Effective Number Of Relativistic Species Research Articles

Constraining holographic dark energy and analyzing cosmological tensions

We investigate cosmological constraints on the holographic dark energy (HDE) using the state-of-the-art cosmological datasets: Planck CMB angular power spectra and weak lensing power spectra, Atacama Cosmology Telescope (ACT) temperature power spectra, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from six-degree-field galaxy survey and Sloan Digital Sky Survey (DR12 & DR16) and the Cepheids-Supernovae measurement from SH0ES team (R22). We also examine the HDE model and ΛCDM with and without Neff (effective number of relativistic species) being treated as a free parameter. We find that the HDE model can relieve the tensions of H0 and S8 to certain degrees. With “Planck+ACT+BAO+RSD” datasets, the constraints are H0=69.70±1.39km s−1Mpc−1 and S8=0.823±0.011 in HDE model, which brings down the Hubble tension down to 1.92σ confidence level (C.L.) and the S8 tension to (1−2)σ C.L. By adding the R22 data, their values are improved as H0=71.86±0.93km s−1Mpc−1 and S8=0.813±0.010, which further brings the Hubble tension down to 0.85σ C.L. and relieves the S8 tension. We also quantify the goodness-of-fit of different models with Akaike information criterion (AIC) and Bayesian information criterion (BIC), and find that the HDE agrees with the observational data better than the ΛCDM and other extended models (treating Neff as free for fitting).

Limits on non-relativistic matter during Big-bang nucleosynthesis

Big-bang nucleosynthesis (BBN) probes the cosmic mass-energy density at temperatures ∼ 10 MeV to ∼ 100 keV. Here, we consider the effect of a cosmic matter-like species that is non-relativistic and pressureless during BBN. Such a component must decay; doing so during BBN can alter the baryon-to-photon ratio, η, and the effective number of neutrino species. We use light element abundances and the cosmic microwave background (CMB) constraints on η and Nν to place constraints on such a matter component. We find that electromagnetic decays heat the photons relative to neutrinos, and thus dilute the effective number of relativistic species to N eff < 3 for the case of three Standard Model neutrino species. Intriguingly, likelihood results based on Planck CMB data alone find Nν = 2.800 ± 0.294, and when combined with standard BBN and the observations of D and 4He give Nν = 2.898 ± 0.141. While both results are consistent with the Standard Model, we find that a nonzero abundance of electromagnetically decaying matter gives a better fit to these results. Our best-fit results are for a matter species that decays entirely electromagnetically with a lifetime τX = 0.89 sec and pre-decay density that is a fraction ξ = (ρX /ρ rad|10 MeV = 0.0026 of the radiation energy density at 10 MeV; similarly good fits are found over a range where ξτX 1/2 is constant. On the other hand, decaying matter often spoils the BBN+CMB concordance, and we present limits in the (τX ,ξ) plane for both electromagnetic and invisible decays. For dark (invisible) decays, standard BBN (i.e. ξ = 0) supplies the best fit. We end with a brief discussion of the impact of future measurements including CMB-S4.

Towards a reliable calculation of relic radiation from primordial gravitational waves

ABSTRACT Inflationary gravitational waves, behaving as additional radiation in the Early Universe, can increase the effective number of relativistic species (Neff) by a further correction that depends on the integrated energy-density in gravitational waves over all scales. This effect is typically used to constrain (blue-tilted) models of inflation in light of the bounds resulting from the big bang nucleosynthesis. In this paper, we recompute this contribution, discussing some caveats of the state-of-the-art analyses. Through a parametric investigation, we first demonstrate that the calculation is dominated by the ultraviolet frequencies of the integral and therefore by the behaviour of the tensor spectrum on scales corresponding to modes that cross the horizon very close to the end of inflation, when the slow-roll dynamics breaks down and the production of gravitational waves becomes strongly model dependent. Motivated by these results, we realize a theoretical Monte Carlo and, working within the framework of the Effective Field Theory of inflation, we investigate the observable predictions of a very broad class of models. For each model, we solve a system of coupled differential equations whose solution completely specifies the evolution of the spectrum up to the end of inflation. We prove the calculation of $\Delta N_{\rm eff}^{\rm GW}$ to be remarkably model dependent and therefore conclude that accurate analyses are needed to infer reliable information on the inflationary Universe.

Brownian axionlike particles

We study the non-equilibrium dynamics of a pseudoscalar axion-like particle (ALP) weakly coupled to degrees of freedom in thermal equilibrium by obtaining its reduced density matrix. Its time evolution is determined by the in-in effective action which we obtain to leading order in the (ALP) coupling but to \emph{all orders} in the couplings of the bath to other fields within or beyond the standard model. The effective equation of motion for the (ALP) is a Langevin equation with noise and friction kernels obeying the fluctuation dissipation relation. A ``misaligned'' initial condition yields damped coherent oscillations, however, the (ALP) population increases towards thermalization with the bath. As a result, the energy density features a mixture of a cold component from misalignment and a hot component from thermalization with proportions that vary in time $(cold)\,e^{-\Gamma t}+(hot)\,(1-e^{-\Gamma t})$, providing a scenario wherein the ``warmth'' of the dark matter evolves in time from colder to hotter. As a specific example we consider the (ALP)-photon coupling $g a \vec{E}\cdot \vec{B}$ to lowest order, valid from recombination onwards. For $T \gg m_a$ the long-wavelength relaxation rate is substantially enhanced $\Gamma_T = \frac{g^2\,m^2_a\,T}{16\pi} $. The ultraviolet divergences of the (ALP) self-energy require higher order derivative terms in the effective action. We find that at high temperature, the finite temperature effective mass of the (ALP) is $m^2_a(T) = m^2_a(0)\Big[ 1-(T/T_c)^4\Big]$, with $T_c \propto \sqrt{m_a(0)/g}$, \emph{suggesting} the possibility of an inverted phase transition, which when combined with higher derivatives may possibly indicate exotic new phases. We discuss possible cosmological consequences on structure formation, the effective number of relativistic species and birefringence of the cosmic microwave background.

The Challenge of Ruling Out Inflation via the Primordial Graviton Background

Recent debates around the testability of the inflationary paradigm raise the question of how to model-independently discriminate it from competing scenarios. We argue that a detection of the cosmic graviton background (CGB), the relic radiation from gravitons decoupling around Planck time, would rule out the inflationary paradigm, as realistic inflationary models would dilute the CGB to an unobservable level. The CGB contribution to the effective number of relativistic species, ΔN eff,g ≈ 0.054, is well within the reach of next-generation cosmological probes. We argue that detecting the high-frequency stochastic gravitational wave background associated to the CGB will be challenging but potentially feasible. We briefly discuss expectations within alternatives to inflation, focusing on bouncing cosmologies and emergent scenarios.

Anisotropic scalar field dark energy with a disformally coupled Yang–Mills field

In the context of scalar–tensor theories, the inclusion of new degrees of freedom coupled nonminimally to the gravitational sector might produce some appealing effects on the cosmic expansion history. We investigate this premise by including a canonical SU(2) Yang–Mills field to the total energy budget of the universe coupled to the standard quintessential field by a disformal transformation.From the dynamical system analysis, we study three cases of cosmological interest that span most of the physical phase space of the model: the uncoupled limit, the isotropic and the Abelian cases. New scaling solutions with a nonvanishing gauge field are found in all cases which can be interesting for early cosmological scenarios. Some of these scaling solutions even exhibit anisotropic features. Also, the background evolution of the universe is studied by means of numerical analysis. As an interesting result, the disformal coupling changes the equation of state of the gauge field from radiation to matter at some stages of the evolution of the universe, thereby the gauge field can contribute to some fraction of the total dark matter. We have also quantified the redshift-dependent contribution of the gauge field in the form of dark radiation during the radiation era to the effective number of relativistic species. This depends essentially on the initial conditions and, more importantly, on the disformal coupling function.

Baryonic feedback biases on fundamental physics from lensed CMB power spectra

Upcoming measurements of the small-scale primary cosmic microwave background (CMB) temperature and polarization power spectra ($TT$/$TE$/$EE$) are anticipated to yield transformative constraints on new physics, including the effective number of relativistic species in the early universe ($N_{\rm eff}$). However, at multipoles $\ell \gtrsim 3000$, the primary CMB power spectra receive significant contributions from gravitational lensing. While these modes still carry primordial information, their theoretical modeling requires knowledge of the CMB lensing convergence power spectrum, $C_L^{\kappa\kappa}$, including on small scales where it is affected by nonlinear gravitational evolution and baryonic feedback processes. Thus, the high-$\ell$ primary CMB is sensitive to these late-time, nonlinear effects. Here, we show that inaccuracies in the modeling of $C_L^{\kappa\kappa}$ can yield surprisingly large biases on cosmological parameters inferred from the primary CMB power spectra measured by the upcoming Simons Observatory and CMB-S4 experiments. For CMB-S4, the biases can be as large as $1.6\sigma$ on the Hubble constant $H_0$ in a fit to $\Lambda$CDM and $1.2\sigma$ on $N_{\rm eff}$ in a fit to $\Lambda$CDM+$N_{\rm eff}$. We show that these biases can be mitigated by explicitly discarding all $TT$ data at $\ell>3000$ or by marginalizing over parameters describing baryonic feedback processes, both at the cost of slightly larger error bars. We also discuss an alternative, data-driven mitigation strategy based on delensing the CMB $T$ and $E$-mode maps. Finally, we show that analyses of upcoming data will require Einstein-Boltzmann codes to be run with much higher numerical precision settings than is currently standard, so as to avoid similar -- or larger -- parameter biases due to inaccurate theoretical predictions.

Exploration of interacting dynamical dark energy model with interaction term including the equation-of-state parameter: alleviation of the H0 tension

We explore a scenario of interacting dynamical dark energy model with the interaction term Q including the varying equation-of-state parameter w. Using the data combination of the cosmic microwave background, the baryon acoustic oscillation, and the type Ia supernovae, to global fit the interacting dynamical dark energy model, we find that adding a factor of the varying w in the function of Q can change correlations between the coupling constant β and other parameters, and then has a huge impact on the fitting result of β. In this model, the fitting value of H 0 is lower at the 3.54σ level than the direct measurement value of H 0. Comparing to the case of interacting dynamical dark energy model with Q excluding w, the model with Q including the constant w is more favored by the current mainstream observation. To obtain higher fitting values of H 0 and narrow the discrepancy of H 0 between different observations, additional parameters including the effective number of relativistic species, the total neutrino mass, and massive sterile neutrinos are considered in the interacting dynamical dark energy cosmology. We find that the H 0 tension can be further reduced in these models, but is still at the about 3σ level.

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.

When feebly interacting massive particles decay into neutrinos: The Neff story

The existence of feebly interacting massive particles (FIMPs) could have significant implications on the effective number of relativistic species $N_\mathrm{eff}$ in the early Universe. In this work, we investigate in detail how short-lived FIMPs that can decay into neutrinos affect $N_\mathrm{eff}$ and highlight the relevant effects that govern its evolution. We show that even if unstable FIMPs inject most of their energy into neutrinos, they may still decrease $N_{\mathrm{eff}}$, and identify neutrino spectral distortions as the driving power behind this effect. As a case study, we consider Heavy Neutral Leptons (HNLs) and indicate which regions of their parameter space increase or decrease $N_{\mathrm{eff}}$. Moreover, we derive bounds on the HNL lifetime from the Cosmic Microwave Background and comment on the possible role that HNLs could play in alleviating the Hubble tension.

Bounds on neutrino-scalar nonstandard interactions from big bang nucleosynthesis

Coherent forward scattering processes by neutrino-scalar nonstandard interactions (SNSI) induce an effective neutrino mass. In the early Universe, a large neutrino effective mass restricts the production of neutrinos. The SNSI effect is modulated by two effective couplings; these account for the coupling between neutrinos and electrons or positrons, ${G}_{\mathrm{eff}}$, and the neutrino self-interaction ${G}_{\mathrm{S}}$. These parameters are directly related to the effective number of relativistic species, and nonzero values imply a smaller than expected ${N}_{\mathrm{eff}}$. We employ big bang nucleosynthesis to constraint the SNSI effect. We find that ${G}_{\mathrm{eff}}&lt;1.2\text{ }\text{ }{\mathrm{MeV}}^{\ensuremath{-}2}$ and ${G}_{\mathrm{S}}&lt;2.0\ifmmode\times\else\texttimes\fi{}{10}^{7}\text{ }\text{ }{\mathrm{MeV}}^{\ensuremath{-}2}$ at 68% C.L. For a scalar mass in the range ${10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{eV}\ensuremath{\lesssim}{m}_{\ensuremath{\phi}}\ensuremath{\lesssim}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$, our neutrino-scalar coupling constraint is more restrictive than any previous result.

Implications of gravitational-wave production from dark photon resonance to pulsar-timing observations and effective number of relativistic species

The coherent oscillation of axionic fields naturally drives copious production of dark photon particles in the early universe, due to resonance and tachyonic enhancement. During the process, energy is abruptly transferred from the former to the latter, sourcing gravitational wave generation. The resulting gravitational waves are eventually to be observed as stochastic background today. We report analytical results of this production and connect them to the recent pulsar-timing results by the NANOGrav collaboration. We show an available parameter space, around the mass $m_\phi \sim 10^{-13} \, {\rm eV}$ and the decay constant $f_\phi \sim 10^{16} \, {\rm GeV}$ with a dimensionless coupling of ${\cal O}(1)$, for our mechanism to account for the signal. A mechanism to avoid the axion over-dominating the universe is a necessary ingredient of this model, and we discuss a possibility to recover a symmetry and render the axion massless after the production. We also comment on potential implications of the required effective number of relativistic species to the determination of the present Hubble constant.

Robustness of baryon acoustic oscillation constraints for early-Universe modifications ofΛCDMcosmology

Baryon acoustic oscillations (BAO) provide a robust standard ruler, and can be used to constrain the expansion history of the Universe at low redshift. Standard BAO analyses return a model-independent measurement of the expansion rate and the comoving angular diameter distance as function of redshift, normalized by the sound horizon at radiation drag. However, this methodology relies on anisotropic distance distortions of a fixed, pre-computed template (obtained in a given fiducial cosmology) in order to fit the observations. Therefore, it may be possible that extensions to the consensus $\Lambda$CDM add contributions to the BAO feature that cannot be captured by the template fitting. We perform mock BAO fits to power spectra computed assuming cosmological models which modify the growth of perturbations prior to recombination in order to test the robustness of the standard BAO analysis. We find no significant bias in the BAO analysis for the models under study ($\Lambda$CDM with a free effective number of relativistic species, early dark energy, and a model with interactions between neutrinos and a fraction of the dark matter), even for cases which do not provide a good fit to \textit{Planck} measurements of the cosmic microwave background power spectra. This result supports the use of the standard BAO analysis and its measurements to perform cosmological parameter inference and to constrain exotic models. In addition, we provide a methodology to reproduce our study for different models and surveys, as well as discuss different options to handle eventual biases in the BAO measurements.

Can f(T) gravity resolve the H0 tension?

Motivated by the discrepancy in measurements of $H_0$ between local and global probes, we investigate whether teleparallel gravities could be a better model to describe the present days observations or at least to alleviate the $H_0$ tension. Specifically, in this work we study and place constraints on three popular $f(T)$ models in light of the Planck-2018 CMB data release. We find that the $f(T)$ power-law model can alleviate the $H_0$ tension from $4.4\sigma$ to $1.9\sigma$ level, while the $f(T)$ model of two exponential fail to resolve this inconsistency. Moreover, for the first time, we obtain constraints on the effective number of relativistic species $N_{eff}$ and on the sum of the neutrino masses $\Sigma m_\nu$ in $f(T)$ gravity. We find that the constraints obtained are looser than in $\Lambda$CDM. However, the introduction of massive neutrinos into the cosmological model alleviate the $H_0$ tension for the power-law model. Finally, we find that whether a viable $f(T)$ theory can mitigate the $H_0$ tension depends on the mathematical structure of the distortion factor $y(z,\,b)$. These results could provide a clue for theoreticians to write a more physical-motivated expression of $f(T)$ function.

Larger value for H0 by an evolving gravitational constant

We provide further evidence that a massless cosmological scalar field with a non-minimal coupling to the Ricci curvature of the type $M^2_{\rm pl}(1+\xi \sigma^n/M_{\rm pl}^n) $ alleviates the existing tension between local measurements of the Hubble constant and its inference from CMB anisotropies and baryonic acoustic oscillations data in presence of a cosmological constant. In these models, the expansion history is modified compared to $\Lambda$CDM at early time, mimicking a change in the effective number of relativistic species, and gravity weakens after matter-radiation equality. Compared to $\Lambda$CDM, a quadratic ($n=2$) coupling increases the Hubble constant when {\em Planck} 2018 (alone or in combination with BAO and SH0ES) measurements data are used in the analysis. Negative values of the coupling, for which the scalar field decreases, seem favored and consistency with Solar System can be naturally achieved for a large portion of the parameter space without the need of any screening mechanism. We show that our results are robust to the choice of $n$, also presenting the analysis for $n=4$.

New physics in light of the H0 tension: An alternative view

The strong discrepancy between local and inverse distance ladder estimates of the Hubble constant $H_0$ could be pointing towards new physics beyond $\Lambda$CDM. Several attempts to address this tension through new physics rely on extended models, featuring extra free parameters beyond the 6 $\Lambda$CDM parameters. However, marginalizing over extra parameters has the effect of broadening the uncertainties on the inferred parameters, and it is often the case that within these models the $H_0$ tension is addressed due to larger uncertainties rather than a genuine shift in the central value of $H_0$. What happens if a physical theory is able to fix the extra parameters to a specific set of non-standard values? The degrees of freedom of the model are reduced with respect to the standard case where the extra parameters are free to vary. Focusing on the dark energy equation of state $w$ and the effective number of relativistic species $N_{\rm eff}$, I find that physical theories able to fix $w \approx -1.3$ or $N_{\rm eff} \approx 3.95$ would lead to an estimate of $H_0$ from CMB, BAO, and SNeIa data in perfect agreement with the local distance ladder estimate, without broadening its uncertainty. These two non-standard models are, from a model-selection perspective, strongly disfavoured with respect to $\Lambda$CDM. However, models that predict $N_{\rm eff} \approx 3.45$ would be able to bring the tension down to $1.5\sigma$ while only being weakly disfavored with respect to $\Lambda$CDM, whereas models that predict $w \approx -1.1$ would be able to bring the tension down to $2\sigma$ (at the cost of the preference for $\Lambda$CDM being definite). Finally, I estimate dimensionless multipliers relating variations in $H_0$ to variations in $w$ and $N_{\rm eff}$, which can be used to repeat the analysis of this paper in light of future more precise local distance ladder estimates of $H_0$.

Relic neutrino clustering in the Milky Way

The Standard Cosmological Model predicts the existence of relic neutrinos, which are indirectly probed through the effective number of relativistic species in the early Universe. In addition, from neutrino flavour oscillations we know that at least two of the neutrino mass states have a non-zero mass. Since the expansion of the Universe has diluted the energy of relic neutrinos, those that are massive are also non relativistic today. This means that they can be trapped in strong gravitational potentials, such as the one of the Milky Way. We review the calculation of the local overdensity of relic neutrinos produced from the gravitational attraction of our Galaxy, Andromeda and the Virgo cluster, commenting on the implications for an experiment aiming at relic neutrino detection, such as the PTOLEMY project.

Neutrino-dark matter connections in gauge theories

We discuss the connection between the origin of neutrino masses and the properties of dark matter candidates in the context of gauge extensions of the Standard Model. We investigate minimal gauge theories for neutrino masses where the neutrinos are predicted to be Dirac or Majorana fermions. We find that the upper bound on the effective number of relativistic species provides a strong constraint in the scenarios with Dirac neutrinos. In the context of theories where the lepton number is a local gauge symmetry spontaneously broken at the low scale, the existence of dark matter is predicted from the condition of anomaly cancellation. Applying the cosmological bound on the dark matter relic density, we find an upper bound on the symmetry breaking scale in the multi-TeV region. These results imply we could hope to test simple gauge theories for neutrino masses at current or future experiments.

Is the H0 tension suggesting a fourth neutrino generation?

Flavour oscillations experiments are suggesting the existence of a sterile, $4$th neutrino's generation with a mass of an eV order. This would mean an additional relativistic degree of freedom in the cosmic inventory, in contradiction with recent results from the Planck satellite, that have confirmed the standard value $N_{eff} \approx 3$ for the effective number of relativistic species. On the other hand, the Planck best-fit for the Hubble-Lema\^itre parameter is in tension with the local value determined with the Hubble Space Telescope, and adjusting $N_{eff}$ is a possible way to overcome such a tension. In this paper we perform a joint analysis of three complementary cosmological distance rulers, namely the CMB acoustic scale measured by Planck, the BAO scale model-independently determined by Verde {\it et al.}, and luminosity distances measured with JLA and Pantheon SNe Ia surveys. Two Gaussian priors were imposed to the analysis, the local expansion rate measured by Riess {\it et al.}, and the baryon density parameter fixed from primordial nucleosynthesis by Cooke {\it et al.}. For the sake of generality, two different models are used in the tests, the standard $\Lambda$CDM model and a generalised Chaplygin gas. The best-fit gives $N_{eff} \approx 4$ in both models, with a Chaplygin gas parameter slightly negative, $\alpha \approx -0.04$. The standard value $N_{eff} \approx 3$ is ruled out with $\approx 3\sigma$.

Comparison of results on Neff from various Planck likelihoods

In this paper, we study the estimation of the effective number of relativistic species from a combination of cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) data. We vary different ingredients of the analysis: the Planck high-ℓ likelihoods, the Boltzmann solvers, and the statistical approaches. The variation of the inferred values gives an indication of an additional systematic uncertainty, which is of the same order of magnitude as the error derived from each individual likelihood. We show that this systematic uncertainty is essentially associated to the assumptions made in the high-ℓ likelihood implementations, in particular for the foreground residuals modellings. We also compare a subset of likelihoods using only the TE power spectra, expected to be less sensitive to foreground residuals.