arXiv subjects

R. Kantowski

Publications and source records attributed to R. Kantowski.

At least 19 recordsLinked to original sources

arXiv2020

Equivalence of the Fermat potential and the lensing potential approaches to computing the integrated Sachs-Wolfe effect

We show in detail that the recently derived expression for evaluating the integrated Sachs-Wolfe (ISW) temperature shift in the cosmic microwave background (CMB) caused by individual embedded (compensated) lenses is equivalent to the conventional approach for flat background cosmologies. The conventional approach requires evaluating an integral of the time derivative of the lensing potential, whereas the new Fermat potential approach is simpler and only requires taking a derivative of the potential part of the time delay.

astro-ph.CO↗

arXiv2009

Including Absorption in Gordon's Optical Metric

We show that Gordon's optical metric on a curved spacetime can be generalized to include absorption by allowing the metric to become complex. We demonstrate its use in the realm of geometrical optics by giving three simple examples. We use one of these examples to compute corrected distance-redshift relations for Friedman-Lemaître-Robertson-Walker models in which the cosmic fluid has an associated complex index of refraction that represents grey extinction. We then fit this corrected Hubble curve to the type Ia supernovae data and provide a possible explanation (other than dark energy) of the deviation of these observations from dark matter predictions.

astro-ph.CO↗

arXiv2009

Cosmology With A Dark Refraction Index

We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the FLRW cosmologies by associating a refraction index with the cosmic fluid. We then derive an expression for the accumulated effect of a refraction index on the distance redshift relations and fit the Hubble curve of current supernova observations with a non-accelerating cosmological model. We also show that some observational effects caused by inhomogeneities, e.g. the Sachs-Wolfe effect, can be interpreted as being caused by an effective index of refraction, and hence this theory could extend to other speed of light communications such as gravitational radiation and neutrino fluxes.

astro-ph↗

arXiv2007

Steps for Solving the Transfer Equation for Arbitrary Flows in Stationary Spacetimes

We derive the radiative transfer equation for arbitrary stationary relativistic flows in stationary spacetimes, i.e. for steady-state transfer problems. We show how the standard characteristics method of solution developed by Mihalas and used throughout the radiative transfer community can be adapted to multi-dimensional applications with isotropic sources. Because the characteristics always coincide with geodesics and can always be specified by constants, direct integration of the characteristics derived from the transfer equation as commonly done in 1-D applications is not required. The characteristics are known for a specified metric from the geodesics. We give details in both flat and static spherically symmetric spacetimes. This work has direct application in 3-dimensional simulations of supernovae, gamma-ray bursts, and active galactic nuclei, as well as in modeling neutron star atmospheres.

astro-ph↗

arXiv2006

Chang-Refsdal Microlensed Type Ia Supernova Light Curves

A description of the light curves of microlensed Type Ia supernovae (SNe Ia) as extended and expanding sources is presented. We give examples of what microlensing by stellar-mass Chang-Refsdal lenses can do to a small percentage of supernova light curves. We find that in addition to overall brightening, significant changes in light--curve shapes can also occur. Peaks can be distorted, plateaus can appear, and even secondary peaks can be formed. The effects of both the relative motion of the lens and the supernova and the expansion of the supernova are given and compared. The effects of relative motion are more pronounced when a distant supernova ($z_s \sim 1$) impacts well within the Einstein ring of a nearby microlens ($z_d \sim 0.05$) and are less important for more distant deflectors. We also find that the increase in shear that comes with increased deflector distance tends to reduce the time variability of microlensing. We briefly discuss the probability of observing these effects.

astro-ph↗

arXiv2005

Effects of Gravitational Microlensing on P-Cygni Profiles of Type Ia Supernovae

A brief description of the deformed spectra of microlensed SNe Ia is presented. We show that microlensing amplification can have significant effects on line profiles. The resonance-scattering code SYNOW is used to compute the intensity profile in the rest frame of the supernova. The observed (microlensed) spectral lines are predicted assuming a simple stellar-size deflector, and are compared to unlensed cases to show the effects microlensing by solar-size deflectors can have on spectral lines. We limit our work to spherically symmetric deflectors.

astro-ph↗

arXiv2005

Light Curves of Microlensed Type Ia Supernovae

A detailed description of the apparent light curves of microlensed SNe Ia as extended and expanding sources is presented. We show that microlensing amplification can have significant effects on supernova observation. A model light curve is used to compare lensed and unlensed cases and we find that significant changes in shape can occur because of microlensing. We briefly discuss the probability of observing such effects as well. Throughout the paper we consider the redshift of the source to be 1.0 and we limit our work to spherically symmetric deflectors.

astro-ph↗

arXiv2003

The Lame$^{\prime}$ Equation for Distance-Redshift in Partially Filled Beam Friedmann-Lema\^ıtre-Robertson-Walker Cosmology

The differential equation governing distance-redshift for partially filled-beam optics in pressure-freeFriedmann-Lema\^ıtre-Robertson-Walker Cosmology (FLRW) is shown to be the Lame$^{\prime}$ equation. The distance-redshift, $D(z)$, discussed is appropriate for observations in inhomogeneous cosmologies for which lensing by masses external to the observing beam are negligible and for which lensing by transparent matter within the beam can be approximated by a homogeneous mass density expanding with the FLRW background. Some solutions of the derived Lame$^{\prime}$ equation are given in terms of Weierstrass elliptic integrals. A new simplified and useful expression for filled-beam $D(z)$ in standard flat FLRW is also given.

astro-ph↗

arXiv2001

Distance-Redshift in Inhomogeneous $Omega_0=1$ Friedmann-Lemaitre-Robertson-Walker Cosmology

Distance--redshift relations are given in terms of associated Legendre functions for partially filled beam observations inspatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free, flat FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame$^{\prime}$ equation for arbitrary FLRW and is shown to simplify to the associated Legendre equation for the spatially flat, i.e. $Ω_0=1$ case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter $Ω_m$ and the beam filling parameter $ν$. We find that current data are inadequate to limit $ν$. However, we are able to estimate what limits are possible when the number of observed SNe is increased by factor of 10 or 100, sample sizes achievable in the near future with the proposed SuperNova Acceleration Probe satellite.

astro-ph↗

arXiv2000

Vilkovisky-DeWitt Effective Action for Einstein Gravity on Kaluza-Klein Spacetimes $M^4\times S^N$

We evaluate the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on even-dimensional Kaluza-Klein spacetimes of the form $M^{4}\times S^{N}$. Explicit results are given for $N$=2, 4, and 6. Trace anomalies for gravitons are also given for these cases. Stable Kaluza-Klein configurations are sought, unsuccessfully, assuming the divergent part of the effective action dominates the dynamics.

hep-th↗

arXiv2000

The Age-Redshift Relation for Standard Cosmology

We present compact, analytic expressions for the age-redshift relation $τ(z)$ for standard Friedmann-Lema\^ \itre-Robertson-Walker (FLRW) cosmology. The new expressions are given in terms of incomplete Legendre elliptic integrals and evaluate much faster than by direct numerical integration.

astro-ph↗

arXiv2000

Distance-Redshift in Inhomogeneous FLRW

We give distance--redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure free FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. They are the filled-beam model (standard FLRW), the empty-beam model (no mass density exists in the observing beams) and the 2/3 filled-beam model. For special $\OM$-- $\OL$ values the elliptic integrals reduce to more familiar functions. These new expressions for distance-redshift significantly reduce computer evaluation times.

astro-ph↗

arXiv1998

The Effects of Inhomogeneities on Evaluating the mass parameter $Ω_m$ and the cosmological constant $Λ$

Analytic expressions for distance-redshift relations which have been corrected for the effects of inhomogeneities in the Friedmann-Lemaître-Robertson-Walker (FLRW) mass density are given in terms of Heun functions and are used to illustrate the significance of inhomogeneities on a determination of the mass parameter $Ω_m$ and the cosmological constant $Λ$. The values of these parameters inferred from a given set of observations depend on the fractional amount of matter in inhomogeneities and can significantly differ from those obtained by using the standard magnitude-redshift ($m$-$z$) result for pure dust FLRW models. As an example a determination of $Ω_m$ made by applying the homogeneous distance-redshift relation to SN 1997ap at $z=0.83$ could be as much as 50% lower than its true value.

astro-ph↗

arXiv1998

Inhomogeneities and the Intergalactic Distance-Redshift Relation

Modifications in Friedmann-Lemaitre-Robertson-Walker (FLRW) Hubble diagrams caused by mass density inhomogeneities are used to illustrate possible effects on a determination of the mass parameter $Ω_m$ and the cosmological constant $Λ$. The values of these parameters inferred from a given set of observations depend on the fractional amount of matter in inhomogeneities and can differ from those obtained by using standard FLRW Hubble diagrams by as much as a factor of two.

astro-ph↗

arXiv1996

The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime

The renormalization group (RG) is used to study the asymptotically free $ϕ_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop effective potential as well as its explicit forms in the case of strong gravitational fields and strong scalar fields. Using zeta function techniques, the one-loop and corresponding RG improved vacuum energies are found for the Kaluza-Klein backgrounds $R^4\times S^1\times S^1$ and $R^4\times S^2$. They are given in terms of exponentially convergent series, appropriate for numerical calculations. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification can be qualitatively different when the RG improved energy is used.

hep-th↗

arXiv1995

The Effects of Inhomogeneities on Evaluating the Deceleration Parameter q$_0$

Analytic expressions for distance-redshift relations which have been corrected for the effects of some inhomogeneities in the Friedmann-Robertson-Walker (FRW) mass density are used to illustrate the significance of inhomogeneities on a determination of $q_0$ made by using Type Ia supernovae. The value of $q_0$ inferred from a given set of observations depends on the fractional amount of matter in inhomogeneities and is up to 50 percent larger than that obtained by using the standard Mattig $m$-$z$ result for pure dust FRW models.

astro-ph↗

arXiv1995

Zeta-Functions for Non-Minimal Operators

We evaluate zeta-functions $ζ(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate $ζ(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $ζ(0)$ values for dimensions 2 to 10 are given in the Appendix.

hep-th↗

arXiv1995

Gauge Independent Trace Anomaly for Gravitons

We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell. We then use the gauge independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some N-sphere background spacetimes.

hep-th↗