Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1305.6989

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Xi Yang·Hao-Ran Yu·Tong-Jie Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter $α$ to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, $D_L(z)(1+z)^{-2}/D_A(z)=1$, should be valid for all cosmological models that are described by Riemannian geometry, where $D_L$ and $D_A$ are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we use Union2.1 SNe Ia data to constrain the smoothness parameter $α$ and test whether the Dyer-Roeder equation satisfies the DD relation. By using $χ^2$ minimization, we get $α=0.92_{-0.32}^{+0.08}$ at $1σ$ and $0.92_{-0.65}^{+0.08}$ at $2σ$, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at $1σ$.

Explore related subjects

astro-ph.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xi Yang, Hao-Ran Yu, Tong-Jie Zhang. 2013-06-14. Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae. https://doi.org/10.1088/1475-7516%2F2013%2F06%2F007

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constraining spinning primordial black holes with interstellar dust heating

Primordial black holes (PBHs) are a well-motivated dark matter candidate, and their cosmic abundance is constrained by a variety of observational probes. PBHs in the mass range $10^{15}\,\text{g}\,{-}\,10^{17}\,\text{g}$ are evaporating today via Hawking radiation, a process that can heat interstellar dust and modify its thermal emission. Recent studies have used this effect to place constraints on the abundance of non-spinning PBHs. We extend this approach by investigating the influence of PBH spin on dust-heating constraints. Furthermore, we account for secondary photons that originate not only from the decay of gauge bosons but also from the decay of hadrons produced via the fragmentation of primary quarks and gluons emitted through Hawking radiation. By comparing the dust heating rate induced by spinning PBHs with the maximum cooling rate of dust, considering both silicate and graphite grains, we derive new upper limits on the fraction of dark matter in the form of PBHs, $f_{\rm PBH}$. Our results show that the constraints depend on both PBH mass and spin. Smaller PBHs with higher spin yield stronger limits. For example, in the cases we investigated, the strongest constraint is $f_{\rm PBH} \sim 1.5 \times 10^{-4}$ for $M_{\rm PBH} = 10^{15}{\rm g}$ and spin parameter $a_{*} = 0.9999$. Although these limits are less stringent than existing constraints in the same mass range, they provide a distinct and complementary approach to constraining the abundance of PBHs.

astro-ph.CO↗
arXiv2026

Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with $N_\star\in(50,60)$

We present a family of plateau-type inflationary potentials, eq.~\eqref{Vgeneral}, and analyze a two-parameter $\alpha\beta$-Starobinsky specialization that interpolates continuously between a \emph{maximal} plateau ($V\!\to\!V_0$) and a \emph{submaximal} plateau ($V\!\to\!V_\infty 0$ with $x_\star\gg 1/\beta$ the slow-roll scaling laws change to $n_s\simeq 1-\frac{4}{3N_\star},\, r\simeq\mathcal{C}(\alpha,\beta)\,N_\star^{-4/3},$ with an explicit coefficient $\mathcal{C}(\alpha,\beta)$ set by the plateau truncation. This deformation lifts $n_s$ at fixed $N_\star$ while further suppressing $r$, reconciling the Planck~2018 constraint $n_s=0.9649\pm0.0042$ (68\% CL) and BICEP/Keck18 data $r_{0.05}<0.036$ (95\% CL), with the higher central values $n_s\sim0.97$--$0.98$ preferred by ACT+DESI~DR2 (BAO), within the theoretically motivated interval $N_\star\in(50,60)$ and without exotic reheating. We provide an exact identity for $V/V'$ enabling analytic control of $N_\star$, a practical crossover criterion $\beta\,x_\star\ll1$ vs.\ $\gg1$, and a transparent mapping between $(\alpha,\beta)$ and the observables $(n_s,r,N_\star)$. These yield sharp, testable signatures, particularly the softened $N_\star$-scaling of $r$, that distinguish a maximal from a submaximal plateau with upcoming CMB and LSS data.

astro-ph.CO↗
arXiv2026

A Tale of Two Gauges: Effective Field Theory for Relativistic Behavior of Cosmological Axions

In this work, we present a formalism to model the relativistic behavior of axions. The relativistic behavior of axions is surprisingly difficult to model precisely, as it involves oscillations on timescales much shorter than the Hubble timescale. To overcome this challenge, one typically resorts to some form of effective treatment, focusing only on the time-averaged description of the exact oscillations. Salehian, Namjoo & Kaiser provide a systematic framework for such treatment, based on the effective field theory formalism. While the aforementioned study was formulated for axion perturbations in the Newtonian gauge with no anisotropic stress, we extend the formalism to the synchronous gauge that is more conventionally used for numerical implementation in a realistic cosmological setting. Unlike their work, however, we propose a fluid interpretation in which the axion field can be identified as a perfect fluid at all times, both in the exact and effective regimes. Moreover, we present the effective field theory for the Newtonian gauge with non-zero anisotropic stress, making the original formulation more general and useful for scenarios where the matter content of the universe is multi-component. These results lay the theoretical foundation for a companion paper where we discuss how the axion field should be incorporated alongside other species in common cosmological Boltzmann solvers.

astro-ph.CO↗