Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2511.21991

Numerical implementation of flat FLRW models of cosmic expansion with Planck 2018 cosmological parameters

Julio Carlos Bertua Marasca·Homer Davila Gutierrez·Oswaldo Alberto Martinez Osorio·Josue Ismael Mosquera Hadatty·Renato Cristian Videla Ricci
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present an explicit numerical implementation of the Friedmann equations to model the expansion of the Universe in spatially flat, homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. Using cosmological parameters from the Planck 2018 results for the concordance LCDM model, we compute the evolution of the scale factor a(t) by integrating the Friedmann acceleration equation together with the continuity equation for a perfect fluid with barotropic equation of state p = w*rho. The model includes radiation, non-relativistic matter, and a dark-energy component with constant equation-of-state parameter w. An explicit Euler scheme implemented in Python is used to evolve a(t) into the past and the future, allowing exploration of the qualitative behavior of the expansion for different values of w, including the LCDM case (w = -1), phantom energy (w < -1), and values associated with domain walls and cosmic strings. The simulations qualitatively reproduce the standard radiation-, matter-, and dark-energy-dominated expansion regimes. The code is simple and modular, and is intended as a computational and pedagogical tool for undergraduate and graduate cosmology courses.

Explore related subjects

astro-ph.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Julio Carlos Bertua Marasca, Homer Davila Gutierrez, Oswaldo Alberto Martinez Osorio, Josue Ismael Mosquera Hadatty, Renato Cristian Videla Ricci. 2025-12-04. Numerical implementation of flat FLRW models of cosmic expansion with Planck 2018 cosmological parameters. https://arxiv.org/abs/2511.21991

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

KEEP EXPLORING

Related papers

arXiv2026

From quantum fluctuations to galaxy power spectrum multipoles

These notes trace large-scale structure from primordial curvature perturbations generated by inflationary quantum fluctuations to galaxy power-spectrum multipoles. Three core lectures develop the linear matter power spectrum, spherical and anisotropic collapse, galaxy bias, redshift-space distortions, the Kaiser model, and multipole estimators with Gaussian covariance. The extension develops nonlinear bias and the one-loop effective field theory model used in full-shape analyses. Derivations are explicit; appendices collect longer calculations and solutions. The core lectures assume undergraduate-level cosmology; the extension assumes familiarity with perturbation theory.

astro-ph.CO↗
arXiv2026

A universal connection between lens density profiles and low-frequency wave optics in gravitational-wave lensing

We investigate the low-frequency behavior of the amplification factor in gravitational lensing and explore how it encodes information about the density profile of the lensing object. We derive the low-frequency expansion of the amplification factor under the Born approximation for a broad class of projected density profiles. For spherically symmetric profiles that decay faster than any power law at large distances, we derive a systematic expansion of the amplification factor in powers of frequency, with the logarithmic dependence appearing only in the leading term, and show that each expansion coefficient is determined by a finite set of moments of the density profile. We then extend the analysis to profiles with power-law tails and demonstrate that such profiles induce additional non-analytic frequency dependences, including fractional powers and logarithmic terms, which directly reflect the asymptotic behavior of the density distribution. Furthermore, we investigate the effects of non-sphericity and show that contributions from the quadrupole moment appear only as higher-order corrections relative to the spherically symmetric component in the low-frequency regime. Finally, we investigate the validity of the Born approximation in the low-frequency expansion. We derive a criterion for the maximum order of the low-frequency expansion up to which the Born approximation remains dominant over the post-Born corrections.

astro-ph.CO↗
arXiv2026

Initial clustering of primordial black holes: A general formulation for arbitrary local non-Gaussianity

Initial spatial clustering of primordial black holes (PBHs) induced by local-type non-Gaussianity (LNG) can substantially modify cosmological constraints on PBH abundance. Several inflationary scenarios that enhance curvature perturbations at small scales relevant to PBH formation predict LNG that is not necessarily perturbative. Therefore, it is crucial to establish a theoretical framework capable of investigating the initial clustering induced by arbitrary LNG. Here, we present a general analytical formulation for the PBH two-point correlation function applicable to arbitrary LNGs in the alternative approach. Under the assumptions that PBHs form only at the large peaks of perturbations, and that large-scale modes weakly modulate the local variance of small-scale perturbations, we derive an analytic expression for the PBH bias parameter, directly connecting initial clustering to the primordial trispectrum in the collapsed limit. We demonstrate the versatility of our formula by computing the bias parameters in the ultra-slow-roll inflation, curvaton, and modulated reheating scenarios. We also formally generalize the framework to broad power spectra to account for correlations across different PBH mass scales. Because our formulation does not rely on weak or perturbative non-Gaussianity assumptions, our result provides a universal theoretical basis for evaluating initial clustering impact on PBH observables.

astro-ph.CO↗