# The Baryon Phase-Transition Model and the too strange Standard Model of Cosmology

## Abstract

**:**

## 1. Introduction

## 2. Adiabatic Scaling

^{3}($\mathit{h}$ is the Hubble constant in units of 100 km·s

^{−1}per Mpc

^{−1}, and ${n}_{b0}\approx {10}^{-5}$/${h}^{2}$ (typically $h\approx 0.7$). On the other hand, if there were about 20 times more baryons at $z=0$, but unseen in the CMB radiation, the Universe would be critically dense—see the RHS of the right-panel of Figure 1.

## 3. Baryons and the Assumption of Constant η

^{1}H,

^{3}He,

^{4}He, and with somewhat more difficulty,

^{2}H and

^{7}Li, were calculated using well-established nuclear reaction physics at these high temperatures and densities. However, there were some inconsistencies starting with

^{7}Li. A crucial point (emphasized by McGaugh [6]) was that the baryon density inferred from

^{2}H and

^{3}He was originally consistent with the value inferred from

^{7}Li, but following the CMB observations, the baryon density inferred from

^{2}H and

^{3}He began to “creep upward” until it became consistent with the SMC concordance value. Eventually, the SMC model calculations compared reasonably well with the estimated quantities from astrophysical observations. The agreement can be seen in the left panel of Figure 1 where the calculated nuclides (solid-lines) and observations (blurred-bands) are presented color-coded along with the vertical yellow band at $\eta \approx 6.9\times {10}^{-10}$. This agreement, even considering η as a somewhat adjustable parameter—see left panel of Figure 1— has been widely argued as the principle justification of the SMC. It is important, however, to recall that BBN calculations go back to a few seconds after the big-bang which means back to $z\approx {10}^{12}$ where the density and temperatures are extremely high. The backward extrapolation to the BBN era was nine orders of magnitude from the recombination era when the CMB was formed. It is important to understand that this extrapolation (conserving η) has assumed, without saying so, that there were no phase-transitions specifically of baryons relative to photons. That this could be a large error is of basic importance to our Baryon Phase-Transition (BPT) cosmology [1], but more generally important as well.

^{2}H (deuterium) produced because it would have been so rapidly burned up at the higher densities and temperatures in this era (see Weinberg [5] (p. 165)). In such a case, how would there be low-Z nuclide production? We considered this conflict and resolved it in the first of our BPT papers [1] where we showed that these same nuclides could have just as readily been produced during the BPT at $z\approx {10}^{5}$. That is to say, at a much lower density than in standard BBN, but still agreeing well with astrophysical observations. So, the Standard Model BBN calculations, by themselves, do not uniquely satisfy late-time astrophysical nuclide observations to justify the SMC.

## 4. Type Ia Supernovae to the Rescue

## 5. The Mass-Energy Components

## 6. Closing Remarks

## Conflicts of Interest

## References

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**Figure 1.**Two plots of BBN calculations for the low-Z nuclei relative to H as a function of η (left-panel) and as a function of the density normalized to critical-density ${\rho}_{0,crit}$ (right-panel). The horizontal colored blurred bands on the LHS panel (expected to be similar on the RHS) represent average levels of astrophysical observations for the specified nuclei.

**Figure 2.**Schematic of the Hubble flow through the baryon transition time. Red indicates the flow before the transition, purple after the transition. Yellow indicates the expansion of free protons and tresinos; this region can be usefully compared to the Sun and its corona (see [2]).

© 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Mayer, F.
The Baryon Phase-Transition Model and the too strange Standard Model of Cosmology. *Universe* **2017**, *3*, 18.
https://doi.org/10.3390/universe3010018

**AMA Style**

Mayer F.
The Baryon Phase-Transition Model and the too strange Standard Model of Cosmology. *Universe*. 2017; 3(1):18.
https://doi.org/10.3390/universe3010018

**Chicago/Turabian Style**

Mayer, Frederick.
2017. "The Baryon Phase-Transition Model and the too strange Standard Model of Cosmology" *Universe* 3, no. 1: 18.
https://doi.org/10.3390/universe3010018