Energy Density Driven Cosmology – a ΛCDM Alternative · to drive complete formation of...

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COSMOLOGICAL ENERGY DENSITY AND GRAVITATIONAL FORCE LAW

RC-SP dynamics agree with the general consensus that in the very early universe, conditionswere highly relativistic in part due to extreme energy density that existed immediately followingthe big bang. It is only during this time that energy levels were high and distances short enoughto drive complete formation of relatively ‘mature’ disks. Perhaps the most controversial aspectof this proposal is the assumption of relativistically driven non-Keplerian gravitational forcesgoverning matter and structure creation in this very early environment. Per RC-SP, highlyrelativistic conditions immediately following the big band were governed by a pseudo 1/r forcelaw. As the energy density rapidly declined and relativistic effects waned, the universetransformed to one governed by Keplerian gravitational dynamics and 1/r2 force law that is ineffect now.

Why is 1/r-based force law associated with proto-galactic formation and rapid evolution?Based on RC-SP cosmology, this effective force law is the result of dimensional reduction(Lorentz contraction, relativistic velocities and/or geometric influence) and its physical impacton flux behavior and conservative scalar forces. This view requires no extra dimensions, ‘new-physics,’ nor dark entities, just an appreciation of the remarkable physics that can occur at thisunique epoch of history. If a dimensionally reduced (2+1) and 1/r-governed early universecreated galaxies immediately following the big bang, what would their expected properties be?The answer lies in the morphological and kinematic characteristics disk galaxies exhibit in thecurrent universe; highly planar exponential surface mass density profiles, constant / flatrotation curves and non-Keplerian dynamics. In fact, 1/r force law has been a central tenet ofMOdified Newtonian Dynamics (MOND) for over forty-years as a functional means toreproduce asymptotically flat galactic rotation curves. Unfortunately, MOND has beenhampered as fundamental for lack of a satisfactory physical explanation for this particular forcelaw. On the other hand, ΛCDM relies exclusively on Newtonian mechanics and massive darkmatter halos. This non-relativistic approach does not describe conditions during this very earlyepoch of galaxy formation when energy densities were ten million of times greater than today.

GALACTIC FORMATION AND EVOLUTION – INTERPRETING NEW EVIDENCE

PHYSICS

Energy Density Driven Cosmology – a ΛCDM AlternativeJEFFREY M. LA FORTUNE

This work advances a conceptual cosmological model as presented in the original publication, “Energy Density DrivenGalactic Formation and Evolution” (La Fortune 2015). Termed the Rotation Curve-Spin Parameter (RC-SP) model, itdescribes a singular, universal relativistically driven process providing for very early and rapid galactic disk formation inagreement with latest high red-shift astrophysical observations. In stark contrast to ΛCDM’s hierarchical accretion scenario,RC-SP completes nearly all galactic formation and significant evolution within the first 500Myr and greatly simplifies theunderstanding of galactic morphologies, kinematics and currently misunderstood gravitational “anomalies.”

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What if any evidence supports this early, intense and rapid galaxy formation? As we can peerinto the more distant past, there has been a trend in finding extremely old “fully developedspiral galaxies” inhabiting the universe at a very early stage (Steinhardt 2015). Steinhardt’s titleof his paper is, “The Impossibly Early Galaxy Problem,” implying galaxies like these should notexist in a ΛCDM governed universe – but they do and in great numbers. What are the favoredproperties and evolutionary fate for this these very early galaxies? An H-ATLAS/GAMAcalorimetry survey has already answered this question (Eales 2015). Their findings showhighly red shift galaxies are “disk-dominated” and undergo significant morphologicaltransformation in the early universe. This study was given support by another survey of 10billion year old galaxies in which over ninety-percent had rotational signatures (Price 2015).This implies angular momentum was present and played a significant role right from the start.

In addition to proto-galactic formation, star formation has also been regulated via the RC-SPprocess described above. Figure 1 shows observed the galactic Star Formation Rate (SFR)over the life of the universe. (Snaith 2014). This figure is meant to be illustrative indicatingthere is correspondence between SFR and the decline in cosmic energy density over time.

Figure 1: Radiation Energy Density vs. Observed Star Formation Rate (Snaith 2014).Georgia State University Hyper Physics App for radiation energy density calculation.

Nearly all primordial galaxy formation occurs in the extremely condensed time frame on theright-side of the plot. At around 250 million years, stars are physically able to form in theemerging Keplerian dynamic (1/r → 1/r2) and fully realized in three “isotropic” dimensional"space" in the form of truly spheroidal entities. This transition to Keplerian dynamics andelevated SFR rates following the ‘knee’ in the energy density curve is evidence of thisassociation. Stars continued to form at high rates for a couple billion years afterwards untilsecular and environmental processes began to dominate galactic evolution. Perhaps just asimportant, Price found little evidence of significant evolution over the past several billion yearsas suggested by the SFR tracking of cosmological energy density’s slow decline to presentday.

THE DARK MATTER HALO AND GALACTIC ROTATIONAL VELOCITY SUPPORT

This section gives a very brief overview of ΛCDM dynamics and dark matter influence ongalactic kinematics. This provides a direct comparison between RC-SP dynamics and dark

ENERGY DENSITY DRIVEN COSMOLOGY – A ΛCDM ALTERNATIVE : PHYSICS


matter halo rotational velocity and angular momentum support. Figure 2 below depicts anidealized ΛCDM velocity curve scaled to the dimensions of the (Milky Way) MW.

Figure 2: Idealized Dark Matter Halo Contribution to the MW’s Rotation Curve.

This figure shows the MW with a flat disk rotation velocity of 230 km/s represented by thehorizontal blue dashed line. Halo velocity support is denoted by the thick black curve and thebaryonic velocity contribution by the peaked thin curve near the left side of the plot. Thevertical double light-blue arrows highlight the extent of rotational support. We see that halovelocity support becomes progressively prominent at larger radii and is almost entirelyresponsible for flat rotation beyond 40 kpc (the stellar disk’s edge). The red dotted curve is theKeplerian velocity expectation for a 5x1011Mʘ point mass, the importance of which will becovered in the next sections.

RC-SP DYNAMICS – REINTERPRETING THE PHYSICAL EVIDENCE

This section presents a dark matter free alternative based on the latest, most advancedobservations of the MW and M31. First, we challenge the notion of highly extended flat galacticrotation velocities against new findings indicating a Keplerian decline outside the baryonic disk.Figure 3 below represents the latest estimate of rotation velocities inside 25 kpc for the MW,versus the calculated baryonic (gray band/thin black curve) contribution as reproduced in theprevious figure (Pato 2015).



Figure 3: Milky Way “Actual” Rotation Curve vs. Estimated Baryonic Contribution (Pato 2015).

These latest measurements clearly indicate a flat rotation curve (red points with error bars).We definitely observe flat rotation inside 25 kpc, but can this be arbitrarily extended to the edgeof the dark matter halo? New data is increasingly suggesting flat rotation does not extend tothe halo’s edge, but terminates at the edge of the baryonic disk.

Figure 4 shows a combined extended view of MW satellite data out to 200 kpc (Küpper 2015).The Keplerian rotation curve (red dashed curve) represents an equivalent point mass of5x1011Mʘ (Moffat 2015), the same as shown in Figure 2.

Figure 4: Measured Circular Velocities of Extended Milky Way Satellites (Küpper2015).

The horizontal blue dashed line in Figure 4 is the same shown in the previous figure, but drawn“to scale” highlighting the limited extent of Pato’s data set. Blue data points represent MWsatellite galaxy orbital radius against circular velocity. Note that these satellites define aKeplerian curve, not the ΛCDM flattened asymptotic rotation curves depicted by the black solidlines extending to the far right. A fact that can be drawn from this data is that at least for theMW, flat rotation does not extend past the disk.

Figure 5 reconfigures the data presented in Figures 3 and 4 to create an idealized full rotationcurve for the MW per RC-SP. Similar to previous figures, the vertical blue arrows representrotational velocity support.



Figure 5: Idealized RC-SP Velocity Contribution to the Milky Way’s RotationCurve.

Compared to the ΛCDM/dark matter halo depiction in Figure 2, we see an entirely newphenomenon - rotational velocity suppression (represented by vertical red arrows). We find flatdisk rotation is the net action of imparted/retained angular momentum inherent in the baryonicdisk. Maximal Keplerian suppression occurs near the galactic core, declining toward the disk’sedge tracking with the decline in baryonic surface mass density. Beyond the baryonic disk,rotational velocity follows the Keplerian point mass equivalent and MW satellite galaxykinematics.

Note that velocity suppression is not possible for dark matter as its contribution is alwaysadditive to the overall rotation curve. Even MOND proponents have acknowledged this velocitydecline and have modified their models to account for this fact (Hees 2015).

RC-SP DYNAMICS - MW AND M31 PHYSICAL EVIDENCE

This bold restating of the galactic dynamics in Figure 5 requires one to ask, where is thephysical evidence for suppressed rotation velocities? Evidence is revealed in a recent paperinvestigating the influence of dark matter halos within the Local Group (Sofue 2015). In thiswork, Sofue updated rotational velocity data for MW and M31 and termed them the new“Grand Rotation Curves” (GRCs). The updated MW GRC is reproduced in Figure 6 below.



Figure 6: The New GRC of the Milky Way and Kinematic Disruption (Sofue 2015), inset(King 2015).

In the above figure, we fit the same 5x1011Mʘ point mass equivalent Keplerian declineobtained from the satellite data to the GRC and find it matches the GRC data. We see that theRC-SP dynamic mass estimate (red dash) is corroborated by two independent measures. Asthe MW is a real system and not idealized as depicted in previous figure, the light gray datapoints indicate partial suppression / velocity lift in the outer disk toward the Keplerian curve. Inaddition to gross velocity deviation, the inset shows a significant disruption in velocitydispersion, as described by the Anisotropy Coefficient “β” (King 2015). These exceptionallynegative velocity anisotropy coefficients (β < -3) correspond to very fast, highly tangentialorbits that boarder on the “unphysical” for well equilibrated, relaxed systems. Neither ΛCDMnor MOND proponents have advanced any plausible (internally consistent) solutions for thisparticular significant kinematic signature. In fact, this signature has been downplayed ordismissed by the mainstream due to inability to explain this feature within their frameworks.

We now turn our attention to the GRC for M31, as reproduced below in Figure 7 todemonstrate the applicability of this method beyond a single galaxy.

Figure 7: The GRC of M31 and the RC-SP Fit to Rotation Curve (Sofue 2015). Log-logformat linearizes the Keplerian decline.



As with the MW, we visually fit a Keplerian curve to M31’s GRC providing a dynamic mass at14x1011M ʘ. Although Figures 6 and 7 indicate little or no dark matter halo velocity supportbeyond the baryonic disk, the GRC curve fit is consistent with other estimated dynamicmasses for the local pair, MW at 6x1011Mʘ and M31 at 12x1011Mʘ (Fattahi 2015).

DISK GALAXIES - FUNDAMENTAL PHYSICAL PARAMETERS AND CONSTRAINTS

RC-SP dynamics assumes disk galaxies are inherently fully self-gravitating and rotationallysupported baryonic entities. The early-era transformation process, although not perceptible intoday’s static, low energy environment, maintains maximal angular momentum over galacticlifetimes. Based on this assumption, what is the guiding physical and dynamical relationshipthat drives galaxies to a common morphology and similar phenomena? We find galaxies aregoverned and constrained by the dimensionless ratio termed Spin Parameter (λ). Thisparticular equation is the fundamental relationship for fully self-gravitating disks havingaxisymmetric exponentially declining mass density profiles, a useful description for rotationallysupported disk (spiral) galaxies:

Where J = Angular Momentum, E = Total Energy, MDyn = Dynamic mass, and Total E = K + PE.

The concept of assuming maximal, self-gravitating disks is not new and has been used byothers in the past. This approach employing the Spin Parameter to characterize spiral galaxieshas recently been revived substituting a galactic disk log-normal surface density profile for thestandard exponential parameter shown above (Marr 2015). Marr found the log-normal diskmodel may provide a better fit than the exponential model with observations supporting a valuewith very little deviation (λ = 0.423±0.014).

The Spin Parameter is a simple relation/equation that obeys the concept of simpleproportionality. With this capability, we can estimate the total baryonic content of other diskgalaxies within this broad class of rotationally supported galaxies. Also, by combining the SpinParameter with the GRC, it constrains dynamic to baryonic mass ratios. In other words, if wecan determine the baryonic mass for one galaxy, we can apply this same ratio to others andcan estimate many disk galaxy properties from a few examples.

By most recent estimates, the stellar baryonic mass of the MW disk is ~5x1010Mʘ (McGaugh2015). The MW is considered an unremarkable quiescent disk galaxy, perfectly suited for ouranalysis (Mutch 2011). Using the dynamic mass estimate of 5x1011Mʘ obtained from the GRCfit, we find the dynamic to stellar baryonic mass ratio for the MW:

Since both MW and M31 adhere to the same Spin Parameter class, we calculate M31’s disk tocontain 14x1010Mʘ baryons, 3x the baryonic mass of the MW:

Note that this 10:1 ratio is based on the stellar disk mass where the majority of angularmomentum resides. If all bound galactic baryons: bulge, thick disk, thin disk, stellar halo, andneutral/ionized gas are considered, this ratio would naturally be reduced. This type of baryonicaccounting, so important for ΛCDM is a simple bookkeeping exercise for RC-SP.

As RC-SP dynamics predict proportionality between galactic properties, we expect a



consistent mass-size ratio for all baryonic constituents in the disk. Our Local Group pairprovides an excellent example to estimate the stellar disk mass-size ratio:

Note this 3:2 (m=1.5) ratio correspond to total galactic dynamic mass, including all angularmomentum and energy carried by the baryons according to the spin parameter equation. Wecan compare the stellar disk ratio with measurements obtained for the physical properties of HIdisk inhabiting spiral galaxies (Martinsson 2015). Figure 8 provides the relationship betweenHI disk mass and diameter and a demonstration how the gas content of the Milky Way isestimated from a first order perspective.

Figure 8: The HI mass-size relationship [fig 6 (Martinsson 2015)]. The estimated HI percentage for theMW is determined from the standard D25 photometric value (blue square). The arrow to the left of D25is the ratio of the diameter of HI disks compared to the D25 values (DHI ≈ 1.35D25) obtained fromMartinsson. This figure illustrates how direct observation provides a realistic HI gas proportion for theMilky Way.

We can obtain a reasonable estimate of the MW’s HI disk mass by employing the DHI/D25 =1.35 ± 0.22 relationship obtained by Martinsson. Using a Küpper derived dynamic mass of2.1x1011Mʘ inside a radius of 19 kpc (close to 27 kpc for an estimate). The MW HI gas fractionis estimated made using the RC-SP inferred baryonic (stellar) mass 2.1x1010Mʘ isapproximately 15%, wholly consistent with observational expectations. Applying the standardratio of HI to total gas (x1.33), the estimated gas content is close to 20% for the MW.

The next section compares results obtained from RC-SP from a ΛCDM perspective. We pointout several issues with the current paradigm and suggest RC-SP based solutions without theneed for a dark matter placeholder. With equivalency between M200 and MRC-SP alreadyestablished, the RC-SP 10:1 ratio can be directly related to ΛCDM’s “baryonic fraction,” fb ≡



(MBaryons/M200) = 0.1.

RC-SP DYNAMICS: COMPARISONS TO ΛCDM (DARK MATTER HALO) SIMULATIONS

As ΛCDM simulations become more sophisticated, we are beginning to see a convergence ofphysically observed and simulated baryonic properties. HI gas is now considered an integralcomponent in the accurate reproduction of baryon physics and is incorporated in the latestEAGLE ΛCDM-based hydrodynamical simulations summarized below in Figure 9 (Bahé2015). This figure from Bahé depicts neutral hydrogen (HI + H2) gas fraction as a function ofgalactic stellar mass for EAGLE simulations and GASS observations.

Figure 9: EAGLE simulation for neutral gas (HI+H2) gas fractions (blue line and shade) for a widerange of galactic stellar mass [Fig 1. (Bahé 2015)]. The MW RC-SP estimated mass and gas fractionis depicted in red.

The blue curve denotes simulation results (blue solid/shade) and GASS observations (graytriangles). The RC-SP disk HI gas fraction is shown in red. We find the simulations matchobservations well as does the RC-SP value for the MW. EAGLE results depict a smooth butsubstantial fall-off in neutral gas fraction for more massive galaxies. This substantial decline inHI gas with galactic mass appears to be an artifact of the simulation. Based on the estimatedgas fraction of M31 (log stellar mass = 11.1), the simulation returns a HI gas fraction of lessthan three-percent, an unrealistically low value based on observation.

Now we begin to investigate ΛCDM simulation results beyond the Local Group and compareRC-SP expectations for a broad class of disk galaxies.

A basic tenet of ΛCDM simulations is that baryonic matter receives its angular momentumdirectly from the dark matter halo. Simulations and numerical methods have shown darkmatter halos exhibit a median Spin Parameter λ ≈ 0.04 which is ten times lower than baryonicdisks with Spin Parameter λ ≈ 0.425. Therefore, the halo must at least be ten times moremassive than the baryons to satisfy the total disk moment, leading to an expected galacticbaryonic fraction of ≈0.1, the same as the RC-SP dynamic/stellar mass ratio. Employing theassumption of angular momentum conservation between the halo and disk, GADGET-3



simulations were performed focusing on momentum transfer and its effect on baryonicconstituents – stars and gas shown in Figure 10 (Pedrosa 2015). These simulations results

provide a theoretical angular momentum-mass relationship for the dark matter halo based on the proposition that all baryons receive their observed angular momentum (and totalenergy) from the dark matter halo - exclusively. This basic tenet has not been proved to bephysical, but is mathematically required to reproduce the baryonic spin parameter.

Figure 10: Specific Angular Momentum versus Galactic Component Mass [Fig 2,z=0, Pedrosa 2015: Relation ji − mi medians for the stellar (red dashed lines) andgaseous (green dashed lines) disc components, the stellar spheroidal components(pink dashed lines), the total stellar component (blue line) and the total baryoniccomponent (black lines). The solid black line represents the relation in the case ofangular momentum conservation for the dark matter halos. The dashed black lineis the Total Baryonic Spin Parameter expectation (added to original figure).

GADGET-3 results presented in Figure 10 confirm the anticipated ΛCDM-based relationship for individual baryonic constituents. However, when the total baryonic content isaccounted for, it shifts to the fundamental Spin Parameter relationship already provided -

.

Next, we return to results obtained from the EAGLE simulation from a largerperspective (Schaller 2015). Figure 11 compares EAGLE simulation output with RC-SPderived MW and M31 ‘baryonic fractions’ and dynamic masses. We show the differences (andsimilarities) between ɅCDM models and the RC-SP prescription.



Figure 11: The median ratio of stellar (M*) and DM halo mass (M200) (Schaller 2015).

The above figure reproduces Shaller’s results for the baryonic fraction (M*(stellar)/M200) as afunction of M200 (equivalent to MRC-SP dynamic mass values). We observe a short horizontalplateau near baryon fraction fb = 0.1, decreasing on either side. Setting MRC-SP ≌ M200 andnormalizing Ωb/Ωm ≡ 1 (no dark matter) the results of RC-SP and ΛCDM can be compared inthe same plot. Open circles represent MW and M31 dynamic masses with a dynamic/stellarratio of 10:1 or the equivalent baryonic fraction fb = 0.1. Included in Figure 11 are Sofue’svalues for the MW and M31 (orange triangles) via ΛCDM. It is interesting to note that the samereference providing the new GRCs (Figures 6 and 7) also report viral mass and baryonicfraction for the pair of galaxies. We see Sofue’s MW and M31 values deviate from the modelsand almost appear to be outliers indicating the methodology is amiss or that both MW and M31do not represent typical disk galaxies in the ΛCDM universe.

Please note that RC-SP results span a very short mass range delimited by the two data points,MW and M31. The full RC-SP expectation is that fb = 0.1 should remain consistent over a widerange of dynamic mass, not just the narrow plateau depicted above. With RC-SP, it isexpected that the galactic baryonic fraction to remain reasonably consistent over a muchbroader range of dynamic mass. We need to look beyond this specific simulation result todetermine if the plateau near fb = 0.1 is realistic or an artifact of the methodology. Thisquestion can be answered by comparing ΛCDM simulation results (Gadget2-SPH + Ref inFigure 10) with galactic survey data as provided in Figure 12 below reproduced from a morerecent publication from Sofue (Y.Sofue 2015).



Figure 12: GADGET2-SPH ΛCDM Simulation (Schaller 2015) and RC-SP ResultsComparison. Figure from (Y.Sofue 2015)

The above plot depicts the observed halo/baryon relationship for dwarf and spiral (disk)galaxies spanning a wide range of galactic mass. Using this format provided by Sofue, we candetermine the general accuracy and interpretation of ΛCDM simulations results againstobservation. From a simple visual analysis, we observe an obvious flaw in the simulation. Itdirectly links spiral to dwarfs by a falling baryonic fraction curve extending between the twopopulations. The open white circles represent RC-SP dynamics for the MW and M31 forbaryonic fractions equivalent to 0.11 (dashed blue line intersecting MW and M31). TheGADGET2-SPH + Ref result is interesting in that it attempts to directly link spirals and dwarfgalaxies through a decreasing baryonic fraction. This linkage might make sensecomputationally, but highlights a cognitive disconnect existing between fundamental physicsand unresolved galactic phenomena.

We reinterpret the data in Figure 12 by fitting the correct baryonic fraction to the dwarf galaxypopulation (fb ≌ 0.1) and see that the dwarf population parallels the more massive spiralgalaxies. This suggests all rotationally supported galaxies regardless of mass are governed bythe same Spin Parameter constraint. An Occam’s razor argument directs us to conclude thisvertical offset is due to an incomplete inventory (probably gas) of total baryonic mass for thesedwarf galaxies. Nothing “dark” is required to harmonize both low and high mass galaxies.

To finish up the discussion, we are beginning to witness ΛCDM simulations starting to deliverreal-world results for some of the basic baryonic properties of galactic disks. The downside isΛCDM is has achieved convergence using very complex assumptions and tortuous logic whenmore simple methods are available to arrive at the same result. Moreover, we show darkmatter can be completely eliminated from the cosmological process using a RC-SP dynamical



approach. As precision astrophysical observations continue to tighten physical constraints andrelationships for all theories, we need to remember it is not the what, but the how that is crucialto understanding galactic phenomena.

CONCLUSION

A new galactic formation and evolution process (RC-SP Dynamics) has been proposed. Thisprocess, driven by the extreme energy density decline within the very early universe results inthe morphological and kinematic properties of the Milky Way and other rotationally supportedgalaxies. RC-SP side-steps “angular momentum catastrophe” and “missing mass” problemsinflicting ΛCDM and provides alternative classically obtained solutions. The goal of this letter isto bring substance and structure to the original RC-SP proposition through improveddiscussion, evidence and examples. Thanks to the Winnower for the opportunity to share mythoughts to a wide audience and a means for public response and review.

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