Theoretical Cosmology

Motion of the Local Group as a cosmological probe

by Maciej Bilicki

Doctoral thesis written under the supervision of prof. Michal Chodorowski, defended on March 30, 2012, at the Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences.

In this thesis, we use the motion of the Local Group of galaxies (LG) through the Universe to measure the cosmological... more In this thesis, we use the motion of the Local Group of galaxies (LG) through the Universe to measure the cosmological parameter of non-relativistic matter density, Omega_m. For that purpose, we compare the peculiar velocity of the LG with its gravitational acceleration. The former is known from the dipole of the cosmic microwave background radiation and the latter is estimated here from the clustering dipole of galaxies in the Two Micron All Sky Survey (2MASS) Extended Source Catalog. We start by presenting the general framework of perturbation theory of gravitational instability in the expanding Universe and how it applies to the peculiar motion of the LG. Next, we study a particular effect for the dipole measurement, related to the fact that a nearby Local Void is partially hidden behind our Galaxy. We then describe in detail how we handled the 2MASS extragalactic data for the purpose of our analysis. Finally, we present two methods to estimate the density Omega_m, combined with the linear biasing b into the parameter beta = (Omega_m)^{0.55} / b, from the comparison of the LG velocity and acceleration. The first approach is to study the growth of the 2MASS clustering dipole with increased depth of the sample and compare it with theoretical expectations. The second is to apply the maximum-likelihood method in order to improve the precision of the measurement. With both these methods we find beta=0.4 and Omega_m=0.2, which is consistent with various independent estimates. We also briefly mention some future prospects in the field.

Zero-point quantum fluctuations in cosmology

by Lukas Hollenstein

Co-authored with Maud Jaccard, Michele Maggiore, Ermis Mitsou

We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a... more 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 Newton's 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.

Nonlinear cosmological consistency relations and effective matter stresses

by Lukas Hollenstein

Co-authored with Guillermo Ballesteros, Rajeev Kumar Jain and Martin Kunz

We propose a completely nonlinear framework to construct consistency relations for testing generic cosmological... more We propose a completely nonlinear framework to construct consistency relations for testing generic cosmological scenarios using the evolution of large scale structure. It is based on the covariant approach in combination with a frame that is purely given by the metric, the normal frame. As an example, we apply this framework to the LCDM model, extending the usual first order conditions on the metric potentials to second order. We argue that working in the normal frame is not only a practical choice but one that closely resembles our actual situation as observers. In this frame, effective pressures and anisotropic stresses appear at second order in perturbation theory, even for dust. We quantify this effect and compare it, for illustration, with the pressure of a generic clustering dark energy fluid and the anisotropic stress in the DGP model. Besides, we also discuss the effect of a mismatch of the potentials on the determination of galaxy bias.

Resonant magnetic fields from inflation

by Lukas Hollenstein

Co-authored with Christian T. Byrnes, Rajeev K. Jain and Federico R. Urban
Published in JCAP 1203 (2012) 009.
http://dx.doi.org/10.1088/1475-7516/2012/03/009

We propose a novel scenario to generate primordial magnetic fields during inflation induced by an oscillating coupling... more 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 order 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.

An astrophysical peek into Einstein's static universe

by Abhas Mitra

Cosmological properties of eternally collapsing objects (ECOs)

by Abhas Mitra

The Strained State Cosmology

by Angelo Tartaglia

Chapter of the book Aspects of Today´s Cosmology, Antonio Alfonso-Faus (Ed.), ISBN: 978-953-307-626-3, InTech (2011), Available from: http://www.intechopen.com/articles/show/title/the-strained-state-cosmology

The cosmology of a four-dimensional space-time treated as a strained elastic continuum is illustrated. Various... more The cosmology of a four-dimensional space-time treated as a strained elastic continuum is illustrated. Various cosmological tests are performed, with positive results.

Early dark energy from zero-point quantum fluctuations

by Lukas Hollenstein

Co-authored with Michele Maggiore, Maud Jaccard and Ermis Mitsou
Published in Phys. Lett. B 704 (2011) 102.
http://dx.doi.org/10.1016/j.physletb.2011.09.010

We examine a cosmological model with a dark energy density of the form \rho_{DE}(t)=\rho_X(t)+\rho_Z(t), where \rho_X... more We examine a cosmological model with a dark energy density of 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). This form of \rho_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 Newton's constant only under the assumption 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 the conservation of the total energy-momentum tensor, including both the classical term T^X_{\mu\nu} and the vacuum expectation value of T_{\mu\nu}. 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 \rho_X and \rho_Z and we show that the total dark energy density \rho_{DE}(t)=\rho_X(t)+\rho_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.

Is the Two Micron All Sky Survey clustering dipole convergent?

by Maciej Bilicki

The Astrophysical Journal 741 (2011) 31.
Co-authors: Michał Chodorowski, Thomas Jarrett, Gary A. Mamon.

There is a long-standing controversy about the convergence of the dipole moment of the galaxy angular distribution... more There is a long-standing controversy about the convergence of the dipole moment of the galaxy angular distribution (the so-called clustering dipole). We study the growth of the clustering dipole of galaxies as a function of the limiting flux of the sample from the Two Micron All Sky Survey (2MASS). Contrary to some earlier claims, we find that the dipole does not converge before the completeness limit of the 2MASS Extended Source Catalog, i.e. up to 13.5 mag in the near-infrared K_s band (equivalent to an effective distance of 300 Mpc/h). We compare the observed growth of the dipole with the theoretically expected, conditional one (i.e., given the velocity of the Local Group relative to the CMB), for the LambdaCDM power spectrum and cosmological parameters constrained by WMAP. The observed growth turns out to be within 1-sigma confidence level of its theoretical counterpart once the proper observational window of the 2MASS flux-limited catalog is included. For a contrast, if the adopted window is a top-hat, then the predicted dipole grows significantly faster and converges to its final value for a distance of about 300 Mpc/h. By comparing the observational windows, we show that for a given flux limit and a corresponding distance limit, the 2MASS flux-weighted window passes less large-scale signal than the top-hat one. We conclude that the growth of the 2MASS dipole for effective distances greater than 200 Mpc/h is only apparent. On the other hand, for a distance of 80 Mpc/h (mean depth of the 2MASS Redshift Survey) and the LambdaCDM power spectrum, the true dipole is expected to reach only ~80% of its final value. Eventually, since for the window function of 2MASS the predicted growth is consistent with the observed one, we can compare the two to evaluate beta = (Omega_m)^0.55 / b. The result is beta = 0.38+-0.04, which leads to an estimate of the density parameter Omega_m = 0.20+-0.08.

Influence of the Local Void on Measurements of the Clustering Dipole

by Maciej Bilicki

Monthly Notices of the Royal Astronomical Society, Volume 406, Issue 2, pp. 1358-1363.
Co-author: Michał Chodorowski.

In measurements of the clustering dipole from all-sky surveys, an important problem is the lack of information about... more In measurements of the clustering dipole from all-sky surveys, an important problem is the lack of information about galaxy distribution in the so-called Zone of Avoidance (ZoA). The existence of the Local Void (LV) has a systematic effect on these measurements. If the ZoA is randomly filled with mock galaxies, then the calculated acceleration of the Local Group of galaxies (LG) has a spurious component, resulting from the lack of real galaxies in the intersection of the LV with the ZoA. This component affects both the misalignment angle between the clustering dipole and the CMB dipole, and the inferred value of mean matter density Omega_m. We calculate the amplitude of the spurious acceleration acting on the LG due to the LV. Its value depends on the geometry and size of the LV, as well as on its density contrast. However, under the simplest assumption of the LV being spherical and completely empty, within the linear theory this amplitude amounts only to about 45 km/s in units of velocity. The resulting change in the misalignment angle is smaller than 1 degree, and the fractional change in the deduced value of Omega_m is about 5%. Accounting for observationally indicated elongation of the LV and maintaining the maximising assumption of a complete lack of galaxies inside increases these numbers only moderately. Specifically, the amplitude of the spurious acceleration rises to about 60 km/s, the misalignment angle remains still smaller than 1 degree, and the fractional change in the deduced value of Omega_m is enhanced to about 7%. Thus, despite the overall importance of the Local Void for the motion of the Local Group, the influence of the intersection of the LV with the ZoA on measurements of the clustering dipole is found to be only a minor systematic effect.

The Velocity-Density Relation in the Spherical Model

by Maciej Bilicki

Monthly Notices of the Royal Astronomical Society, Volume 391, Issue 4, pp. 1796-1805.
Co-author: Michał Chodorowski.

We study the cosmic velocity-density relation using the spherical collapse model (SCM) as a proxy to non-linear... more We study the cosmic velocity-density relation using the spherical collapse model (SCM) as a proxy to non-linear dynamics. Although the dependence of this relation on cosmological parameters is known to be weak, we retain the density parameter Omega_m in SCM equations, in order to study the limit Omega_m -> 0. We show that in this regime the considered relation is strictly linear, for arbitrary values of the density contrast, on the contrary to some claims in the literature. On the other hand, we confirm that for realistic values of Omega_m the exact relation in the SCM is well approximated by the classic formula of Bernardeau (1992), both for voids (delta<0) and for overdensities up to delta ~ 3. Inspired by this fact, we find further analytic approximations to the relation for the whole range delta from -1 to infinity. Our formula for voids accounts for the weak Omega_m-dependence of their maximal rate of expansion, which for Omega_m < 1 is slightly smaller that 3/2. For positive density contrasts, we find a simple relation div v = 3 H_0 (Omega_m)^(0.6) [ (1+delta)^(1/6) - (1+delta)^(1/2) ], that works very well up to the turn-around (i.e. up to delta ~ 13.5 for Omega_m = 0.25 and neglected Omega_Lambda). Having the same second-order expansion as the formula of Bernardeau, it can be regarded as an extension of the latter for higher density contrasts. Moreover, it gives a better fit to results of cosmological numerical simulations.

Constraints on Early Dark Energy From CMB Lensing and Weak Lensing Tomography

by Lukas Hollenstein

Co-authored with Domenico Sapone, Robert Crittenden and Bjoern Malte Schaefer
Published in JCAP 04 (2009) 012.
http://dx.doi.org/10.1088/1475-7516/2009/04/012

Dark energy can be studied by its influence on the expansion of the Universe as well as on the growth history of the... more 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.

Can Slow Roll Inflation Induce Relevant Helical Magnetic Fields?

by Lukas Hollenstein

Co-authored with Ruth Durrer and Rajeev Kumar Jain
Published in JCAP 03 (2011) 037.
http://dx.doi.org/10.1088/1475-7516/2011/03/037

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the... more 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 $B^2(k) \propto k$, 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.

Exact Solutions of f(R) Gravity Coupled to Nonlinear Electrodynamics

by Lukas Hollenstein

Co-authored with Francisco S. N. Lobo
Published in Phys. Rev. D 78 (2008) 124007.
http://dx.doi.org/10.1103/PhysRevD.78.124007

In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories... more 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_{tt}g_{rr} = -1. Using the dual P formalism of nonlinear electrodynamics, an exact general solution is deduced in terms of the structural function HP. 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_{tt}g_{rr} ≠ -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).

Stability of the Einstein Static Universe In Modified Theories of Gravity

by Lukas Hollenstein

Co-authored with Christian G. Boehmer, Francisco S. N. Lobo and Sanjeev S. Seahra
Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by T. Damour, R. T. Jantzen and R. Ruffini, World Scientific, Singapore (2010).

We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of... more We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of gravity, like f(R) gravity, Gauss-Bonnet or f(G) gravity, and Horava-Lifshitz gravity.

Theoretical Priors on Modified Growth Parametrisations

by Lukas Hollenstein

Co-authored with Yong-Seon Song, Gabriela Caldera-Cabral and Kazuya Koyama
Published in JCAP 04 (2010) 018.
http://dx.doi.org/10.1088/1475-7516/2010/04/018

Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will... more 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.

Stability of the Einstein Static Universe In f(R) Gravity

by Lukas Hollenstein

Co-authored with Christian G. Boehmer and Francisco S. N. Lobo
Published in Phys. Rev. D 76 (2007) 084005.
http://dx.doi.org/10.1103/PhysRevD.76.084005

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the... more 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.

Dark Matter Distribution Function From Non-Extensive Statistical Mechanics

by Lukas Hollenstein

Co-authored with Steen H. Hansen, Daniel Egli and Christoph Salzmann
Published as New Astron. 10 (2005) 379.
http://dx.doi.org/10.1016/j.newast.2005.01.005

We present an analytical and numerical study of the velocity distribution function of self gravitating collisionless... more We present an analytical and numerical study of the velocity distribution function of self gravitating collisionless particles, which include dark matter and star clusters. We show that the velocity distribution derived through the Eddington's formula is identical to the analytical one derived directly from the generalized entropy of non-extensive statistical mechanics. This implies that self gravitating collisionless structures are to be described by non-extensive thermo-statistics. We identify a connection between the density slope of dark matter structures, \gamma, from \rho ~ r^{-\gamma}, and the entropic index, q, from the generalized entropy, S_q. Our numerical result confirms the analytical findings of earlier studies and clarifies which is the correct connection between the density slope and the entropic index. We use this result to conclude that from a fundamental statistical mechanics point of view the central density slope of self gravitating collisionless dark matter structures is not constrained, and even cored dark matter structures are allowed with \gamma = 0. We find that the outer density slope is bounded by \gamma= 10/3.

Applications of Cosmological Perturbation Theory to Dynamical Dark Energy and Primordial Magnetogenesis

by Lukas Hollenstein

THE THESIS IS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF PORTSMOUTH.

Director of studies: Dr. Robert G. Crittenden
Second supervisor: Prof. Roy Maartens
External examiner: Prof. Pedro G. Ferreira
Internal examiner: Dr. Kazuya Koyama

Submitted: September 2009

Copyright 2009 by Lukas Hollenstein. All rights reserved. The copyright of this thesis rests with the Author. Copies (by any means) either in full, or of extracts, may not be made without the prior written consent from the Author.

We investigate two important problems in concordance cosmology: the nature of dark energy and the origin of... more We investigate two important problems in concordance cosmology: the nature of dark energy and the origin of large-scale magnetic fields. Although the cosmological constant seems to be consistent with the major observational results, there is no theoretical understanding of its nature. Alternative dynamical models have been proposed, but are difficult to distinguish from the cosmological constant as yet. Large-scale magnetic fields are observed in cosmic structure while their origin is still obscure. Their ubiquity suggests a primordial origin and some influence on structure formation. With this theme in mind we apply the framework of cosmological perturbation theory to both problems. We present a review of the linearised theory with some attention to the physical interpretation of the perturbation variables with respect to the covariant formalism, and to the description of general fluids rather than just perfect fluids.

We aim at investigating dynamical dark energy models by means of upcoming weak lensing observations. Therefore we draw up a Fisher matrix formalism to make predictions for CMB lensing and cosmic shear tomography, and discuss the capabilities and drawbacks of these observables. Subsequently we apply these results to the specific case of a class of dark energy models with a non-negligible contribution to the energy density already in the early universe, called early dark energy. We forecast statistical uncertainties from the CMB, CMB lensing, and weak cosmic shear tomography and find that CMB lensing starts breaking the degeneracies between late universe parameters, already with the noise levels expected for Planck. Combining these results with cosmic shear measurements from a space-borne survey will allow us to rule out the cosmological constant.

Although gravitational structure formation is a quite well-understood process within the concordance model, the origin of large-scale magnetic fields is not addressed in that framework. We review the observational evidence for cosmic magnetism and the bounds on primordial magnetic fields, and observe that fields generated just before recombination are not strongly constrained yet. Therefore we re-analyse in linear perturbations the Harrison mechanism which proposes magnetogenesis from vortical currents. We find that non-vanishing initial vorticity is needed for the mechanism to work and not even active sources of vector perturbations can amend this result.

Effects of a Cut, Lorentz-Boosted sky on the Angular Power Spectrum

by Amanda Yoho

co-authors Thiago Pereira, Maik Stuke, and Glenn D. Starkman

    Abstract: The largest fluctuation in the observed CMB temperature field is the dipole, its origin being... more     Abstract: The largest fluctuation in the observed CMB temperature field is the dipole, its origin being usually attributed to the Doppler Effect - the Earth's velocity with respect to the CMB rest frame. The lowest order boost correction to temperature multipolar coefficients appears only as a second order correction in the temperature power spectrum, $C_{\ell}$. Since v/c - 10-3, this effect can be safely ignored when estimating cosmological parameters [4-7]. However, by cutting our galaxy from the CMB sky we induce large-angle anisotropies in the data. In this case, the corrections to the cut-sky $C_{\ell}$s show up already at first order in the boost parameter. In this paper we investigate this issue and argue that this effect might turn out to be important when reconstructing the power spectrum from the cut-sky data.