T2K Excludes Zero CP Violation In PMNS Matrix At Two Sigma

The best fit value for a CP violating phase based upon the latest T2K measurements is -0.6pi. Maximal CP violation is -0.5pi. Zero CP violation (zero or pi) is excluded at more than two sigma significance. 

This tends to corroborate results from other neutrino physics experiments attempting to measure the CP violating phase of the PMNS matrix. See, e.g., here. Various predictions have been made regarding the value of the CP violating phase.

Conjectures, Thoughts and Questions To Explore

This post is just a rambling stream of consciousness and should provoke thought but not be considered a reliable source of information.

The energy density of dark energy is about four times the energy density of the cosmic microwave background radiation.

In a quantum gravity theory, what would be the average energy density of gravitons in the universe? How would that compare to dark energy?

Numerically, how would Alexander Deur's conception of dark energy as at least partially due to diversion of gravitons excessively towards places where dark matter effects are observed work out?

Does a calculation of the Schwarzschild radius of the universe include dark energy?

The Schwarzschild radius of the universe is slightly smaller than the size of the universe (13.7 billion light years v. 13.8 billion light years). Does that mean that we are inside a black hole? The 0.7% discrepancy is not statistically significant, could they be an exact match. What would that imply?

I considered the notion that dark energy is a soup of energy outside the universe that is gobbled up as it expands. But this doesn't address the pull of gravity from outside the universe that we would feel if that was the case. On the other hand, if the soup of energy outside the universe were spherically symmetric, would we observe it at all?

If gravity is the curvature of space-time, why is a non-vacuum universe almost perfectly flat?

The only baryon number violating and lepton violating interaction in the Standard Model is the sphaleron. But, the energy scale where it should be possible for sphaleron events to take place is ca. 10 TeV. This is a temperature 100,000 times greater than the 100 MeV = 2 trillion degrees kelvin temperature at which quark-gluon plasma would occur (i.e. 2*10^20 K). It corresponds to a conventional cosmology time after the Big Bang time of 10^-14 seconds (considerably after "inflation" but prior to everything else in the standard cosmology). This isn't long enough to reach modern matter-antimatter asymmetry levels in baryons and charged leptons from pure energy and maybe didn't happen at all. Rather than devising ways to reach a pure energy starting point, we have to assume that the starting part was not pure energy.

Also, renormalization of all of the Standard Model constants cannot be ignored at this energy scale, and more importantly, the impact of quantum gravity on the renormalization of the Standard Model constants probably cannot be safely ignored at that energy scale. What direction does including a graviton in the model have on the other Standard Model constant renormalizations? How material is the tweak? Could it lead to gauge unification within the Standard Model?

If the timeline of the Big Bang prior to 10^-12 seconds (where the "quark era" of quark-gluon plasma  starts), is unreliable, then maybe this never happens.

Whose frame of reference is being used in the standard cosmology chronology? Everything is moving at relativistic speeds at this point so the time frame of the moving particles is very different from a hypothetical outside observer.

We know that the ratio of particles in the universe is 15 up quarks per 9 down quarks per 1 electron per 10^9 photons. But what about other particles?

We know that there are about 10^80 baryons in the universe, and we know that about 49% of the mass of a proton or neutron comes from gluons (49% comes from the kinetic energy of the quarks and 2% comes from the Higgs field derived mass of the quarks). There are also quite precise gluon density measurements, but I don't know how to convert that to how many gluons at present at any given time in an average proton or neutron. But, with that you could get the number of gluons on the universe at any given time.

We think that there are a much higher number of neutrinos in the universe, but don't know the neutrino-antineutrino ratio, and have only weak support for the lamdaCDM assumption that the number of electron neutrinos is approximately equal to the number of muon neutrinos is approximately equal to the number of tau neutrinos as a result of neutrino oscillation.

We know that in addition to these components that there are a relatively negligible number of top quarks, bottom quarks, charm quarks, strange quarks, W+ bosons, W- bosons, and Z bosons at any given time. This is because all of these particles have very short mean lifetimes and only emerge "on shell" in high energy environments which are relatively rare. But, nonetheless, this isn't zero. My intuition is that the frequency of each depends upon the amount of ordinary matter that it is at the requisite temperature at any given time adjusted by the creation rate and decay rate of these particles.

We have extremely precise figures on all of these factors except the temperature mix of the matter in the universe and actually can do pretty well even with the temperature mix because we have a pretty good census of stars (which are pretty much the only places in the universe hot enough) and we know quite a bit about the temperature of stars.

Given that QGP is almost entirely absent in Nature because the universe hasn't been at 100 MeV temperatures for about 13.8 billion years, it seems likely that while there may be some places hot enough for muon and strange quark formation (and we do see muons in nature), that almost no place is hot enough for top quarks, bottom quarks, charm quarks and tau leptons to be created and that W and Z bosons and Higgs bosons that are on shell should likewise be very rare.

In quantum gravity, we also don't know how many gravitons there are in the universe, on average. This could be appreciable and at least on the same order of magnitude as the CMB.

In quantum gravity, gravitational energy is localized and is a source of gravitons.

I think that mass-energy is conserved in quantum gravity and the cheat that denies this is general relativity is a serious chink in the armor of general relativity as a theory.

I think that it is plausible that the Big Bang never had a density greater than the black hole-neutron star threshold density (about 10^20 g/m^3), and that there are no primordial black holes, hence that there is a maximum density in the universe which may be, or may be a consequence of, an ultraviolet fixed point. What is the mass of the universe? 10^55 grams. What is its volume of the mass of the universe at this density? 10^35 m^3. What is the radius of this volume if it is spherical? About 3*10^12 meters. This is 3*10^9 km and is 0.000317107023 light years (about 167 light minutes) and is 20.0537614 Astronomical Units. This is about 5% larger than the size of a sphere centered in the Sun and extending to the orbit of the planet Uranus. This would be quite different from standard theory however and might screw up Big Bang nucleosynthesis, although it is hard to be clear how. If you cut it to 4% of the mass (removing dark matter and dark energy), this cuts the radius by roughly one-third to about 6.5 AU and about 56 light minutes (about 15% farther than the orbit of Jupiter).

I remain deeply skeptical of cosmological inflation as a theory.

The temperature of the universe is proportionate to 1/t^3 where t is time. The estimated age of the universe is 13.8 +/0.21 billion years. The estimated temperature at ca. 10^-12 to 10^-6 seconds is 100 MeV.

Suppose that there is no dark energy or dark matter, then the Schwartzchild radius is 548 million light years because only about 4% of the mass-energy of the universe in lambda CDM is ordinary matter. So, this would be a black hole from the inception. Are we inside a black hole?

Do black holes have an internal shell structure of density with black hole's interior mass always containing sufficient mass to form a black hole at every radius?

Big Bang nucleosynthesis, which is more precisely confirmed than ever, is a tight constraint on alternatives to the Standard Model of Cosmology and other BSM theories.

The precision with which we know the up and down quarks recently significantly improved and strongly rules out the otherwise attractive zero mass up quark.

We know that the Schwarzschild radius establishes a minimum density to form a black hole. Is it possible that there is another upper boundary threshold of some sort (density, mass, who knows) at which a black hole explodes or leaks? How could that be tested?

How different would the universe be if it had two generations of fermions instead of three? I don't think it would be very different. What kind of mathematical structure or mechanism would require three and exactly three generations of fermions?

Final Planck Results

These final results from the Planck mission are likely to be the definitive Cosmic Microwave Background (CMB) measurements for the foreseeable future. 

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. 

We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2=0.120±0.001, baryon density Ωbh2=0.0224±0.0001, scalar spectral index ns=0.965±0.004, and optical depth τ=0.054±0.007 (in this abstract we quote 68%confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ∗=1.0411±0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. 

Assuming the base-ΛCDM cosmology, the inferred late-Universe parameters are: Hubble constant H0=(67.4±0.5)km/s/Mpc; matter density parameter Ωm=0.315±0.007; and matter fluctuation amplitude σ8=0.811±0.006. We find no compelling evidence for extensions to the base-ΛCDM model. 

Combining with BAO we constrain the effective extra relativistic degrees of freedom to be Neff=2.99±0.17, and the neutrino mass is tightly constrained to ∑mν<0.12eV. 

The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the base-ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. 

The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001±0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r_0.002 < 0.07. 

Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data. 

From here.

Neutrino Physics Implications

These constraints strongly disfavor the existence of a light sterile neutrino (under 10 eV in mass, a heavier sterile neutrino would be degenerate in the CMB data with dark matter) that oscillates with active neutrinos (the expected value of Neff is 3.046 if there are three active neutrino flavors), a light sterile neutrino is disfavored at the six sigma level. Weak force decay measurements already strongly disfavor more than (or less than) three active neutrino flavors.

The data also favor a "normal" neutrino mass hierarchy. The 0.12 eV cap for the sum of the three neutrino masses is more than the minimum mass in an inverted hierarchy scenario, but that is the 95% probability upper limit, so a significantly lower value, which would be inconsistent with an inverted hierarchy, is favored by the data.

The body text notes that:

The normal hierarchy, in which the lowest two mass eigenstates have the smallest mass splitting, can give any P mν >∼ 0.06 eV; an inverted hierarchy, in which the two most massive eigenstates have the smallest mass separation, requires P mν >∼ 0.1 eV. A constraint that P mν < 0.1 eV would therefore rule out the inverted hierarchy. . . . This is consistent with constraints from neutrino laboratory experiments which also slightly prefer the normal hierarchy at 2–3σ[.]

Cosmological Inflation and the Topology of the Universe

The scalar spectral index value of n_s=0.965±0.004 (which corresponds to the vertical yellow lines in the figure below) and the tensor-scalar ratio of less than 0.064 tightly constraints the parameter space of cosmological inflation theories. Basically, the parameter space allowed by the latest observations corresponds to the dark blue hump in the bottom center of the figure below. 

Earlier Planck results combined with other data indicated that the best fit tensor-scalar ratio is zero (i.e. no primordial gravitational waves (i.e. at the very bottom center boundary of the figure below) and a one sigma value from the best fit value is probably 0.032 or less.

The constraint that the universe is flat is also very strong. The body text states that "our Universe is spatially flat to a 1σ accuracy of 0.2 %."

A separate final Planck result paper on cosmological inflation says this in its abstract:

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be ns=0.9649±0.0042 at 68% CL and show no evidence for a scale dependence of ns. Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002<0.10, is further tightened by combining with the BICEP2/Keck Array BK14 data to obtain r0.002<0.064. 

In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, V"(ϕ)<0,  are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

From the body text:

– The inflationary predictions (Mukhanov & Chibisov 1981; Starobinsky 1983) originally computed for the R 2 model (Starobinsky 1980) to lowest order, 

ns − 1 is approximately equal to − 2/N,  r  is approximately equal to 12 N^2,   (48) 

are in good agreement with Planck 2018 data, confirming the previous 2013 and 2015 results. The 95% CL allowed range 49 < N∗ < 58 is compatible with the R^2 basic predictions N∗ = 54, corresponding to Treh ∼ 10^9 GeV (Bezrukov & Gorbunov 2012). A higher reheating temperature Treh ∼ 10^13 GeV, as predicted in Higgs inflation (Bezrukov & Shaposhnikov 2008), is also compatible with the Planck data. 

– Monomial potentials (Linde 1983) V(φ) = λM4 Pl (φ/MPl) p with p ≥ 2 are strongly disfavoured with respect to the R^2 model. For these values the Bayesian evidence is worse than in 2015 because of the smaller level of tensor modes allowed by BK14. Models with p = 1 or p = 2/3 (Silverstein & Westphal 2008; McAllister et al. 2010, 2014) are more compatible with the data. 

– There are several mechanisms which could lower the predictions for the tensor-to-scalar ratio for a given potential V(φ) in single-field inflationary models. Important examples are a subluminal inflaton speed of sound due to a nonstandard kinetic term (Garriga & Mukhanov 1999), a nonminimal coupling to gravity (Spokoiny 1984; Lucchin et al. 1986; Salopek et al. 1989; Fakir & Unruh 1990), or an additional damping term for the inflaton due to dissipation in other degrees of freedom, as in warm inflation (Berera 1995; Bastero-Gil et al. 2016). In the following we report on the constraints for a non-minimal coupling to gravity of the type F(φ)R with F(φ) = M2 Pl + ξφ2 . To be more specific, a quartic potential, which would be excluded at high statistical significance for a minimally-coupled scalar inflaton as seen from Table 5, can be reconciled with Planck and BK14 data for ξ > 0: we obtain a 95 % CL lower limit log10 ξ > −1.6 with ln B = −1.6. 

– Natural inflation (Freese et al. 1990; Adams et al. 1993) is disfavoured by the Planck 2018 plus BK14 data with a Bayes factor ln B = −4.2. 

– Within the class of hilltop inflationary models (Boubekeur & Lyth 2005) we find that a quartic potential provides a better fit than a quadratic one. In the quartic case we find the 95 % CL lower limit log10(µ2/MPl) > 1.1. 

– D-brane inflationary models (Kachru et al. 2003; Dvali et al. 2001; Garc´ıa-Bellido et al. 2002) provide a good fit to Planck and BK14 data for a large portion of their parameter space. 

– For the simple one parameter class of inflationary potentials with exponential tails (Goncharov & Linde 1984; Stewart 1995; Dvali & Tye 1999; Burgess et al. 2002; Cicoli et al. 2009) we find ln B = −1.0. 

– Planck 2018 data strongly disfavour the hybrid model driven by logarithmic quantum corrections in spontaneously broken supersymmetric (SUSY) theories (Dvali et al. 1994), with ln B = −5.0. 

– Planck and BK14 data set tight constraints on α attractors (Kallosh et al. 2013; Ferrara et al. 2013). We obtain log10 α E 1 < 1.5 and log10 α E 2 < 1.2 at 95 % CL for the Emodel. We obtain slightly tighter 95 % CL bounds for the T-model, i.e., log10 α T 1 < 1.1 and log10 α T 2 < 1.0. Given the relation |RK| = 2/(3α) between the curvature of the Kahler ¨ geometry RK and α in some of the T-models motivated by supergravity, Planck and BK14 data imply a lower bound on |RK|, which is still in the low-curvature regime. The discrete set of values α = i/3 with an integer i in the range [1, 7] motivated by maximal supersymmetry (Ferrara & Kallosh 2016; Kallosh et al. 2017) is compatible with the current data.