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Register a new userWhat can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?
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Added by
Marcelo J. Reboucas
Publication date
2011
fields
Physics
and research's language is
English
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In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for nearly antipodal pairs of such circles in cosmic microwave background maps have so far been unsuccessful. Previously we had shown that the negative outcome of such searches, if confirmed, should in principle be sufficient to exclude a detectable non-trivial spatial topology for most observers in very nearly flat ($0<midOmega_{text{tot}}-1mid lesssim10^{-5}$) (curved) universes. More recently, however, we have shown that this picture is fundamentally changed if the universe turns out to be {it exactly} flat. In this case there are many potential pairs of circles with large deviations from antipodicity that have not yet been probed by existing searches. Here we study under what conditions the detection of a single pair of circles-in-the-sky can be used to uniquely specify the topology and the geometry of the spatial section of the Universe. We show that from the detection of a emph{single} pair of matching circles one can infer whether the spatial geometry is flat or not, and if so we show how to determine the topology (apart from one case) of the Universe using this information. An important additional outcome of our results is that the dimensionality of the circles-in-the-sky parameter space that needs to be spanned in searches for matching pair of circles is reduced from six to five degrees of freedom, with a significant reduction in the necessary computational time.
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[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for nearly antipodal circles in maps of cosmic microwave background have so far been unsuccessful. This negative outcome along with recent theoretical results concerning the detectability of nearly flat compact topologies is sufficient to exclude a detectable nontrivial topology for most observers in very nearly flat positively and negatively curved Universes ($0<|Omega_{tot}-1| lesssim 10^{-5}$). Here we investigate the consequences of these searches for observable nontrivial topologies if the Universe turns out to be exactly flat ($Omega_{tot}=1$). We demonstrate that in this case the conclusions deduced from such searches can be radically different. We show that for all multiply-connected orientable flat manifolds it is possible to directly study the action of the holonomies in order to obtain a general upper bound on the angle that characterizes the deviation from antipodicity of pairs of matching circles associated with the shortest closed geodesic. This bound is valid for all observers and all possible values of the compactification length parameters. We also show that in a flat Universe there are observers for whom the circles-in-the-sky searches already undertaken are insufficient to exclude the possibility of a detectable nontrivial spatial topology. It is remarkable how such small variations in the spatial curvature of the Universe, which are effectively indistinguishable geometrically, can have such a drastic effect on the detectability of cosmic topology.
Deep observations of galaxy outskirts reveal faint extended stellar components (ESCs) of streams, shells, and halos, which are ghostly remnants of the tidal disruption of satellite galaxies. We use cosmological galaxy formation simulations in Cold Dark Matter (CDM) and Warm Dark Matter (WDM) models to explore how the dark matter model influences the spatial, kinematic, and orbital properties of ESCs. These reveal that the spherically averaged stellar mass density at large galacto-centric radius can be depressed by up to a factor of 10 in WDM models relative to the CDM model, reflecting the anticipated suppressed abundance of satellite galaxies in WDM models. However, these differences are much smaller in WDM models that are compatible with observational limits, and are comparable in size to the system-to-system variation we find within the CDM model. This suggests that it will be challenging to place limits on dark matter using only the unresolved ESC.
In inflationary cosmology, cosmic reheating after inflation sets the initial conditions for the hot big bang. We investigate how CMB data can be used to study the effective potential and couplings of the inflaton during reheating and constrain the underlying microphysics. If there is a phase of preheating that is driven by a parametric resonance or other instability, then the thermal history and expansion history during the reheating era depend on a large number of microphysical parameters in a complicated way. In this case the connection between CMB observables and microphysical parameters can only established with intense numerical studies. Such studies can help to improve CMB constraints on the effective inflaton potential in specific models, but parameter degeneracies usually make it impossible to extract meaningful best-fit values for individual microphysical parameters. If, on the other hand, reheating is driven by perturbative processes, then it can be possible to constrain the inflaton couplings and the reheating temperature from CMB data. This provides an indirect probe of fundamental microphysical parameters that most likely can never be measured directly in the laboratory, but have an immense impact on the evolution of the cosmos by setting the stage for the hot big bang.
[Abridged] An observable signature of a detectable nontrivial spatial topology of the Universe is the circles-in-the-sky in the CMB sky. In the most general search, pairs of circles with deviation from antipodality $0^circ leq theta leq 169^circ$ and radii $10^circ leq lambda leq 90^circ$ were investigated, but no matching circles were found. Assuming this negative result, we examine the question as to whether there are nearly flat universes with compact topology that would give rise to circles whose observable parameters $lambda$ and $theta$ fall o outside the ranges covered by this search. We derive the expressions for the deviation from antipodality and for the radius of the circles associated to a pair elements ($gamma,$,$gamma^{-1}$) of the holonomy group $Gamma$ which define the spatial section of any positively curved universe with a nontrivial topology. We show that there is a critical position that maximizes the deviation from antipodality, and prove that no matter how nearly flat the Universe is, it can always have a nontrivial spatial topology that gives rise to circles whose deviation from antipodality $theta$ is larger than $169^circ$, and whose radii of the circles $lambda$ are smaller than $10^circ$ for some observers. This makes apparent that slightly positively curved universes with cosmological parameters within Planck bounds can be endowed with a nontrivial spatial topology with values of the parameters $lambda$ and $theta$ outside the ranges covered by the searches for circles carried out so far. Thus, these circles searches so far undertaken are not sufficient to exclude the possibility of a universe with a detectable nontrivial cosmic topology. We present concrete examples of such nearly flat universes, and discuss the implications of our results in view of unavoidable practical limits of the circles-in-the-sky method.
This review focuses on the current status of lattice calculations of three observables which are both phenomenologically and experimentally relevant and have been scrutinized recently. These three observables are the nucleon electromagnetic form factors, the momentum fraction, <x>, and the nucleon axial coupling, gA.
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