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Register a new userGeneralized Boltzmann hierarchy for massive neutrinos in cosmology
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Caio Bastos de Senna Nascimento
Publication date
2021
fields
Physics
and research's language is
English
Authors
Caio Bastos de Senna Nascimento
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Boltzmann solvers are an important tool for the computation of cosmological observables in the linear regime. They involve solving the Boltzmann equation, followed by an integration in momentum space, to arrive at the desired fluid properties. This is a cumbersome, computationally expensive procedure. In this work we introduce the so-called generalized Boltzmann hierarchy (GBH) for massive neutrinos in cosmology, a simpler alternative to the usual Boltzmann hierarchy, where the momentum dependence is integrated out leaving us with a two-parameter infinite set of ordinary differential equations. Along with the usual expansion in multipoles, there is now also an expansion in higher velocity weight integrals of the distribution function. We show that the GBH produces the density contrast neutrino transfer function to a per mille level accuracy at both large and intermediate scales compared to the neutrino free-streaming scale. Furthermore, by introducing a switch to a viscous fluid approximation after horizon crossing, we show that the GBH can achieve over all scales the same accuracy as the standard CLASS approach in its default precision settings. The GBH is then a powerful tool to include neutrino anisotropies in the computation of cosmological observables in linear theory, with integration being simpler and potentially faster than standard methods.
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The impact of dark matter-neutrino interactions on the measurement of the cosmological parameters has been investigated in the past in the context of massless neutrinos exclusively. Here we revisit the role of a neutrino-dark matter coupling in light of ongoing cosmological tensions by implementing the full Boltzmann hierarchy for three massive neutrinos. Our tightest 95% CL upper limit on the strength of the interactions, parameterized via $u_chi =frac{sigma_0}{sigma_{Th}}left(frac{m_chi}{100 text{GeV}}right)^{-1}$, is $u_chileq3.34 cdot 10^{-4}$, arising from a combination of Planck TTTEEE data, Planck lensing data and SDSS BAO data. This upper bound is, as expected, slightly higher than previous results for interacting massless neutrinos, due to the correction factor associated with neutrino masses. We find that these interactions significantly relax the lower bounds on the value of $sigma_8$ that is inferred in the context of $Lambda$CDM from the Planck data, leading to agreement within 1-2$sigma$ with weak lensing estimates of $sigma_8$, as those from KiDS-1000. However, the presence of these interactions barely affects the value of the Hubble constant $H_0$.
In the standard approaches to neutrino transport in the simulation of core-collapse supernovae, one will often start from the classical Boltzmann equation for the neutrinos spatial, temporal, and spectral evolution. For each neutrino species, and its anti-particle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the right-hand-side of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasi-classical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including resonant flavor conversion (the MSW effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.
Calculations of the evolution of cosmological perturbations generally involve solution of a large number of coupled differential equations to describe the evolution of the multipole moments of the distribution of photon intensities and polarization. However, this Boltzmann hierarchy communicates with the rest of the system of equations for the other perturbation variables only through the photon-intensity quadrupole moment. Here I develop an alternative formulation wherein this photon-intensity quadrupole is obtained via solution of two coupled integral equations -- one for the intensity quadrupole and another for the linear-polarization quadrupole -- rather than the full Boltzmann hierarchy. This alternative method of calculation provides some physical insight and a cross-check for the traditional approach. I describe a simple and efficient iterative numerical solution that converges fairly quickly. I surmise that this may allow current state-of-the-art cosmological-perturbation codes to be accelerated.
The combination of current large scale structure and cosmic microwave background (CMB) anisotropies data can place strong constraints on the sum of the neutrino masses. Here we show that future cosmic shear experiments, in combination with CMB constraints, can provide the statistical accuracy required to answer questions about differences in the mass of individual neutrino species. Allowing for the possibility that masses are non-degenerate we combine Fisher matrix forecasts for a weak lensing survey like Euclid with those for the forthcoming Planck experiment. Under the assumption that neutrino mass splitting is described by a normal hierarchy we find that the combination Planck and Euclid will possibly reach enough sensitivity to put a constraint on the mass of a single species. Using a Bayesian evidence calculation we find that such future experiments could provide strong evidence for either a normal or an inverted neutrino hierachy. Finally we show that if a particular neutrino hierachy is assumed then this could bias cosmological parameter constraints, for example the dark energy equation of state parameter, by > 1sigma, and the sum of masses by 2.3sigma.
In light of the improved sensitivities of cosmological observations, we examine the status of quasi-degenerate neutrino mass scenarios. Within the simplest extension of the standard cosmological model with massive neutrinos, we find that quasi-degenerate neutrinos are severely constrained by present cosmological data and neutrino oscillation experiments. % % We find that Planck 2018 observations of cosmic microwave background (CMB) anisotropies disfavour quasi-degenerate neutrino masses at $2.4$ Gaussian $sigma$s, while adding Baryon acoustic oscillations (BAO) data brings the rejection to 5.9$sigma$s. % The highest statistical significance with which one would be able to rule out quasi-degeneracy would arise if the sum of neutrino masses is $Sigma m_ u = 60$ meV (the minimum allowed by neutrino oscillation experiments); % indeed a sensitivity of 15 meV, as expected from a combination of future cosmological probes, would further improve the rejection level up to 17$sigma$. % We discuss the robustness of these projections with respect to assumptions on the underlying cosmological model, and also compare them with bounds from $beta$ decay endpoint and neutrinoless double beta decay studies.
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