Effective Number Of Relativistic Degrees Research Articles

PRyMordial: the first three minutes, within and beyond the standard model

In this work we present PRyMordial: A package dedicated to efficient computations of observables in the Early Universe with the focus on the cosmological era of Big Bang Nucleosynthesis (BBN). The code offers fast and precise evaluation of BBN light-element abundances together with the effective number of relativistic degrees of freedom, including non-instantaneous decoupling effects. PRyMordial is suitable for state-of-the-art analyses in the Standard Model as well as for general investigations into New Physics active during BBN. After reviewing the physics implemented in PRyMordial, we provide a short guide on how to use the code for applications in the Standard Model and beyond. The package is written in Python, but more advanced users can optionally take advantage of the open-source community for Julia. PRyMordial is publicly available on GitHub.

Extended analysis of neutrino-dark matter interactions with small-scale CMB experiments

We explore an extension of the standard ΛCDM model by including an interaction between neutrinos and dark matter, and making use of the ground based telescope data of the Cosmic Microwave Background (CMB) from the Atacama Cosmology Telescope (ACT). An indication for a non-zero coupling between dark matter and neutrinos (both assuming a temperature independent and T2 dependent cross-section) is obtained at the 1σ level coming from the ACT CMB data alone and when combined with the Planck CMB and Baryon Acoustic Oscillations (BAO) measurements. This result is confirmed by both fixing the effective number of relativistic degrees of freedom in the early Universe to the Standard Model value of Neff=3.044, and allowing Neff to be a free cosmological parameter. Furthermore, when performing a Bayesian model comparison, the interacting νDM (+Neff) scenario is mostly preferred over a baseline ΛCDM (+Neff) cosmology. The preferred value is then used as a benchmark and the potential implications of dark matter’s interaction with a sterile neutrino are discussed.

Imprints of MeV scale hidden dark sector at Planck data

New light species can contribute to the number of effective relativistic degrees of freedom (Neff) at Cosmic Microwave Background (CMB) which is precisely measured by Planck. In this work, we consider an MeV scale thermally decoupled non-minimal dark sector and study the imprint of the dark sector dynamics on the measurement of Neff at the time of CMB formation. We have predicted the allowed region of model parameter space in the light of constraints arising from the measurements of both Neff and dark matter relic density by Planck. It turns out that the impact of the dark sector dynamics on Neff is significant in case of a non-hierarchical mass spectrum of the dark sector particles.

Effects of an intermediate mass sterile neutrino population on the early Universe

The hot and dense early Universe combined with the promise of high-precision cosmological observations provide an intriguing laboratory for Beyond Standard Model (BSM) physics. We simulate the early Universe to examine the effects of the decay of thermally populated sterile neutrino states into Standard Model products around the time of weak decoupling. These decays deposit a significant amount of entropy into the plasma as well as produce a population of high-energy out-of-equilibrium active neutrinos. As a result, we can constrain these models by their inferred value of $N_{\rm eff}$, the effective number of relativistic degrees of freedom. In this work, we explore a variety of models with $N_{\rm eff}{}$ values consistent with CMB observations, but with vastly different active neutrino spectra which will challenge the standard cosmological model, affect lepton capture rates on free nucleons, and may significantly affect Big Bang Nucleosynthesis (BBN).

Unraveling the Dirac neutrino with cosmological and terrestrial detectors

We point out a correlation between the effective number of relativistic degrees of species Neff, the cosmologically measured mν,sterileeff, and the terrestrially measured neutrino mass sum and effective electron neutrino mass, Σmν and mνe, which arises in the Dirac neutrino hypothesis. If the neutrinos are Dirac particles, and if the active neutrinos' sterile partners were once thermalized in the early universe, then this new cosmological relic would simultaneously contribute to the effective number of relativistic species, Neff, and also lead to a correlation between the cosmologically-measured effective sterile neutrino mass mν,sterileeff and the terrestrially-measured active neutrino mass sum Σmν. We emphasize that specifically correlated deviations in Neff≳3, mν,sterileeff and Σmν above their standard predictions could be the harbinger revealing the Dirac nature of neutrinos. We provide several benchmark examples, including Dirac leptogenesis, that predict a thermal relic population of the sterile partners, and we discuss the relevant observational prospects with current and near-future experiments. If the correlation highlighted in this work is observed in future surveys, it could be interpreted as supporting evidence of Dirac neutrino masses.

Constraints on ΛCDM extensions from the SPT-3G 2018 EE and TE power spectra

We present constraints on extensions to the ΛCDM cosmological model from measurements of the E-mode polarization autopower spectrum and the temperature-E-mode cross-power spectrum of the cosmic microwave background (CMB) made using 2018 SPT-3G data. The extensions considered vary the primordial helium abundance, the effective number of relativistic degrees of freedom, the sum of neutrino masses, the relativistic energy density and mass of a sterile neutrino, and the mean spatial curvature. We do not find clear evidence for any of these extensions, from either the SPT-3G 2018 dataset alone or in combination with baryon acoustic oscillation and Planck data. None of these model extensions significantly relax the tension between Hubble-constant, H0, constraints from the CMB and from distance-ladder measurements using Cepheids and supernovae. The addition of the SPT-3G 2018 data to Planck reduces the square-root of the determinants of the parameter covariance matrices by factors of 1.3–2.0 across these models, signaling a substantial reduction in the allowed parameter volume. We also explore CMB-based constraints on H0 from combined SPT, Planck, and ACT DR4 datasets. While individual experiments see some indications of different H0 values between the TT, TE, and EE spectra, the combined H0 constraints are consistent between the three spectra. For the full combined datasets, we report H0=67.49±0.53 km s−1 Mpc−1, which is the tightest constraint on H0 from CMB power spectra to date and in 4.1σ tension with the most precise distance-ladder-based measurement of H0. The SPT-3G survey is planned to continue through at least 2023, with existing maps of combined 2019 and 2020 data already having ∼3.5×lower noise than the maps used in this analysis.Received 29 March 2021Accepted 18 August 2021DOI:https://doi.org/10.1103/PhysRevD.104.083509© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic microwave backgroundCosmological parametersCosmologyGravitation, Cosmology & Astrophysics

CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods

We introduce CosmoBit, a module within the open-source GAMBIT software framework for exploring connections between cosmology and particle physics with joint global fits. CosmoBit provides a flexible framework for studying various scenarios beyond ΛCDM, such as models of inflation, modifications of the effective number of relativistic degrees of freedom, exotic energy injection from annihilating or decaying dark matter, and variations of the properties of elementary particles such as neutrino masses and the lifetime of the neutron. Many observables and likelihoods in CosmoBit are computed via interfaces to AlterBBN, CLASS, DarkAges, MontePython, MultiModeCode, and plc. This makes it possible to apply a wide range of constraints from large-scale structure, Type Ia supernovae, Big Bang Nucleosynthesis and the cosmic microwave background. Parameter scans can be performed using the many different statistical sampling algorithms available within the GAMBIT framework, and results can be combined with calculations from other GAMBIT modules focused on particle physics and dark matter. We include extensive validation plots and a first application to scenarios with non-standard relativistic degrees of freedom and neutrino temperature, showing that the corresponding constraint on the sum of neutrino masses is much weaker than in the standard scenario.

Can dark neutrino interactions phase out the Hubble tension?

New interactions of neutrinos can stop them from free streaming even after the weak interaction freeze-out. This results in a phase shift in the cosmic microwave background (CMB) acoustic peaks which can alleviate the Hubble tension. In addition, the perturbations in neutrinos do not decay away on horizon entry and contribute to metric perturbation enhancing the matter power spectrum. We demonstrate that this acoustic phase shift can be achieved using new interactions of standard left-handed neutrinos with dark matter without changing the number of effective relativistic degrees of freedom. Using Planck CMB and the WiggleZ galaxy survey $(k\ensuremath{\le}0.12h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1})$ data, we demonstrate that in this model the Hubble tension reduces to approximately $2.1\ensuremath{\sigma}$. Our model predicts potentially observable modifications of the CMB $B$ modes and the matter power spectrum that can be observed in future datasets.

Thermalization of large energy release in the early Universe

ABSTRACT Spectral distortions of the cosmic microwave background (CMB) provide a unique tool for learning about the early phases of cosmic history, reaching deep into the primordial Universe. At redshifts z ≲ 106, thermalization processes become inefficient and existing limits from COBE/FIRAS imply that no more than Δρ/ρ ≲ 6 × 10−5 ($95{{\ \rm per\ cent}}$ c.l.) of energy could have been injected into the CMB. However, at higher redshifts, when thermalization is efficient, the constraint weakens and Δρ/ρ ≃ 0.01−0.1 could in principle have occurred. Existing computations for the evolution of distortions commonly assume Δρ/ρ ≪ 1 and thus become inaccurate in this case. Similarly, relativistic temperature corrections become relevant for large energy release, but have previously not been modelled as carefully. Here, we study the evolution of distortions and the thermalization process after single large energy release at z ≳ 105. We show that for large distortions the thermalization efficiency is significantly reduced and that the distortion visibility is sizeable to much earlier times. This tightens spectral distortions constraints on low-mass primordial black holes with masses $M_{\rm PBH}\lesssim 2 \times 10^{11}\, {\rm g}$. Similarly, distortion limits on the amplitude of the small-scale curvature power spectrum at wavenumbers $k\gtrsim 10^4\, {\rm Mpc}^{-1}$ and short-lived decaying particles with lifetimes $t_X\lesssim 10^7\, {\rm s}$ are tightened, however, these still require a more detailed time-dependent treatment. We also briefly discuss the constraints from measurements of the effective number of relativistic degrees of freedom and light element abundances and how these complement spectral distortion limits.

Combining full-shape and BAO analyses of galaxy power spectra: a 1.6% CMB-independent constraint on H0

We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra, which are analyzed in combination with the unreconstructed spectra in a full-shape (FS) likelihood using a joint covariance matrix, giving stronger parameter constraints than FS-only or BAO-only analyses. We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error, which is shown to be simple, robust, and applicable to any flavor of density-field reconstruction. Assuming ΛCDM with massive neutrinos, we analyze clustering data from two redshift bins zeff=0.38,0.61 and obtain 1.6% constraints on the Hubble constant H0, using only a single prior on the current baryon density ωb from Big Bang Nucleosynthesis (BBN) and no knowledge of the power spectrum slope ns. This gives H0 = 68.6±1.1 km s−1Mpc−1, with the inclusion of BAO data sharpening the measurement by 40%, representing one of the strongest current constraints on H0 independent of cosmic microwave background data, comparable with recent constraints using BAO data in combination with other data-sets. Restricting to the best-fit slope ns from Planck (but without additional priors on the spectral shape), we obtain a 1% H0 measurement of 67.8± 0.7 km s−1Mpc−1. Finally, we find strong constraints on the cosmological parameters from a joint analysis of the FS, BAO, and Planck data. This sets new bounds on the sum of neutrino masses ∑ mν < 0.14 eV (at 95% confidence) and the effective number of relativistic degrees of freedom Neff = 2.90+0.15−0.16, though contours are not appreciably narrowed by the inclusion of BAO data.

Constraining axion inflation with gravitational waves from preheating

We study gravitational wave production from gauge preheating in a variety of inflationary models, detailing its dependence on both the energy scale and the shape of the potential. We show that preheating into Abelian gauge fields generically leads to a large gravitational wave background that contributes significantly to the effective number of relativistic degrees of freedom in the early universe, $N_\mathrm{eff}$. We demonstrate that the efficiency of gravitational wave production is correlated with the tensor-to-scalar ratio, $r$. In particular, we show that efficient gauge preheating in models whose tensor-to-scalar ratio would be detected by next-generation cosmic microwave background experiments ($r \gtrsim 10^{-3}$) will be either detected through its contribution to $N_\mathrm{eff}$ or ruled out. Furthermore, we show that bounds on $N_\mathrm{eff}$ provide the most sensitive probe of the possible axial coupling of the inflaton to gauge fields regardless of the potential.

Constraining Axion Inflation with Gravitational Waves across 29 Decades in Frequency.

We demonstrate that gravitational waves generated by efficient gauge preheating after axion inflation generically contribute significantly to the effective number of relativistic degrees of freedom N_{eff}. We show that, with existing Planck limits, gravitational waves from preheating already place the strongest constraints on the inflaton's possible axial coupling to Abelian gauge fields. We demonstrate that gauge preheating can completely reheat the Universe regardless of the inflationary potential. Further, we quantify the variation of the efficiency of gravitational wave production from model to model and show that it is correlated with the tensor-to-scalar ratio. In particular, when combined with constraints on models whose tensor-to-scalar ratios would be detected by next-generation cosmic microwave background experiments, r≳10^{-3}, constraints from N_{eff} will probe or rule out the entire coupling regime for which gauge preheating is efficient.

All-inclusive interacting dark sector cosmologies

In this paper we explore possible extensions of Interacting Dark Energy cosmologies, where Dark Energy and Dark Matter interact non-gravitationally with one another. In particular, we focus on the neutrino sector, analyzing the effect of both neutrino masses and the effective number of neutrino species. We consider the Planck 2018 legacy release data combined with several other cosmological probes, finding no evidence for new physics in the dark radiation sector. The current neutrino constraints from cosmology should be therefore regarded as robust, as they are not strongly dependent on the dark sector physics, once all the available observations are combined. Namely, we find a total neutrino mass $M_\nu<0.15$ eV and a number of effective relativistic degrees of freedom of $N_{\rm eff}=3.03^{+0.33}_{-0.33}$, both at 95\% CL, which are close to those obtained within the $\Lambda$CDM cosmology, $M_\nu<0.12$ eV and $N_{\rm eff}=3.00^{+0.36}_{-0.35}$ for the same data combination.

Observing Dirac neutrinos in the cosmic microwave background

Planned CMB Stage IV experiments have the potential to measure the effective number of relativistic degrees of freedom in the early Universe, $N_\text{eff}$, with percent-level accuracy. This probes new thermalized light particles and also constrains possible new-physics interactions of Dirac neutrinos. Many Dirac-neutrino models that aim to address the Dirac stability, the smallness of neutrino masses or the matter--anti-matter asymmetry of our Universe endow the right-handed chirality partners $\nu_R$ with additional interactions that can thermalize them. Unless the reheating temperature of our Universe was low, this leads to testable deviations in $N_\text{eff}$. We discuss well-motivated models for $\nu_R$ interactions such as gauged $U(1)_{B-L}$ and the neutrinophilic two-Higgs-doublet model, and compare the sensitivity of SPT-3G, Simons Observatory, and CMB-S4 to other experiments, in particular the LHC.

Constraints on scalar and tensor spectra from Neff

At the linear level, the gravitational wave (GW) spectrum predicted by inflation, and many of its alternatives, can have arbitrarily small amplitude and consequently an unconstrained tilt. However, at second order, tensor fluctuations are sourced by scalar fluctuations that have been measured in the cosmic microwave background (CMB). These second order fluctuations generically produce a minimum amount of tensor perturbations corresponding to a tensor-to-scalar ratio of r∼ 10−6. Inverting this relationship yields a bound on the tensor tilt sourced by scalar fluctuations. Since this induced GW spectrum depends on the scalar spectrum, we derive a new indirect bound that involves all scales of the scalar spectrum based on CMB observations. This bound comes from the constraint on the number of effective relativistic degrees of freedom, Neff. We estimate the bound using current data, and the improvements expected by future CMB experiment. The bound forces the running and running of running to conform to standard slow-roll predictions of α,β ≲ (ns−1)2 where α≡ d ns/d ln k and β ≡ d ns2/d ln k2, improving on current CMB measurements by an order of magnitude. This bound has further implications for the possibility of primordial black holes as dark matter candidates. Performing a likelihood analysis including this new constraint, we find that positive α and/or β are disfavored at least at 1σ. Even using conservative analysis, β + 0.074 α>8.6× 10−4 are ruled out at 3σ. Finally, using bounds on the fractional energy density of gravitational waves today obtained by LIGO and the Pulsar Timing Array, we obtain a bound on the primordial scalar spectrum on these scales and give forecast for future measurements.

Warm Little Inflaton Becomes Cold Dark Matter.

We present a model where the inflaton can naturally account for all the dark matter in the Universe within the warm inflation paradigm. In particular, we show that the symmetries and particle content of the warm little inflaton scenario (i)avoid large thermal and radiative corrections to the scalar potential, (ii)allow for sufficiently strong dissipative effects to sustain a radiation bath during inflation that becomes dominant at the end of the slow-roll regime, and (iii)enable a stable inflaton remnant in the postinflationary epochs. The latter behaves as dark radiation during nucleosynthesis, leading to a non-negligible contribution to the effective number of relativistic degrees of freedom, and becomes the dominant cold dark matter component in the Universe shortly before matter-radiation equality for inflaton masses in the 10^{-4}-10^{-1} eV range. Cold dark matter isocurvature perturbations, anticorrelated with the main adiabatic component, provide a smoking gun for this scenario that can be tested in the near future.

Primordial gravitational waves and the H0 -tension problem

We analyse the H0-tension problem in the context of models of the early universe that predict a blue tilted spectrum of primordial gravitational waves (GW's). By considering the GW's contribution, Neff^GW, to the effective number of relativistic degrees of freedom, Neff, and assuming standard particle physics, we discuss the effects of Neff^GW on the background expansion, especially the constraints on the Hubble parameter H0. We analyse three scenarios which take into account the contribution of Neff^GW and perform a statistical study using recent data of cosmic microwave background, baryon acoustic oscillation, the latest measurement of the local expansion rate, along with the LIGO constraints on the tensor to scalar ratio and the tensor index. For the models explored, we show that an additional contribution from the primordial GW's background to Neff does not solve but alleviate the current H0-tension problem.

Disentangling dark physics with cosmic microwave background experiments

We forecast constraints on dark matter (DM) scattering with baryons in the early Universe with upcoming and future cosmic microwave background (CMB) experiments, for DM particle masses down to 15 keV. In terms of the upper limit on the interaction cross section for a velocity-independent spin-independent elastic scattering, compared to current Planck results, we find a factor of $\sim$6 improvement with CMB-Stage 3, a factor of $\sim$26 with CMB-Stage 4, and a factor of $\sim$200 with a cosmic-variance limited experiment. Once the instrumental noise reaches the proximity of 1 $\mu$K-arcmin, the constraints are entirely driven by the lensing measurements. The constraints benefit from a wide survey, and show gradual improvement for instrumental noise levels from 10 $\mu$K-arcmin to 1 $\mu$K-arcmin and resolution from 5 arcmin to 1 arcmin. We further study degeneracies between DM interactions and various other signatures of new physics targeted by the CMB experiments. In the primary temperature and polarization only, we find moderate degeneracy between the effects of DM scattering, signals from massive neutrinos, and from the effective number of relativistic degrees of freedom. The degeneracy is almost entirely broken once the lensing convergence spectrum is included into the analyses. We discuss the implications of our findings in context of planned and upcoming CMB measurements and other cosmological probes of dark-sector and neutrino physics.

ΔNeff and entropy production from early-decaying gravitinos

Gravitinos are a fundamental prediction of supergravity, their mass ($m_{G}$) is informative of the value of the SUSY breaking scale, and, if produced during reheating, their number density is a function of the reheating temperature ($T_{\text{rh}}$). As a result, constraining their parameter space provides in turn significant constraints on particles physics and cosmology. We have previously shown that for gravitinos decaying into photons or charged particles during the ($\mu$ and $y$) distortion eras, upcoming CMB spectral distortions bounds are highly effective in constraining the $T_{\text{rh}}-m_{G}$ space. For heavier gravitinos (with lifetimes shorter than a few $\times10^6$ sec), distortions are quickly thermalized and energy injections cause a temperature rise for the CMB bath. If the decay occurs after neutrino decoupling, its overall effect is a suppression of the effective number of relativistic degrees of freedom ($N_{\text{eff}}$). In this paper, we utilize the observational bounds on $N_{\text{eff}}$ to constrain gravitino decays, and hence provide new constaints on gravitinos and reheating. For gravitino masses less than $\approx 10^5$ GeV, current observations give an upper limit on the reheating scale in the range of $\approx 5 \times 10^{10}- 5 \times 10^{11}$GeV. For masses greater than $\approx 4 \times 10^3$ GeV they are more stringent than previous bounds from BBN constraints, coming from photodissociation of deuterium, by almost 2 orders of magnitude.

The H0 and σ8 tensions and the scale invariant spectrum

In a previous communication [1] it was shown that a joint analysis of Cosmic Microwave Background (CMB) data and the current measurement of the local expansion rate favours a model with a scale invariant spectrum (HZP) over the minimal ΛCDM scenario provided that the effective number of relativistic degrees of freedom, Neff, is taken as a free parameter. Such a result is basically obtained due to the Hubble Space Telescope (HST) value of the Hubble constant, H0 = 73.24 ± 1.74 km . s−1.Mpc−1 (68% C.L.), as the CMB data alone discard the HZP+Neff model. Although such a model is not physically motivated by current scenarios of the early universe, observations pointing to a scale invariant spectrum may indicate that the origin of cosmic perturbations lies in an unknown physical process. Here, we extend the previous results performing a Bayesian analysis using joint CMB, HST, and Baryon Acoustic Oscillations (BAO) measurements. In order to take into account the well-known tension on the value of the fluctuation amplitude parameter, σ8, we also consider Cluster Number counts (CN) and Weak Lensing (WL) data. We use two different samples of BAO data, which are obtained using two-point spatial (BAO 2PCF) and angular (BAO 2PACF) correlation functions. Our results show that the joint CMB+HST+WL+NC dataset favor the extensions of the ΛCDM model over its minimal parameterization. Also, analysis with the BAO 2PCF always discard the HZP+Neff model with respect to standard scenario, whereas the combinations using BAO 2PACF favor the former model. We, therefore, find that all dataset disfavor the ΛCDM model with respect to the HZP+Neff extension, the only exception being the joint analysis with BAO (2PCF).