that topological defects can have, it is important to determine whether any proposed models of physics beyond the standard model admit such structures. In this vein, Tanmay Vachaspati and I investigated

little Higgs models. Focusing on the littlest Higgs model, we were able to show that three types of topological defects exist. One is a global cosmic string that is truly topological. The second is more subtle; a semilocal cosmic string, which may be stable due to dynamical effects. The final defect is a Z2 monopole solution with an unusual structure. These nonperturbative structures may have important cosmological consequences, such as those mentioned earlier. However, these will depend crucially on the fermionic content of the models.

In thinking about the role of CP-violation in baryogenesis, Arthur Lue (then at Columbia) and I became interested in the relationship between fermions and the theta term in SU(2) gauge theories. We considered

the effect of adding a CP-odd, theta term to the electroweak Lagrangian without fermions. Although this term affects neither the classical nor perturbatively quantum physics, it can be observed through non-perturbative quantum processes. We gave an example of such a process by modifying the theory so that it supported Higgs-winding solitons and showing that the rates of decay of these solitons to specific final states are CP violating. We also discussed how the CP symmetry is restored when fermions are included.


My publication list contains links to online versions of my papers from the SLAC archive.  I've been fortunate enough to pursue my work on early universe cosmology at a number of wonderful institutions: