Thorsten Battefeld

String Gas Cosmology

A critical review and summary of string gas cosmology is presented. A pedagogical derivation of the effective action starting from string theory, emphasizing the necessary approximations that must be invoked, is included. Working in the effective theory, that at late times it is not possible to stabilize the extra dimensions by a gas of massive string winding modes is demonstrated. Additional string gases are considered that contain so-called enhanced symmetry states. These string gases are very heavy initially, but drive the moduli to locations that minimize the energy and pressure of the gas. Both classical and quantum gas dynamics are considered, where in the former the validity of the theory is questionable and some fine-tuning is required, but in the latter a consistent and promising stabilization mechanism that is valid at late times is found. In addition, string gases provide a framework to explore dark matter, presenting alternatives to the cold dark matter model recently considered by Gubser and Peebles. Also quantum trapping with string gases as a method for including dynamics on the string landscape is discussed.

Effective field theory approach to string gas cosmology

We derive the 4D low energy effective field theory for a closed string gas on a time dependent FRW background. We examine the solutions and find that although the Brandenberger–Vafa mechanism at late times no longer leads to radion stabilization, the radion rolls slowly enough that the scenario is still of interest. In particular, we find a simple example of the string inspired dark matter recently proposed by Gubser and Peebles.

Vector perturbations in a contracting Universe

In this note we show that vector perturbations exhibit growing mode solutions in a contracting Universe, such as the contracting phase of the pre big bang or the cyclic/ekpyrotic models of the Universe. This is not a gauge artifact and will in general lead to the breakdown of perturbation theory--a severe problem that has to be addressed in any bouncing model. We also comment on the possibility of explaining, by means of primordial vector perturbations, the existence of the observed large-scale magnetic fields. This is possible since they can be seeded by vorticity.

Nonsingular perturbations in a bouncing brane model

The question of how perturbations evolve through a bounce in the Cyclic and Ekpyrotic models of the Universe remains a topical one. Issues concerning singularities at the background level and at the level of perturbation theory continue to be a matter of debate. In this report we hope to demonstrate a nonsingular collision between the boundary branes at the background level, and circumstances under which all perturbation variables remain bounded through the collision. As expected, we find most collisions to be singular even in the full 5D formalism, where first order perturbation theory breaks down for at least one perturbation variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, nonsingular solution be found. It is then possible to follow the perturbations explicitly until the actual collision. In this case, we find that if a scale-invariant spectrum developed on the hidden brane, it will get transferred to the visible brane during the bounce.

Probing two-field open inflation by resonant signals in correlation functions

We derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of detecting these tell-tale signs in current experiments, which is challenging, but not impossible. At the technical level, we pay special attention to the applicability conditions for truncating fluctuations to the light (inflaton) field and derive upper limits on the oscillation amplitude of the heavy field. A violation of these bounds requires a multi-field analysis at the perturbed level.

Comment on perturbations during a regular bounce

We point out an inconsistency of a method used in the literature, first advocated by P. Peter and N. Pinto-Neto in [Phys. Rev. D 66, 063509 (2002)], for studying adiabatic scalar perturbations in a regular bouncing universe (in four dimensions). The method under scrutiny consists of splitting the Bardeen potential into two pieces with independent evolutions, in order to avoid a singular behavior at the boundaries of the region where the null energy condition (NEC) is violated. However, we argue that this method violates energy-momentum conservation. We then introduce a novel method which provides two independent solutions for the Bardeen potential around the boundaries, even in the case of adiabatic perturbations. The two solutions are well behaved and not divergent.

Perturbations in a regular bouncing universe

We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra timelike dimension, which leads to a sign flip of the {rho}{sup 2} term in the effective four dimensional Randall Sundrum-like description. We find a wide class of possible bounces: big bang avoiding ones for regular matter content, and big rip avoiding ones for phantom matter. Focusing on radiation as the matter content, we discuss the evolution of scalar, vector and tensor perturbations. We compute a spectral index of n{sub s}=-1 for scalar perturbations and a deep blue index for tensor perturbations after invoking vacuum initial conditions, ruling out such a model as a realistic one. We also find that the spectrum (evaluated at Hubble crossing) is sensitive to the bounce. We conclude that it is challenging, but not impossible, for cyclic/ekpyrotic models to succeed, if one can find a regularized version.

Perturbations in a holographic universe and in other stiff fluid cosmologies

We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state p={rho}. The recently proposed holographic universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the p={rho} fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector perturbations grow during the stiff fluid dominated epoch and may result in a turbulent and anisotropic universe at the end of the holographic phase. Therefore, the required period of inflation following the holographic phase cannot be much shorter than that required in standard inflationary models.

Random functions via Dyson Brownian Motion: progress and problems

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.

A smooth landscape: ending saddle point inflation requires features to be shallow

We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and find a negative, potentially large, local non-linearity parameter. To be consistent with current observational bounds, the hole needs to be shallow, i.e. considerably wider than deep in natural units. To avoid singling out our vacuum as special (i.e. more special than a positive cosmological constant entails), we deduce that all features on field space should be similarly shallow, severely limiting the type of landscapes one may use for inflationary model building. We justify the use of a truncated Fourier series with random coefficients, which are suppressed the higher the frequency, to model such a smooth landscape by a random potential, as is often done in the literature without a good a priory reason.