Jan Pieter van der Schaar

WMAP7 constraints on oscillations in the primordial power spectrum

We use the 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) data to place constraints on oscillations supplementing an almost scale-invariant primordial power spectrum. Such oscillations are predicted by a variety of models, some of which amount to assuming that there is some non-trivial choice of the vacuum state at the onset of inflation. In this paper, we will explore data-driven constraints on two distinct models of initial state modifications. In both models, the frequency, phase and amplitude are degrees of freedom of the theory for which the theoretical bounds are rather weak: both the amplitude and frequency have allowed values ranging over several orders of magnitude. This requires many computationally expensive evaluations of the model cosmic microwave background (CMB) spectra and their goodness of fit, even in a Markov chain Monte Carlo (MCMC), normally the most efficient fitting method for such a problem. To search more efficiently, we first run a densely-spaced grid, with only three varying parameters: the frequency, the amplitude and the baryon density. We obtain the optimal frequency and run an MCMC at the best-fitting frequency, randomly varying all other relevant parameters. To reduce the computational time of each power spectrum computation, we adjust both comoving momentum integration and spline interpolation (in l) as a function of frequency and amplitude of the primordial power spectrum. Applying this to the WMAP7 data allows us to improve existing constraints on the presence of oscillations. We confirm earlier findings that certain frequencies can improve the fitting over a model without oscillations. For those frequencies we compute the posterior probability, allowing us to put some constraints on the primordial parameter space of both models.

Derivation of the Null Energy Condition

We derive the null energy condition, understood as a constraint on the Einstein-frame Ricci tensor, from world sheet string theory. For a closed bosonic string propagating in a curved geometry, the spacetime interpretation of the Virasoro constraint condition is precisely the null energy condition, to leading nontrivial order in the α′ expansion. Thus the deepest origin of the null energy condition lies in world sheet diffeomorphism invariance.

Constrained superfields on metastable anti-D3-branes

A bstractWe study the effect of brane polarization on the supersymmetry transformations of probe anti-D3-branes at the tip of a Klebanov-Strassler throat geometry. As is well known, the probe branes can polarize into NS5-branes and decay to a supersymmetric state by brane-flux annihilation. The effective potential has a metastable minimum as long as the number of anti-D3-branes is small compared to the number of flux quanta. We study the reduced four-dimensional effective NS5-brane theory and show that in the metastable minimum supersymmetry is non-linearly realized to leading order, as expected for spontaneously broken supersymmetry. However, a strict decoupling limit of the higher order corrections in terms of a standard nilpotent superfield does not seem to exist. We comment on the possible implications of these results for more general low-energy effective descriptions of inflation or de Sitter vacua.

Vacua and correlators in hyperbolic de Sitter space

A bstractWe study the power- and bi-spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one-parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch-Davies vacuum state. Selecting the Bunch-Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch-Davies state the hyperbolic de Sitter n-point correlation functions have to match the planar de Sitter n-point correlation functions. The expressions for the planar and hyperbolic Bunch-Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power- and bi-spectrum. For the bi-spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch-Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.

Not one bit of de Sitter information

We formulate the information paradox in de Sitter space in terms of the no-cloning principle of quantum mechanics. We show that energy conservation puts an upper bound on the maximum entropy available to any de Sitter observer. Combined with a general result on the average information in a quantum subsystem, this guarantees that an observer in de Sitter space cannot obtain even a single bit of information from the de Sitter horizon, thereby preventing any observable violations of the quantum no-cloning principle. The result supports the notion of observer complementarity.

On coupling NEC-violating matter to gravity

We show that effective theories of matter that classically violate the null energy condition cannot be minimally coupled to Einstein gravity without being inconsistent with both string theory and black hole thermodynamics. We argue however that they could still be either non-minimally coupled or coupled to higher-curvature theories of gravity.

The exact spectrum of scalar field perturbations in a radiation deformed closed de Sitter universe

We observe that the equation of motion for a free scalar field in a closed universe with radiation and a positive cosmological constant is given by Lames equation. Computing the exact power spectrum of scalar field perturbations, the presence of both curvature and radiation produces a red tilt weakly dependent on the amount of radiation.

Rolling through a vacuum

A bstractWe clarify under what conditions slow-roll inflation can continue almost undisturbed, while briefly evolving through a (semi-classically) metastable false vacuum. Furthermore, we look at potential signatures in the primordial power spectrum that could point towards the existence of traversed metastable false vacua. Interestingly, the theoretical constraints for the existence of traversable metastable vacua imply that Planck should be able to detect the resulting features in the primordial power spectrum. In other words, if Planck does not see features this immediately implies the non-existence of metastable false vacua rolled through during the inflationary epoch.

Extremal tunneling and Anti-de Sitter instantons

A bstractWe rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately regulated extremal and near-horizon limit, relating the tunneling amplitude to a family of gravitational instantons in the near-horizon Anti-de Sitter geometry, reducing to the known result for AdS2 domain walls to leading order in the probe limit. We comment on the relation to the Weak Gravity Conjecture and the conjectured instability of (non-supersymmetric) Anti-de Sitter vacua.