Lukas Hollenstein

Stability of the Einstein static universe in f(R) gravity

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parametrized by a linear equation of state parameter w=p/{rho}. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity.

Can slow roll inflation induce relevant helical magnetic fields

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with

Exact solutions of f(R) gravity coupled to nonlinear electrodynamics

B^2(k) \propto k

Theoretical Priors On Modified Growth Parametrisations

, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.

Early dark energy from zero-point quantum fluctuations

In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. First, we restrict the metric fields to one degree of freedom, considering the specific case of g{sub tt}g{sub rr}=-1. Using the dual P formalism of nonlinear electrodynamics, an exact general solution is deduced in terms of the structural function H{sub P}. In particular, specific exact solutions to the gravitational field equations are found, confirming previous results and new pure electric field solutions are found. Second, motivated by the existence of regular electric fields at the center, and allowing for the case of g{sub tt}g{sub rr}{ne}-1, new specific solutions are found. Finally, we outline alternative approaches by considering the specific case of constant curvature, followed by the analysis of a specific form for f(R)

Resonant magnetic fields from inflation

Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will enable us to test the relationships between matter over-densities, the curvature perturbation and the Newtonian potential. Any large-distance modification of gravity or exotic nature of dark energy modifies these relationships as compared to those predicted in the standard smooth dark energy model based on General Relativity. In linear theory of structure growth such modifications are often parameterised by virtue of two functions of space and time that enter the relation of the curvature perturbation to, first, the matter over- density, and second, the Newtonian potential. We investigate the predictions for these functions in Brans-Dicke theory, clustering dark energy models and interacting dark energy models. We find that each theory has a distinct path in the parameter space of modified growth. Understanding these theoretical priors on the parameterisations of modified growth is essential to reveal the nature of cosmic acceleration with the help of upcoming observations of structure formation.

Constraints on early dark energy from CMB lensing and weak lensing tomography

Abstract We examine a cosmological model with a dark energy density of the form ρ DE ( t ) = ρ X ( t ) + ρ Z ( t ) , where ρ X is the component that accelerates the Hubble expansion at late times and ρ Z ( t ) is an extra contribution proportional to H 2 ( t ) . This form of ρ Z ( t ) follows from the recent proposal that the contribution of zero-point fluctuations of quantum fields to the total energy density should be computed by subtracting the Minkowski-space result from that computed in the FRW space–time. We discuss theoretical arguments that support this subtraction. By definition, this eliminates the quartic divergence in the vacuum energy density responsible for the cosmological constant problem. We show that the remaining quadratic divergence can be reabsorbed into a redefinition of Newtonʼs constant only under the assumption that ∇ μ 〈 0 | T μ ν | 0 〉 = 0 , i.e. that the energy–momentum tensor of vacuum fluctuations is conserved in isolation. However in the presence of an ultra-light scalar field X with m X H 0 , as typical of some dark energy models, the gravity effective action depends both on the gravitational field and on the X field. In this case general covariance only requires ∇ μ ( T μ ν X + 〈 0 | T μ ν | 0 〉 ) . If there is an exchange of energy between these two terms, there are potentially observable consequences. We construct an explicit model with an interaction between ρ X and ρ Z and we show that the total dark energy density ρ DE ( t ) = ρ X ( t ) + ρ Z ( t ) always remains a finite fraction of the critical density at any time, providing a specific model of early dark energy. We discuss the implication of this result for the coincidence problem and we estimate the model parameters by means of a full likelihood analysis using current CMB, SNe Ia and BAO data.

Zero-point quantum fluctuations in cosmology

We propose a novel scenario to generate primordial magnetic fields during inflation induced by an oscillating coupling of the electromagnetic field to the inflaton. This resonant mechanism has two key advantages over previous proposals. First of all, it generates a narrow band of magnetic fields at any required wavelength, thereby allaying the usual problem of a strongly blue spectrum and its associated backreaction. Secondly, it avoids the need for a strong coupling as the coupling is oscillating rather than growing or decaying exponentially. Despite these major advantages, we find that the backreaction is still far too large during inflation if the generated magnetic fields are required to have a strength of (10−15 Gauss) today on observationally interesting scales. We provide a more general no-go argument, proving that this problem will apply to any model in which the magnetic fields are generated on subhorizon scales and freeze after horizon crossing.

Challenges for creating magnetic fields by cosmic defects

Dark energy can be studied by its influence on the expansion of the Universe as well as on the growth history of the large-scale structure. In this paper, we follow the growth of the cosmic density field in early dark energy cosmologies by combining observations of the primary CMB temperature and polarisation power spectra at high redshift, of the CMB lensing deflection field at intermediate redshift and of weak cosmic shear at low redshifts for constraining the allowed amount of early dark energy. We present these forecasts using the Fisher matrix formalism and consider the combination of Planck data with the weak lensing survey of Euclid. We find that combining these data sets gives powerful constraints on early dark energy and is able to break degeneracies in the parameter set inherent to the various observational channels. The derived statistical 1σ-bound on the early dark energy density parameter is σ(Ωed) = 0.0022 which suggests that early dark energy models can be well examined in our approach. In addition, we derive the dark energy figure of merit for the considered dark energy parameterisation and comment on the applicability of the growth index to early dark energy cosmologies.

Generation of helical magnetic fields from inflation

We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the theory with a momentum-space cutoff, and show explicitly how introducing non-covariant counter-terms allows to obtain covariant results for the renormalized vacuum energy-momentum tensor. We clarify some confusion in the literature concerning the equation of state of vacuum fluctuations. Further, we point out that the general structure of the effective action becomes richer if the theory contains a scalar field phi with mass m smaller than the Hubble parameter H(t). Such an ultra-light particle cannot be integrated out completely to get the effective action. Apart from the volume term and the Einstein-Hilbert term, that are reabsorbed into renormalizations of the cosmological constant and Newtons constant, the effective action in general also has a term proportional to F(phi)R, for some function F(phi). As a result, vacuum fluctuations of ultra-light scalar fields naturally lead to models where the dark energy density has the form rho_{DE}(t)=rho_X(t)+rho_Z(t), where rho_X is the component that accelerates the Hubble expansion at late times and rho_Z(t) is an extra contribution proportional to H^2(t). We perform a detailed comparison of such models with CMB, SNIa and BAO data.