C. P. Burgess

De Sitter string vacua from supersymmetric D-terms

We propose a new mechanism for obtaining de Sitter vacua in type-IIB string theory compactified on (orientifolded) Calabi-Yau manifolds similar to those recently studied by Kachru, Kallosh, Linde and Trivedi (KKLT). dS vacuum appears in KKLT model after uplifting an AdS vacuum by adding an anti-D3-brane, which explicitly breaks supersymmetry. We accomplish the same goal by adding fluxes of gauge fields within the D7-branes, which induce a D-term potential in the effective 4D action. In this way we obtain dS space as a spontaneously broken vacuum from a purely supersymmetric 4D action. We argue that our approach can be directly extended to heterotic string vacua, with the dilaton potential obtained from a combination of gaugino condensation and the D-terms generated by anomalous U(1) gauge groups.

The Inflationary Brane-Antibrane Universe

We show how the motion through the extra dimensions of a gas of branes and antibranes can, under certain circumstances, produce an era of inflation as seen by observers trapped on a 3-brane, with the inflaton being the inter-brane separation. Although most of our discussion refers to arbitrary ps, when we need to be specific we assume that they are D-branes of type-II or type-I string theory. For realistic brane couplings, such as those arising in string theory, the inter-brane potentials are too steep to inflate the universe for acceptably long times. However, for special regions of the parameter space of brane-antibrane positions the brane motion is slow enough for there to be sufficient inflation. Inflation would be more generic in models where the inter-brane interactions are much weaker. The spectrum of primordial density fluctuations predicted has index n slightly less than 1, and an acceptable amplitude, provided that the extra dimensions have linear size 1/r ~ 1012 GeV. Reheating occurs as in hybrid inflation, with the tachyonic instability of the brane-antibrane system taking over for small separations. The tachyon field can induce a cascade mechanism within which higher-dimension branes annihilate into lower-dimension ones. We argue that such a cascade naturally stops with the production of 3-branes in 10-dimensional string theory.

Quantum gravity in everyday life: General relativity as an effective field theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.

Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity

Abstract We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r4 when compactified on two dimensions having Kaluza–Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of non-supersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in sub-millimeter tests of gravity and at the Large Hadron Collider. We do find self-tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam–Sezgin gauged 6D supergravity compactified on a 2-sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Power-counting and the Validity of the Classical Approximation During Inflation

We use the power-counting formalism of effective field theory to study the size of loop corrections in theories of slow-roll inflation, with the aim of more precisely identifying the limits of validity of the usual classical inflationary treatments. We keep our analysis as general as possible in order to systematically identify the most important corrections to the classical inflaton dynamics. Although most slow-roll models lie within the semiclassical domain, we find the consistency of the Higgs-Inflaton scenario to be more delicate due to the proximity between the Hubble scale during inflation and the upper bound allowed by unitarity on the new-physics scale associated with the breakdown of the semiclassical approximation within the effective theory. Similar remarks apply to curvature-squared inflationary models.

On Higgs inflation and naturalness

We reexamine recent claims that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Λ ≃ Mp/ξ. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.

General brane geometries from scalar potentials: gauged supergravities and accelerating universes

We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two horizons. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for gauged supergravities in various dimensions, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases preserve a fraction of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, with potentially interesting cosmological interpretation. Further examples are provided.We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. Our construction generates these configurations from the solution of a single nonlinear ordinary differential equation, whose form depends on the scalar potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two (regular) horizons. Their asymptotic behaviour depends on the parameters of the model. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for (compact and non-compact) gauged supergravities in various dimensions, as well as for massive 10D supergravity, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases with a domain wall structure preserve part of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, having potentially interesting cosmological interpretation. We give several additional examples which illustrate the power of our techniques.

Lectures on Cosmic Inflation and its Potential Stringy Realizations

These notes present a brief introduction to hot big bang cosmology and cosmic inflation, together with a selection of some recent attempts to embed inflation into string theory. They provide a partial description of lectures presented at the RTN Winter School at CERN in January 2007, as well as in courses at Dubrovnik in August 2006 and at Cargese in August 2007. Given the substantial overlap between these three courses, the same paper will also appear as part of the proceedings of the latter two schools. It is aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or string theory.

Are inflationary predictions sensitive to very high energy physics

It has been proposed that the successful inflationary description of density perturbations on cosmological scales is sensitive to the details of physics at extremely high (trans-Planckian) energies. We test this proposal by examining how inflationary predictions depend on higher-energy scales within a simple model where the higher-energy physics is well understood. We find the best of all possible worlds: inflationary predictions are robust against the vast majority of high-energy effects, but can be sensitive to some effects in certain circumstances, in a way which does not violate ordinary notions of decoupling. This implies both that the comparison of inflationary predictions with CMB data is meaningful, and that it is also worth searching for small deviations from the standard results in the hopes of learning about very high energies.