Effects Of Spatial Curvature Research Articles

Bose-Einstein condensate in an elliptical waveguide

We investigate the effects of spatial curvature for an atomic Bose-Einstein condensate confined in an elliptical waveguide. The system is well described by an effective 1D Gross-Pitaevskii equation with a quantum-curvature potential, which has the shape of a double-well but crucially depends on the eccentricity of the ellipse. The ground state of the system displays a quantum phase transition from a two-peak configuration to a one-peak configuration at a critical attractive interaction strength. In correspondence of this phase transition the superfluid fraction strongly reduces and goes to zero for a sufficiently attractive Bose-Bose interaction.

Spatial curvature at the sound horizon

The effect of spatial curvature on primordial perturbations is controlled by ΩK,0/cs2 , where ΩK,0 is today's fractional density of spatial curvature and cs is the speed of sound during inflation. Here we study these effects in the limit cs≪ 1 . First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on ΩK,0/cs2 , but it is necessary to go beyond our linear-order treatment.

Environment dependence of the growth of the most massive objects in the Universe

This paper investigates the growth of the most massive cosmological objects. We utilize the Simsilun simulation, which is based on the approximation of the silent universe. In the limit of spatial homogeneity and isotropy the silent universes reduce to the standard FLRW models. We show that within the approximation of the silent universe the formation of the most massive cosmological objects differs from the standard background-dependent approaches. For objects with masses above $10^{15} M_\odot$ the effect of spatial curvature (overdense regions are characterized by positive spatial curvature) leads to measurable effects. The effect is analogous to the effect that the background cosmological model has on the formation of these objects (i.e. the higher matter density and spatial curvature the faster the growth of cosmic structures). We measure this by the means of the mass function and show that the mass function obtained from the Simsilun simulation has a higher amplitude at the high-mass end compared to standard mass function such as the Press-Schechter or the Tinker mass function. For comparison, we find that the expected mass of most massive objects using the Tinker mass function is $4.4^{+0.8}_{-0.6} \, \times 10^{15} M_\odot$, whereas for the Simsilun simulation is $6.3^{+1.0}_{-0.8} \, \times 10^{15} M_\odot$. We conclude that the nonlinear relativistic effects could affect the formation of the most massive cosmological objects, leading to a relativistic environment-dependence of the growth rate of the most massive clusters.

Effects of spatial curvature on the f (R) gravity phase space: no inflationary attractor?

In this paper we study the effects of spatial curvature of the metric on the phase space of vacuum gravity. Particularly, we appropriately choose the variables of the dynamical system, in order for this to be autonomous, and we study the phase space of the resulting theory, focusing on de Sitter, matter and radiation domination fixed points. Our analysis indicates that the effect of spatial curvature on the phase space is radical, since it destabilizes all the stable de Sitter vacua of the flat spacetime vacuum gravity phase space, making the phase space having non-trivial unstable submanifolds. This instability occurs regardless if the spacetime has elliptic or hyperbolic spatial sections, and it is also robust towards the choice of initial conditions. We investigate the source of the instability in the system, and also we discuss the stability of the matter and radiation domination vacua, which, as we demonstrate, are also highly unstable. Our results for de Sitter attractors indicate that the stable de Sitter attractors of the vacuum gravity theory for a flat Universe, are destabilized by the presence of curvature, and this shows that inflation for vacuum gravity in non-flat spacetime is problematic, at least at the phase space level. This result holds true for both elliptic and hyperbolic spacetimes.

THE EFFECT OF CURVATURE IN DETERMINING THE PROPERTY OF DARK ENERGY FROM TYPE IA SUPERNOVA WITH A MODEL INDEPENDENT METHOD

The effect of spatial curvature in reconstructing the cosmic expansion history and the property of dark energy is studied in this paper by smoothing the noise of the Union2.1 Type Ia Supernovae (SNIa) data with a Gaussian smoothing function. We find that the spatial curvature induces an apparent effect in reconstructing the Hubble parameter H(z), the deceleration parameter q(z), and especially on the equation of state w(z) of dark energy. Thus, when one probes the dark energy property, an assumption of a flat universe may induce critical bias and it is imperative to take account of the spatial curvature.

Cosmic behavior, statefinder diagnostic and w−w ′ analysis for interacting new agegraphic dark energy model in non-flat universe

We investigate the interacting NADE model in non-flat universe. The effects of spatial curvature Ω k , interaction coefficient α and the main parameter of NADE, n, on EoS parameter w d and deceleration parameter q are studied. We obtain a minimum value for n in both early and present time, in order to that our DE model crosses the phantom divide. Also in a closed universe, changing the sign of q is strongly dependent on α. It has been shown that the quantities w d and q have a different treatment for various spatial curvature. At last, we calculate the statefinder diagnostic and w−w ′ analysis in non flat universe. In non flat universe, the statefinder trajectories are discriminated by both n and α.

Bounds on cold dark matter and neutrino isocurvature perturbations from CMB and LSS data

Early universe models for the origin of structure typically produce a spectrum of initial fluctuations with a mixture of adiabatic and isocurvature perturbations. Using the observed anisotropies of the cosmic microwave backgound, the matter power spectra from large scale structure surveys and the luminosity distance vs. redshift relation from supernovae of type Ia, we obtain strong bounds on the possible cold dark matter/baryon as well as neutrino isocurvature contributions to the primordial fluctations in the Universe. Neglecting the possible effects of spatial curvature and tensor perturbations, we perform a Bayesian likelihood analysis with 13 free parameters, including independent spectral indexes for each of the modes and for their cross-correlation angle. We find that around a pivot wave number of $k=0.05h\text{ }\text{ }{\mathrm{M}\mathrm{p}\mathrm{c}}^{\ensuremath{-}1}$ the amplitude of the correlated isocurvature component cannot be larger than about 60% for the cold dark matter mode, 40% for the neutrino density mode, and 30% for the neutrino velocity mode, at two sigma. In the first case, our bound is larger than the WMAP first-year result, presumably because we prefer not to include any data from Lyman-$\ensuremath{\alpha}$ forests, but then obtain large blue spectral indexes for the nonadiabatic contributions. We also translate our bounds in terms of constraints on double inflation models with two uncoupled massive fields.

Bounds on isocurvature perturbations from cosmic microwave background and large scale structure data.

We obtain very stringent bounds on the possible cold dark matter, baryon, and neutrino isocurvature contributions to the primordial fluctuations in the Universe, using recent cosmic microwave background and large scale structure data. Neglecting the possible effects of spatial curvature, tensor perturbations, and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the amplitude of the isocurvature component cannot be larger than about 31% for the cold dark matter mode, 91% for the baryon mode, 76% for the neutrino density mode, and 60% for the neutrino velocity mode, at 2sigma, for uncorrelated models. For correlated adiabatic and isocurvature components, the fraction could be slightly larger. However, the cross-correlation coefficient is strongly constrained, and maximally correlated/anticorrelated models are disfavored. This puts strong bounds on the curvaton model.

Pre-big-bang inflation requires fine-tuning

The pre-big-bang cosmology inspired by superstring theories has been suggested as an alternative to slow-roll inflation. We analyze, in both the Jordan and Einstein frames, the effect of spatial curvature on this scenario and show that too much curvature --- of either sign --- reduces the duration of the inflationary era to such an extent that the flatness and horizon problems are not solved. Hence, a fine-tuning of initial conditions is required to obtain enough inflation to solve the cosmological problems.

THE EFFECT OF SPATIAL CURVATURE ON CLASSICAL AND QUANTUM STRINGS

We study the effects of spatial curvature on classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson–Walker space-times with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the space-time: the self-consistent solution to the Einstein equations is a spatially closed (K>0) space-time with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K≤0 exist. We semiclassically quantize the circular strings and find the mass m in each case. For K>0, the very massive strings, oscillating on the full hypersphere, have m2~Kn2(n∈N0)independent of α' and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m2α′~n and a finite number of states N~1/Kα′. For K<0, there are infinitely many string states with masses m log m ~ n, i.e. the level spacing grows slower than n. The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.

Gordon decomposition of Dirac current in curved space

The scheme outlined earlier to formulate Dirac equation in curved space-times is now extended to discuss the effect of spatial curvature on Gordon decomposition of the Dirac current.

Free-streaming radiation in cosmological models with spatial curvature

view Abstract Citations (15) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Free-streaming radiation in cosmological models with spatial curvature Wilson, M. L. Abstract The effects of spatial curvature on radiation anisotropy are examined for the standard Friedmann-Robertson-Walker model universes. The effect of curvature is found to be very important when considering fluctuations with wavelengths comparable to the horizon. It is concluded that the behavior of radiation fluctuations in models with spatial curvature is quite different from that in spatially flat models, and that models with negative curvature are most strikingly different. It is therefore necessary to take the curvature into account in careful studies of the anisotropy of the microwave background. Publication: The Astrophysical Journal Pub Date: February 1982 DOI: 10.1086/183735 Bibcode: 1982ApJ...253L..53W Keywords: Background Radiation; Cosmology; Curvature; Relic Radiation; Spatial Dependencies; Anisotropy; Space-Time Functions; Astrophysics full text sources ADS |