Abstract The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well‐understood. This fact allows us to take into account a very large variety of physical processes, still finding potentially measurable consequences for the energy spectrum and temperature anisotropies of the Cosmic Microwave Background (CMB). In this contribution we provide a short historical overview in connection with the cosmological recombination epoch and its connection to the CMB. Also we highlight some of the detailed physics that were studied over the past few years in the context of the cosmological recombination of hydrogen and helium . The impact of these considerations is two‐fold: (i) The associated release of photons during this epoch leads to interesting and unique deviations of the CosmicMicrowave Background (CMB) energy spectrum from a perfect blackbody , which, in particular at decimeter wavelength and the Wien part of the CMB spectrum, may become observable in the near future. Despite the fact that the abundance of helium is rather small, it still contributes a sizeable amount of photons to the full recombination spectrum, leading to additional distinct spectral features. Observing the spectral distortions from the epochs of hydrogen and helium recombination, in principle would provide an additional way to determine some of the key parameters of the Universe (e.g. the specific entropy, the CMB monopole temperature and the pre‐stellar abundance of helium). Also it permits us to confront our detailed understanding of the recombination process with direct observational evidence . In this contribution we illustrate how the theoretical spectral template of the cosmological recombination spectrum may be utilized for this purpose. We also show that because hydrogen and helium recombine at very different epochs it is possible to address questions related to the thermal history of our Universe. In particular the cosmological recombination radiation may allow us to distinguish between Compton y ‐distortions that were created by energy release before or after the recombination of the Universe finished. (ii) With the advent of high precision CMB data, e.g. as will be available using the PLANCK Surveyor or CMBPOL, a very accurate theoretical understanding of the ionization history of the Universe becomes necessary for the interpretation of the CMB temperature and polarization anisotropies. Here we show that the uncertainty in the ionization history due to several processes, which until now were not taken in to account in the standard recombination code RECFAST, reaches the percent level. In particular He II → He I recombination occurs significantly faster because of the presence of a tiny fraction of neutral hydrogen at z ∼ 2400. Also recently it was demonstrated that in the case of H I Lyman α photons the timedependence of the emission process and the asymmetry between the emission and absorption profile cannot be ignored. However, it is indeed surprising how inert the cosmological recombination history is even at percent‐level accuracy. Observing the cosmological recombination spectrum should in principle allow us to directly check this conclusion, which until now is purely theoretical. Also it may allow to reconstruct the ionization history using observational data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

We obtain constraints in a 12 parameter cosmological model using the recent Dark Energy Spectroscopic Instrument Data Release (DR) 2 Baryon Acoustic Oscillations (BAO) data, combined with cosmic microwave background (CMB) power spectra (Planck Public Release, PR, 4) and lensing (Planck PR4 + Atacama Cosmology Telescope DR 6) data, uncalibrated Type Ia supernovae (SNe) data from Pantheon+ and Dark Energy Survey (DES) Year 5 (DESY5) samples, and Weak Lensing (WL; DES Year 1) data. The cosmological model consists of six Λ cold dark matter parameters and additionally, the dynamical dark energy parameters (w0, wa), the sum of neutrino masses (∑mν), the effective number of non-photon radiation species (Neff), the scaling of the lensing amplitude (Alens), and the running of the scalar spectral index (αs). Our major findings are the following: (i) With CMB+BAO+DESY5+WL, we obtain the first 2σ+ detection of a non-zero ∑mν=0.19−0.18+0.15 eV (95%). Replacing DESY5 with Pantheon+ still yields a ∼1.9σ detection. (ii) The cosmological constant lies at the edge of the 95% contour with CMB+BAO+Pantheon+ but is excluded at 2σ+ with DESY5, leaving evidence for dynamical dark energy data-set dependent and inconclusive. (iii) With CMB+BAO+SNe+WL, Alens = 1 is excluded at >2σ, while it remains consistent with unity without WL data—suggesting that the existence of lensing anomaly with Planck PR4 likelihoods may depend on non-CMB data sets. (iv) The Hubble tension persists at 3.6σ–4.2σ with CMB+BAO+SNe; WL data have minimal impact.

We use a combination of the most recent cosmic microwave background (CMB) flat-band power measurements to place constraints on Hubble's constant h and the total density of the universe Ω0 in the context of inflation-based cold dark matter (CDM) models with no cosmological constant. We use χ2 minimization to explore the four-dimensional parameter space having as free parameters, h, Ω0, the power-spectrum slope n, and the power-spectrum normalization at ℓ = 10. Conditioning on Ω0 = 1, we obtain h = 0.33 ± 0.08. Allowing Ω0 to be a free parameter reduces the ability of the CMB data to constrain h, and we obtain 0.26 < h < 0.97 with a best-fit value at h = 0.40. We obtain Ω0 = 0.85 and set a lower limit Ω0 > 0.53. A strong correlation between acceptable h and Ω0 values leads to a new constraint Ω0h1/2 = 0.55 ± 0.10. We quote Δχ2 = 1 contours as error bars; however, because of nonlinearities of the models, these may be only crude approximations to 1 σ confidence limits. A favored open model with Ω0 = 0.3 and h = 0.70 is more than ~4 σ from the CMB data best-fit model and is rejected by goodness-of-fit statistics at the 99% confidence level. High baryonic models (Ωbh2 ~ 0.026) yield the best CMB χ2 fits and are more consistent with other cosmological constraints. The best-fit model has n = 0.91+ 0.29−0.09 and Q10 = 18.0+ 1.2−1.5 μK. Conditioning on n = 1, we obtain h = 0.55+ 0.13−0.19, Ω0 = 0.70 with a lower limit Ω0 > 0.58, and Q10 = 18.0+ 1.4−1.5 μK. The amplitude and position of the dominant peak in the best-fit power spectrum are Apeak = 76+ 3−7 μK and ℓpeak = 260+ 30−20. Unlike the Ω0 = 1 case we considered previously, CMB h results are now consistent with the higher values favored by local measurements of h but only if 0.55 ≲ Ω0 ≲ 0.85. Using an approximate joint likelihood to combine our CMB constraint on Ω0h1/2 with other cosmological constraints, we obtain h = 0.58 ± 0.11 and Ω0 = 0.65+ 0.16−0.15.

The Dark Energy Survey (DES) recently released the final results of its two principal probes of the expansion history: Type Ia Supernovae (SNe) and Baryonic Acoustic Oscillations (BAO). We explore the cosmological implications of these data in combination with external Cosmic Microwave Background (CMB), Big Bang Nucleosynthesis (BBN), and age-of-the-Universe information. The BAO measurement, $\sim2\sigma$ away from Planck's $\Lambda$CDM predictions, pushes for low values of $\Omega_{\rm m}$ compared to Planck, in contrast to SN which prefers a higher value. We identify several tensions among datasets in the $\Lambda$CDM model that cannot be resolved by including either curvature or a constant dark energy equation of state. By combining BAO+SN+CMB despite these mild tensions, we obtain $\Omega_k$=$-5.5^{+4.6}_{-4.2}\times10^{-3}$ in $k\Lambda$CDM, and $w=-0.948^{+0.028}_{-0.027}$ in $w$CDM. In $w$CDM, BAO and SN push again in different directions of parameter space, favoring, respectively $w<-1$ and $w>-1$. If we open the parameter space to $w_0w_a$CDM, all the datasets are mutually more compatible, and we find concordance in the $w_0>-1,w_a<0$ quadrant, with BAO pushing for $w_a<0$ and SN for $[w_0>-1,w_a<0]$. For DES BAO and SN in combination with Planck-CMB, we find a $3.2\sigma$ deviation from $\Lambda$CDM, with $w_0=-0.673^{+0.098}_{-0.097}$, $w_a = -1.37^{+0.51}_{-0.50}$, a Hubble constant of $H_0=67.81^{+0.96}_{-0.86}$km s$^{-1}$Mpc$^{-1}$, and an abundance of matter of $\Omega_{\rm m}=0.3109^{+0.0086}_{-0.0099}$. For the combination of all the background cosmological probes considered we still find a deviation of $2.8\sigma$ from $\Lambda$CDM in the $w_0-w_a$ plane. Assuming a minimal neutrino mass, this work provides tentative evidence for non-$\Lambda$CDM physics, which is consistent with recent claims in support of evolving dark energy, or a source of unknown systematics.

Recent observations of DESI hint that dark matter (DM) may not be cold but have a non-zero equation of state (EoS) parameter, and that dark energy (DE) may not be a cosmological constant. In this work, we explore the possibility of a non-zero DM EoS parameter within the framework of dynamical DE. We perform analysis by using the latest baryon acoustic oscillation (BAO) data from DESI DR2, the cosmic microwave background (CMB) data from Planck, and the type Ia supernova (SN) data from DESY5 and PantheonPlus. When using the combination of CMB, BAO, and SN data, our results indicate a preference for a non-zero DM EoS parameter at the $2.8\sigma$ and $3.3\sigma$ level within the content of a constant DE EoS. In contrast, for a time-evolving DE EoS parameterized by $w_0$ and $w_a$, this preference decreases to $0.8\sigma$ and $1.1\sigma$. Furthermore, allowing a non-zero DM EoS yields best-fit values of $w_0$ and $w_a$ that exhibit smaller deviations from the $\Lambda$CDM expectations, and Bayesian evidence analysis shows a comparable preference for this model relative to $\Lambda$CDM. The overall results of this work indicate that a non-zero DM EoS parameter warrants further exploration and investigation.

ABSTRACT Gravitational lensing magnification of Type Ia supernovae (SNe Ia) allows information to be obtained about the distribution of matter on small scales. In this paper, we derive limits on the fraction $\alpha$ of the total matter density in compact objects (which comprise stars, stellar remnants, small stellar groupings, and primordial black holes) of mass M > 0.03 ${\rm M}_{\odot }$ over cosmological distances. Using 1532 SNe Ia from the Dark Energy Survey Year 5 sample (DES-SN5YR) combined with a Bayesian prior for the absolute magnitude M, we obtain α < 0.12 at the 95 per cent confidence level after marginalization over cosmological parameters, lensing due to large-scale structure, and intrinsic non-Gaussianity. Similar results are obtained using priors from the cosmic microwave background, baryon acoustic oscillations, and galaxy weak lensing, indicating our results do not depend on the background cosmology. We argue our constraints are likely to be conservative (in the sense of the values we quote being higher than the truth), but discuss scenarios in which they could be weakened by systematics of the order of $\Delta \alpha \sim 0.04$.

frequently with matter and the universe became transparent. The highly redshifted photons from this period form the cosmic microwave background. Tiny variations The universe comprises all of existence: all forms of matter and energy, and the structures they form, from sub-atomic particles to entire galactic filaments. Since the early 20th century, the field of cosmology has established that the universe has been expanding for 13.8 billion years, starting from a dense fireball in an event called the Big Bang. The observable portion of the universe is appro A… Cosmologists often work with space-like slices of spacetime that are surfaces of constant time in comoving coordinates. The geometry of these spatial slices is set by the density parameter, Omega (Ω), defined as the average matter density of the universe divided by a critical value. This selects one of three possible geometries depending on whether Ω is equal to, less than, or greater than 1. These are called, respectively, the flat, open and closed universes. Observations, including the Cosmic Background Explorer (COBE), Wilkinson Microwave Anisotropy Probe (WMAP), and Planck maps of the CMB, suggest that the universe is infinite in extent with a finite age, as described by the Friedmann–Lemaître–Robertson–Walker (FLRW) models. These FLRW models thus support inflationary models and the standard model of cosmology, describing a flat, homogeneous universe presently dominated by dark matter and dark energy.

Penzias and Wilson were not cosmologists, but as they began to discuss their puzzling discovery with other scientists, they were quickly put in touch with a group of astronomers and physicists at Princeton University (a short drive away). These astronomers had—as it happened—been redoing the calculations of Alpher and Herman from the 1940s and also realized that the radiation from the decoupling time should be detectable as a faint afterglow of radio waves. The different calculations of what the observed temperature would be for this cosmic microwave background (CMB)2 were uncertain, but all predicted less than 40 K. Penzias and Wilson found the distribution of intensity at different radio wavelengths to correspond to a temperature of 3.5 K. This is very cold—closer to absolute zero than most other astronomical measurements—and a testament to how much space (and the waves within it) has stretched. Their measurements have been repeated with better instruments, which give us a reading of 2.73 K. So Penzias and Wilson came very close.