Cosmology with modified Newtonian dynamics (MOND)

It is well known that the application of Newtonian dynamics to an expanding spherical region leads to the correct relativistic expression (the Friedmann equation) for the evolution of the cosmic scalefactor. Here, the cosmological implications of Milgrom's modified Newtonian dynamics (MOND) are considered by means of a similar procedure. Earlier work by Felten demonstrated that in a region dominated by modified dynamics the expansion cannot be uniform (separations cannot be expressed in terms of a scalefactor) and that any such region will eventually recollapse regardless of the initial expansion velocity and mean density. Here I show that, because of the acceleration threshold for the MOND phenomenology, a region dominated by MOND will have a finite size which, in the earlier Universe ( z >3), is smaller than the horizon scale. Therefore, uniform expansion and homogeneity on the horizon scale are consistent with MOND-dominated non-uniform expansion and the development of inhomogeneities on smaller scales. In the radiation-dominated era, the amplitude of MOND-induced inhomogeneities is much smaller than that implied by observations of the cosmic background radiation, and the thermal and dynamical history of the Universe is identical to that of the standard big bang model. In particular, the standard results for primordial nucleosynthesis are retained. When matter first dominates the energy density of the Universe, the cosmology diverges from that of the standard model. Objects of galaxy mass are the first virialized objects to form (by z =10), and larger structure develops rapidly. At present, the Universe would be inhomogeneous out to a substantial fraction of the Hubble radius.     

Mini-inflation prior to the cosmic confinement transition?

The onset of the confinement transition in the early universe is studied within the Friedmann model. Exploiting a bag model equation of state for the deconfined matter, which is generalized to include also metastable states, the possibility of a mini-inflationary epoch is demonstrated. A criterion of metastability is derived to estimate parameters of this mini-inflation.     

Mattig's relation and dynamical distance indicators

We discuss how the redshift (Mattig) method in the Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is the distance itself (in this case the proper metric distance). As the Friedmann model has a Newtonian analogy, its use to infer distances has instructive similarities to classical dynamical distance indicators. In view of the theoretical exact linear distance‐velocity law, we emphasize that it is conceptually correct to derive the cosmological distance via the route: redshift (primarily observed) → space expansion velocity (not directly observed) → metric distance (physical length in “cm”). Important properties of the proper metric distance are summarized. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

WD 1953−011: a magnetic white dwarf with peculiar field structure

We present a new interpretation of recent observations suggesting that the expansion of the Universe has recently started to accelerate. A cosmological model with a quintessence field driven by a potential motivated by M-theory is used to study the energy density and equation of state for the Universe. We find that late-time acceleration does not have to lead to the usual predictions of perpetual acceleration. The model allows another broad class of scenarios in which today's acceleration is a transient phenomenon, which is succeeded by a return to matter domination and decelerating expansion.     

The cosmic microwave background for a nearly flat compact hyperbolic universe

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy and an extra spatially constant dark energy X -component are considered. The general solution of the Friedmann equation for the cosmic scalefactor a ( η ) is given for the four-component models in terms of the Weierstrass ℘-function. The lower parts of the angular power spectra C _l of the CMB anisotropy are computed for nearly flat models with Ω_tot≤0.95. It is shown that the particular compact fundamental cell that is considered in this paper leads to a suppression in C _l for l ≲10 and Ω_tot≲0.9.     

New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model For a ≈ t^p, especially, if p ≥ 1, this is called power-law inflation. For the Lagrangian L = R^m with p = − (m − 1) (2m − 1)/(m − 2) power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field ϕ in an exponential potential V(ϕ) = exp (μϕ) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we write The general solutions reads Q(a) = (a^b + C)^f/b with free integration constant C (C = 0 gives exact power-law inflation) and m-dependent values b and f: f = −2 + 1/p, b = (4m − 5)/(m − 1). Finally, special solutions for the closed and open Friedmann model are found.     

Distance measurements as a probe of cosmic acceleration

A major recent development in observational cosmology has been an accurate measurement of the luminosity distance–redshift relation out to redshifts z =0.8 from Type Ia supernova standard candles. The results have been argued as evidence for cosmic acceleration. It is well known that this assertion depends on the assumption that we know the equation of state for all mass–energy other than normal pressureless matter; popular models are based either on the cosmological constant or on the more general quintessence formulation. However, this assertion also depends on a number of other assumptions, implicit in the derivation of the standard cosmological field equations: large-scale isotropy and homogeneity, the flatness of the Universe, and the validity of general relativity on cosmological scales (where it has not been tested). A detailed examination of the effects of these assumptions on the interplay between the luminosity distance–redshift relation and the acceleration of the Universe is not possible unless one can define the precise nature of the failure of any particular assumption. However a simple quantitative investigation is possible and reveals a number of considerations about the relative importance of the different assumptions. In this paper we present such an investigation. We find that the relationship between the distant-redshift relation and the sign of the deceleration parameter is fairly robust and is unaffected if only one of the assumptions that we investigate is invalid so long as the deceleration parameter is not close to zero (it would not be close to zero in the currently favoured Ω_Λ=1−Ω_matter=0.7 or 0.8 Universe, for example). Failures of two or more assumptions in concordance may have stronger effects.     

The massive scalar field in a closed Friedmann universe model — new rigorous results

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove D ≥ 1, where D ≥ is the dimension of the set of solutions which can be integrated up to t → ∞ (D > 0 was conjectured by PAGE (1984)). We discuss concepts like “the probability of the appearance of a sufficiently long inflationary phase” and argue that it is primarily a probability measure μ in the space V of solutions (and not in the space of initial conditions) which has to be applied. μ is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of μ can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented.     

Decay of the vacuum energy into cosmic microwave background photons

We examine the possibility of the decay of the vacuum energy into a homogeneous distribution of a thermalized cosmic microwave background (CMB), which is characteristic of an adiabatic vacuum energy decay into photons. It is shown that observations of the primordial density fluctuation spectrum, obtained from CMB and galaxy distribution data, restrict the possible decay rate. When photon creation due to an adiabatic vacuum energy decay takes place, the standard linear temperature dependence   T ( z ) = T ₀(1 + z )  is modified, where T ₀ is the present CMB temperature, and can be parametrized by a modified CMB temperature dependence     . From the observed CMB and galaxy distribution data, a strong limit on the maximum value of the decay rate is obtained by placing a maximum value  β_max≃ 3.4 × 10⁻³  on the β parameter.     

The coincidence of friedmann integrals

The expansion of a two-component Universe with an arbitrary spatial curvature is considered. It is shown that the Friedmann integrals of an almost flat Universe do not coincide.     

Non-linear density evolution from an improved spherical collapse model

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, δ . The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of δ . The key new idea is a Taylor series expansion in (1/ δ ) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two-point correlation function.     

Cosmic structure growth and dark energy

Dark energy has a dramatic effect on the dynamics of the Universe, causing the recently discovered acceleration of the expansion. The dynamics are also central to the behaviour of the growth of large-scale structure, offering the possibility that observations of structure formation provide a sensitive probe of the cosmology and dark energy characteristics. In particular, dark energy with a time-varying equation of state can have an influence on structure formation stretching back well into the matter-dominated epoch. We analyse this impact, first calculating the linear perturbation results, including those for weak gravitational lensing. These dynamical models possess definite observable differences from constant equation of state models. Then we present a large-scale numerical simulation of structure formation, including the largest volume to date involving a time-varying equation of state. We find the halo mass function is well described by the Jenkins et al. mass function formula. We also show how to interpret modifications of the Friedmann equation in terms of a time-variable equation of state. The results presented here provide steps toward realistic computation of the effect of dark energy in cosmological probes involving large-scale structure, such as cluster counts, the Sunyaev–Zel'dovich effect or weak gravitational lensing.     

Large-scale cosmic microwave background anisotropies and dark energy

In this paper we investigate the effects of perturbations in a dark energy component with a constant equation of state on large-scale cosmic microwave background (CMB) anisotropies. The inclusion of perturbations increases the large-scale power. We investigate more speculative dark energy models with   w < −1  and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalize the parametrization of the dark energy fluctuations to allow for an arbitrary constant sound speed, and we show how constraints from CMB experiments change if this is included. Combining CMB with large-scale structure, Hubble parameter and supernovae observations we obtain   w =−1.02 ± 0.16 (1σ)  as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.     

Perturbation theory of N point-mass gravitational lens systems without symmetry: small mass-ratio approximation

This paper makes the first systematic attempt to determine using perturbation theory the positions of images by gravitational lensing due to arbitrary number of coplanar masses without any symmetry on a plane, as a function of lens and source parameters. We present a method of Taylor-series expansion to solve the lens equation under a small mass-ratio approximation. First, we investigate perturbative structures of a single-complex-variable polynomial, which has been commonly used. Perturbative roots are found. Some roots represent positions of lensed images, while the others are unphysical because they do not satisfy the lens equation. This is consistent with a fact that the degree of the polynomial, namely the number of zeros, exceeds the maximum number of lensed images if   N = 3  (or more). The theorem never tells which roots are physical (or unphysical). In this paper, unphysical ones are identified. Secondly, to avoid unphysical roots, we re-examine the lens equation. The advantage of our method is that it allows a systematic iterative analysis. We determine image positions for binary lens systems up to the third order in mass ratios and for arbitrary N point masses up to the second order. This clarifies the dependence on parameters. Thirdly, the number of the images that admit a small mass-ratio limit is less than the maximum number. It is suggested that positions of extra images could not be expressed as Maclaurin series in mass ratios. Magnifications are finally discussed.     

From planes to spheres: about gravitational lens magnifications

We discuss the classic theorem according to which a gravitational lens always produces at least one image with a magnification greater than unity. This theorem seems to contradict the conservation of total flux from a lensed source. The standard solution to this paradox is based on the exact definition of the reference 'unlensed' situation, in which the lens mass can be either removed or smoothly redistributed.
We calculate magnifications and amplifications (in photon number and energy flux density) for general lensing scenarios not limited to regions close to the optical axis. In this way the formalism is naturally extended from tangential planes for the source and lensed images to complete spheres. We derive the lensing potential theory on the sphere and find that the Poisson equation is modified by an additional source term that is related to the mean density and to the Newtonian potential at the positions of observer and source. This new term generally reduces the magnification, to below unity far from the optical axis, and ensures conservation of the total photon number received on a sphere around the source.
This discussion does not affect the validity of the focusing theorem , in which the unlensed situation is defined to have an unchanged affine distance between source and observer. The focusing theorem does not contradict flux conservation, because the mean total magnification (or amplification) directly corresponds to different areas of the source (or observer) sphere in the lensed and unlensed situation. We argue that a constant affine distance does not define an astronomically meaningful reference.
By exchanging source and observer, we confirm that magnification and amplification differ according to Etherington's reciprocity law, so that surface brightness is no longer strictly conserved. At this level we also have to distinguish between different surface brightness definitions that are based on photon number, photon flux and energy flux.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

Cluster formation and the Sunyaev–Zel'dovich power spectrum in modified gravity: the case of a phenomenologically extended DGP model

We investigate the effect of modified gravity on cluster abundance and the Sunyaev–Zel'dovich (SZ) angular power spectrum. Our modified gravity is based on a phenomenological extension of the Dvali–Gabadadze–Porrati model which includes two free parameters characterizing deviation from Λ cold dark matter cosmology. Assuming that Birkhoff's theorem gives a reasonable approximation, we study the spherical collapse model of structure formation and show that while the growth function changes to some extent, modified gravity gives rise to no significant change in the linear density contrast at collapse time. The growth function is enhanced in the so called normal branch, while in the 'self-accelerating' branch it is suppressed. The SZ angular power spectrum is computed in the normal branch, which allows us to put observational constraints on the parameters of the modified gravity model using small scale cosmic microwave background observation data.     

Structure formation in inhomogeneous dark energy models

We investigate how inhomogeneous quintessence models may have a specific signature even in the linear regime of large-scale structure formation. The dynamics of the collapse of a dark matter halo is governed by the value or the dynamical evolution of the dark energy equation of state, the energy density's initial conditions and its homogeneity nature in the highly non-linear regime. These have a direct impact on the redshift of collapse, altering in consequence the linearly extrapolated density threshold above which structures will end up collapsing. We compute this quantity for minimally coupled and coupled quintessence models, examining two extreme scenarios: first, when the quintessence field does not exhibit fluctuations on cluster scales and below – homogeneous dark energy; and secondly, when the field inside the overdensity collapses along with the dark matter – inhomogeneous dark energy. One shows that inhomogeneous dark energy models present distinct features which may be used to confront them with observational data, for instance, galaxy number counting. Fitting formulae for the linearly extrapolated density threshold above which structures will end up collapsing are provided for models of dark energy with constant equation of state.     

About universes with scale‐related total masses and their abolition of presently outstanding cosmological problems

The most recently celebrated cosmological implications of the cosmic microwave background studies with WMAP (2006), though fascinating by themselves, do, however, create some extremely hard conceptual challenges for the present‐day cosmology. These recent extremely refined WMAP observations seem to reflect a universe which was extremely homogeneous at the recombination age and thus is obviously causally closed at the time of the cosmic recombination era. From the very tiny fluctuations apparent at this early epoch the presently observable nonlinear cosmic density structures can, however, only have grown up, if in addition to a mysteriously high percentage of dark matter an even higher percentage of dark energy is admitted as drivers of the cosmic evolution. The required dark energy density, on the other hand, is nevertheless 120 orders of magnitude smaller then the theoretically calculated value. These are outstanding problems of present day cosmology onto which we are looking here under new auspices. We shall investigate in the following, up to what degree a universe simply abolishes all these outstanding problems in case it reveals itself as an universe of constant total energy. As we shall show basic questions like: How could the gigantic mass of the universe of about 10⁸⁰ proton masses at all become created? – Why is the presently recognized and obviously indispensable cosmic vacuum energy density so terribly much smaller than is expected from quantum theoretical considerations, but nevertheless terribly important for the cosmic evolution? – Why is the universe within its world horizon a causally closed system? –, can perhaps simply be answered, when the assumption is made that the universe has a constant total energy with the consequence that the total mass density of the universe (matter and vacuum) scales with . Such a scaling of matter and vacuum energy abolishes the horizon problem, and the cosmic vacuum energy density can easily be reconciled with its theoretical expectation values. In this model the mass of the universe increases linearly with the world extension R_u and can grow up from a Planck mass as a vacuum fluctuation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Testing dark energy with the Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics

The Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics (ALPACA) is a proposed 8-m liquid-mirror telescope surveying  ∼1000 deg²  of the Southern hemisphere sky. It will be a remarkably simple and inexpensive telescope that none the less will deliver a powerful sample of optical data for studying dark energy. The bulk of the cosmological data consist of nightly, high signal-to-noise ratio, multiband light curves of Type Ia supernovae (SNe Ia). At the end of the 3-yr run, ALPACA is expected to collect  ≳100 000  SNe Ia up to   z ∼ 1  . This will allow us to reduce present systematic uncertainties affecting the standard-candle relation. The survey will also provide several other data sets such as the detection of baryon acoustic oscillations in the matter power spectrum and shear weak-lensing measurements. In this preliminary analysis, we forecast constraints on dark energy parameters from SNe Ia and baryon acoustic oscillations. The combination of these two data sets will provide competitive constraints on the dark energy parameters under minimal prior assumptions. Further studies are needed to address the accuracy of weak-lensing measurements.