Search NASA⌕ Search

SEARCH · Search NASA

Results for “LOGARITHM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Ab initio estimates of the size of the observable universe

When one combines multiverse predictions by Bousso, Hall, and Nomura for the observed age and size of the universe in terms of the proton and electron charge and masses with anthropic predictions of Carter, Carr, and Rees for these masses in terms of the charge, one gets that the age of the universe should be roughly the inverse 64th power, and the cosmological constant should be around the 128th power, of the proton charge. Combining these with a further renormalization group argument gives a single approximate equation for the proton charge, with no continuous adjustable or observed parameters, and with a solution that is within 8% of the observed value. Using this solution gives large logarithms for the age and size of the universe and for the cosmological constant that agree with the observed values within 17%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Curvaton model completed

In an inflationary cosmology, the observed primordial density perturbation could come from the quantum fluctuations of another light ''curvaton'' field, rather than the inflaton. In this case, it is essential that the curvaton decays, converting its perturbation to an adiabatic perturbation. For the first time, we consistently account for this decay in the simplest curvaton model V(σ) = 1/2m{sup 2}σ{sup 2}, where the curvaton decays perturbatively. We point out that this decay gives rise to an important logarithmic correction to the potential. Moreover, the potential will also receive a correction from the thermal bath. As a consequence, the dynamics of the curvaton are substantially altered compared to the original model in the majority of the parameter space. It will therefore be necessary to re-calculate all the predictions of the original model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

On topological modifications of Newton's law

Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R{sup 2} × S{sup 1} topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S{sup 1} radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r{sup 2} to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

IR divergences in inflation and entropy perturbations

We study leading order perturbative corrections to the two point correlation function of the scalar field describing the curvature perturbation in a slow-roll inflationary background, paying particular attention to the contribution of entropy mode loops. We find that the infrared divergences are worse than in pure de Sitter space: they are power law rather than logarithmic. The validity of perturbation theory and thus of the effective field theory of cosmological perturbations leads to stringent constraints on the coupling constants describing the interactions, in our model the quartic self-interaction coupling constant of the entropy field. If the self coupling constant is larger than some critical value which depends in particular on the duration of the inflationary phase, then perturbation theory breaks down. Our analysis may have implications for the stability of de Sitter space: the quantum effects which lead to an instability of de Sitter space will be larger in magnitude in the presence of entropy fluctuations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

The behaviour of shape and velocity anisotropy in dark matter haloes

Dark matter haloes from cosmological N-body simulations typically have triaxial shapes and anisotropic velocity distributions. Recently it has been shown that the velocity anisotropy, β, of cosmological haloes and major merger remnants depend on direction in such a way that β is largest along the major axis and smallest along the minor axis. In this work we use a wide range of non-cosmological N-body simulations to examine halo shapes and direction-dependence of velocity anisotropy profiles. For each of our simulated haloes we define 48 cones pointing in different directions, and from the particles inside each cone we compute velocity anisotropy profiles. We find that elongated haloes can have very distinct velocity anisotropies. We group the behaviour of haloes into three different categories, that range from spherically symmetric profiles to a much more complex behaviour, where significant differences are found for β along the major and minor axes. We encourage future studies of velocity anisotropies in haloes from cosmological simulations to calculate β-profiles in cones, since it reveals information, which is hidden from a spherically averaged profile. Finally, we show that spherically averaged profiles often obey a linear relation between β and the logarithmic density slope in the inner parts of haloes, but this relation is not necessarily obeyed, when properties are calculated in cones.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters

Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P(log Δt) = 5.3 × 10{sup −4}Δt{sup β-tilde}/M{sub 250}{sup 2β-tilde}, with β-tilde = 0.77, where M{sub 250} is the projected cluster mass inside 250 kpc (in 10{sup 14}M{sub ☉}), and β-tilde is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M{sub 250} = 2 × 10{sup 14}M{sub ☉}, the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ≥500kms{sup −1}, mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689. A two-component model of estimating the supernova rate is applied in this work. For a magnitude threshold of m{sub AB} = 26.5, the yearly rate of Type Ia (core-collapse) supernovae with time delays less than 1000 days is 0.004±0.002 (0.029±0.001). If the magnitude threshold is lowered to m{sub AB} ∼ 27.0, the rate of core-collapse supernovae suitable for time delay observation is 0.044±0.015 per year.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Perturbation theory approach for the power spectrum: from dark matter in real space to massive haloes in redshift space

We investigate the accuracy of Eulerian perturbation theory for describing the matter and galaxy power spectra in real and redshift space in light of future observational probes for precision cosmology. Comparing the analytical results with a large suite of N-body simulations (160 independent boxes of 13.8 (Gpc/h){sup 3} volume each, which are publicly available), we find that re-summing terms in the standard perturbative approach predicts the real-space matter power spectrum with an accuracy of ∼<2% for k ≤ 0.20 h/Mpc at redshifts z∼<1.5. This is obtained following the widespread technique of writing the resummed propagator in terms of 1-loop contributions. We show that the accuracy of this scheme increases by considering higher-order terms in the resummed propagator. By combining resummed perturbation theories with several models for the mappings from real to redshift space discussed in the literature, the multipoles of the dark-matter power spectrum can be described with sub-percent deviations from N-body results for k ≤ 0.15 h/Mpc at z∼<1. As a consequence, the logarithmic growth rate, f, can be recovered with sub-percent accuracy on these scales. Extending the models to massive dark-matter haloes in redshift space, our results describe the monopole term from N-body data within 2% accuracy for scales k ≤ 0.15 h/Mpc at z∼<0.5; here f can be recovered within < 5% when the halo bias is known. We conclude that these techniques are suitable to extract cosmological information from future galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Effective action for the Abelian Higgs model in FLRW

We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in R{sub ξ} gauge we show that the result is gauge invariant upon using the equations of motion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Living with ghosts in Lorentz invariant theories

We argue that theories with ghosts may have a long lived vacuum state even if all interactions are Lorentz preserving. In space-time dimension D = 2, we consider the tree level decay rate of the vacuum into ghosts and ordinary particles mediated by non-derivative interactions, showing that this is finite and logarithmically growing in time. For D > 2, the decay rate is divergent unless we assume that the interaction between ordinary matter and the ghost sector is soft in the UV, so that it can be described in terms of non-local form factors rather than point-like vertices. We provide an example of a nonlocal gravitational-strength interaction between the two sectors, which appears to satisfy all observational constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Emergence of spacetime dynamics in entropy corrected and braneworld models

A very interesting new proposal on the origin of the cosmic expansion was recently suggested by Padmanabhan [arXiv:1206.4916]. He argued that the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space drives the accelerated expansion of the universe, as well as the standard Friedmann equation through relation ΔV = Δt(N{sub sur}−N{sub bulk}). In this paper, we first present the general expression for the number of degrees of freedom on the holographic surface, N{sub sur}, using the general entropy corrected formula S = A/(4L{sub p}{sup 2})+s(A). Then, as two example, by applying the Padmanabhan's idea we extract the corresponding Friedmann equations in the presence of power-law and logarithmic correction terms in the entropy. We also extend the study to RS II and DGP braneworld models and derive successfully the correct form of the Friedmann equations in these theories. Our study further supports the viability of Padmanabhan's proposal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Non-Gaussian bias: insights from discrete density peaks

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

On the non-linear scale of cosmological perturbation theory

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The Role of Electroweak Corrections for the Dark Matter Relic Abundance

We analyze the validity of the theorems concerning the cancellation of the infrared and collinar divergences in the case of dark matter freeze-out in the early universe. In particular, we compute the electroweak logarithmic corrections of infrared origin to the annihilation cross section of a dark matter particle being the neutral component of a SU(2){sub L} multiplet. The inclusion of processes with final state W can modify significantly the cross sections computed with only virtual W exchange. Our results show that the inclusion of infrared logs is necessary for a precise computation of the dark matter relic abundance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Asymptotic freedom, asymptotic flatness and cosmology

Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free β-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically-soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability, naturalness and other problems of such inflationary models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Further stable neutron star models from f(R) gravity

Neutron star models in perturbative f(R) gravity are considered with realistic equations of state. In particular, we consider the FPS, SLy and other equations of state and a case of piecewise equation of state for stars with quark cores. The mass-radius relations for f(R) = R+R(e{sup −R/R{sub 0}}−1) model and for R{sup 2} models with logarithmic and cubic corrections are obtained. In the case of R{sup 2} gravity with cubic corrections, we obtain that at high central densities (ρ > 10ρ{sub ns}, where ρ{sub ns} = 2.7 × 10{sup 14} g/cm{sup 3} is the nuclear saturation density), stable star configurations exist. The minimal radius of such stars is close to 9 km with maximal mass ∼ 1.9M{sub ⊙} (SLy equation). A similar situation takes place for AP4 and BSK20 EoS. Such an effect can give rise to more compact stars than in General Relativity. If observationally identified, such objects could constitute a formidable signature for modified gravity at astrophysical level. Another interesting result can be achieved in modified gravity with only a cubic correction. For some EoS, the upper limit of neutron star mass increases and therefore these EoS can describe realistic star configurations (although, in General Relativity, these EoS are excluded by observational constraints)

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Multi-scale gravity and cosmology

The gravitational dynamics and cosmological implications of three classes of recently introduced multi-scale spacetimes (with, respectively, ordinary, weighted and q-derivatives) are discussed. These spacetimes are non-Riemannian: the metric structure is accompanied by an independent measure-differential structure with the characteristics of a multi-fractal, namely, different dimensionality at different scales and, at ultra-short distances, a discrete symmetry known as discrete scale invariance. Under this minimal paradigm, five general features arise: (a) the big-bang singularity can be replaced by a finite bounce, (b) the cosmological constant problem is reinterpreted, since accelerating phases can be mimicked by the change of geometry with the time scale, without invoking a slowly rolling scalar field, (c) the discreteness of geometry at Planckian scales can leave an observable imprint of logarithmic oscillations in cosmological spectra and (d) give rise to an alternative mechanism to inflation or (e) to a fully analytic model of cyclic mild inflation, where near scale invariance of the perturbation spectrum can be produced without strong acceleration. Various properties of the models and exact dynamical solutions are discussed. In particular, the multi-scale geometry with weighted derivatives is shown to be a Weyl integrable spacetime.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Evolution of entanglement entropy in the early universe

We investigate the entropy evolution in the early universe by computing the change of the entanglement entropy in Freedmann-Robertson-Walker quantum cosmology in the presence of particle horizon. The matter is modeled by a Chaplygin gas so as to provide a smooth interpolation between inflationary and radiation epochs, rendering the evolution of entropy from early time to late time trackable. We found that soon after the onset of the inflation, the total entanglement entropy rapidly decreases to a minimum. It then rises monotonically in the remainder of the inflation epoch as well as the radiation epoch. Our result is in qualitative agreement with the area law of Ryu and Takayanagi including the logarithmic correction. We comment on the possible implication of our finding to the cosmological entropy problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Strong gravitational lensing with Gauss-Bonnet correction

In this paper we investigate the strong gravitational lensing in a five dimensional background with Gauss-Bonnet gravity, so that in 4-dimensions the Gauss-Bonnet correction disappears. By considering the logarithmic term for deflection angle, we obtain the deflection angle α-circumflex and corresponding parameters ā and b-bar . Finally, we estimate some properties of relativistic images such as θ{sub ∞}, s and r{sub m}.

79 ASTRONOMY AND ASTROPHYSICS↗