N.S.B. Cosmology

This page is intended to present the development of ideas pertaining to our Realistic Non-Singular Cosmology.

The following article corresponds to our paper viXra:1504.0007 submitted on 2015-04-01 06:51:00, . Here we reproduce the same paper with minor variations, adding various highlights.

1. Introduction

What we call realistic non-singular cosmology is based on the idea [1] that the expanding (and subsequently contracting) universe is an oscillating system with two turning points. The lower turning point (that of minimal scale) is determined by the (negative) pressure of electromagnetic radiation (photons) that is produced by stellar matter, while the upper turning point is determined by the (positive) pressure of gravitational radiation (gravitons, or curvature). In our initial proposal [1],[2],[3], we have regarded the cosmic microwave background [4]-[8] as a possible description of the average photonic density of the universe, and used the measured temperature (T ~ 2.726 K) to determine the minimal cosmic scale a when the photonic density (scaling like 1/a⁴) equates matter density (scaling like 1/a³). The measured temperature of the microwave background implies a photonic density of ρ_r ~ 4.7×10^‐31 kg/m³. Comparing this with the present value of matter density (ρ_m ~ 5.2×10^‐27 kg/m³), we obtain the value of a ~ 0.00009 (notice that the cosmic scale a is normalized to be equal to 1 at the present state of the universe). Consequently, the matter density at minimal scale (ρ_m/a³ ~ 7.1×10^‐15 kg/m³), and the temperature (T/a ~ 3×10⁴ K ~ 2.6 eV) would imply that the universe was in a state consisting of whole and active stars, the latter (rather than highly energetic particles) being the main constituents that are essential to cosmology, whose global motion is governed by their radiational emissions as well as their gravitational attraction.

The fate of galaxies in the ensuing picture is that they would merge together as we go back in time to the contracted state, loosing their identity, and leaving the stage for the stellar bodies as the main protagonists. However, when we realize that the whole scheme is very sensitive to the present value of the photonic density, we cannot but contemplate the idea that if the present value of photonic temperature could be higher than that suggested by the microwave background then the scenario for galaxies could be altered. In fact, if the universe is expanding at all, the balance between photonic density and matter density must have occurred in the past. Hence from the fact that the present value of photonic density must be less than the density of matter, we can estimate an upper bound for the corresponding temperature to be ~ 30 K (see later). Our purpose in this article is to reconsider our scheme for realistic non-singular cosmology, and to show that an acceptable scheme could be proposed whose implications would lead to a universe with an initial state consisting of whole galaxies, with a very low background temperature. Such a scenario depends on a higher value of the present-time background photonic temperature, somewhere between 3 K and 30 K.

At this point, we should remark that the value to be chosen for the background photonic temperature would correspond in Friedmann's equation [9],[10],[11] to a photonic density fraction that yields a higher value for the minimal cosmic scale. Now noting, from the relation (1 + z) = 1/a that such a higher value for the minimal scale a would imply a lower upper bound for any observable redshift z. Of course, we must choose a value of the photonic density fraction whose z upper bound does not conflict with already observed redshifts. We shall make our choice compatible, as well, with the supernovae data for magnitudes and redshifts [12]-[17], and an acceptable value for the Hubble constant.

In the following sections, we shall begin by reviewing the Friedmann equation pertaining to our scheme of realistic non-singular cosmology. We shall then make appropriate choices for the density fraction terms, and show how they can be made compatible with the supernovae data for magnitudes and redshifts, demonstrating agreeable graphics. We shall compute the age of the expansion since minimal scale, as well as the tentative remaining time before the return to contraction. Subsequently, we shall assess and discuss the state of the universe at minimal scale.

2. The Friedmann Equation for Realistic Non-Singular Cosmology

Our scheme for realistic non-singular cosmology is based on Friedmann's equation taking the following form:

Here a(t) is the cosmic scale as a function of cosmic time, the dot represents the time derivative, and H is the Hubble constant. The parameters r‚g are both positive. Hence, we have introduced a negative photonic density term with fractional coefficient ‐r and a negative gravitonic (or curvature) density term with fractional coefficient ‐g, leaving the positive matter density term with a coefficient (1 + r + g). Notice that when a = 1, corresponding to the present state of the universe, the RHS of the above equation reduces to H².

According to the above equation, the expansion and the contraction of the universe is governed by two turning points, making the RHS vanish, and corresponding to the roots of the quadratic equation

In earlier works [1]-[3], we have taken r to be a very small fraction ( ~ 9×10^‐5) that corresponds to the ratio of the mass density of the photonic background (as suggested by the microwave radiation with temperature ~ 2.726 K) to the total mass density, while g ≈ 0.1 was taken tentatively. In this work, we shall take the illustrative and tentative values of r ≈ 0.1 and g ≈ 0.1. Notice that the maximal value (upper bound) of observable redshifts corresponds to the equation (1 + z) = 1/a with a the lower solution of the above equation. With our prescription for r and g, we obtain z ≈ 11 as the highest value of redshift that can be observed! As far as we know, all observed redshifts are comfortably below this value.

Before discussing the state of the universe at its lower turning point, we shall confront the implications of our scheme with the supernovae data for magnitudes and redshifts.

3. Supernovae Data & the Hubble Constant

A large list giving supernovae magnitudes against redshifts is given in the appendix (this was used in our last work on the subject [3]). The corresponding graphic (magnitude against redshift) is given below:

This is another graphic with a better resolution for the points with lower redhifts:

Now in order to relate our Friedmann equation to the above supernovae data, we recall that stellar magnitudes are given by the expression [10],[11],

where d_L is the luminosity distance in Mpc, or mega parsec ( ≈ 3.08568×10²² m). With the scale parameter a related to the redshift z by the expression a = 1/(1 + z), we obtain from the foregoing Friedmann equation,

with c being the speed of light, using r = 0.1 and g = 0.1, and a Hubble fraction of h = 0.65. Using the foregoing two formulas, we can plot the curve of magnitude against redshift on the same graphic, given before, for supernovae data (showing graphics for long range and short range side by side):

It is clear that the curve goes much below the data points.

Lowering the value of the Hubble fraction to h = 0.6, we obtain:

Lowering further to h = 0.55, we obtain

And further to h = 0.5,

It is clear from the above graphics that a value of h ≈ 0.55 provides the best fit, and that with such a value, which corresponds to a Hubble constant of 55 km/sec/Mega parsec, our scheme for the Friedmann equation is compatible with supernovae data for magnitudes and redshifts.

4. Times, Densities, & Temperatures

With the choice of r = 0.1 and g = 0.1, the turning points of cosmic oscillation are given by the solution of the equation − 0.1 + 1.2a − 0.1a² = 0, and we obtain a = 0.0839202 for the lower turning point (minimal scale) and a = 11.9161 for the upper turning point (maximal scale). The age of the current expansion since minimal scale is obtained from the following integral (using the appropriate H with h = 0.55):

On the other hand, the remaining time before returning to contraction is obtained from:

Moving to questions of matter density and temperature, recall that the total mass density on the RHS of our Friedmann equation is given by 3H²/8πG. With our choice of the Hubble constant, this gives a total density of ~ 5.68344×10^‐27 kg/m³. Multiplying this by r = 0.1 we obtain the photonic mass density, while multiplying by (1 + r + g) = 1.2 we obtain the matter mass density. Now the photonic mass density as a function of temperature is given by:

where we have used k = 1.38066×10^‐23 joule/K for the Boltzmann constant, c = 2.99792458×10⁸ for the speed of light constant, and ℏ = 1.05457×10^‐34 joule.sec for the reduced Planck constant. Equating the above to the matter density implemented in our equation, we obtain T ≈ 30 K as an upper bound on the present photonic temperature if the universe is to be expanding at all. On the other hand, dividing the above by the total mass density and equating to r = 0.1, we obtain T ≈ 16.1194 K as the actual value of the implemented temperature for the present-time photonic background. This should be contrasted with T = 2.726 K associated with the microwave background. The temperature of photonic radiation at minimal scale (a ≈ 0.0839202) is given by T/a or ~ 192.08 K. This value should be contrasted with ~ 30,298 K obtained in our earlier work [1] associated with the microwave background, and with infinity in the conventional singular cosmology.

Whereas the density of matter at present is given by (1 + r + g) = 1.2 times the total mass density, or ρ_m ≈ 6.82013×10^‐27 kg/m³, the value at minimal scale is ρ = ρ_m/a³ ≈ 1.15397×10^‐23 kg/m³. Notice that if a typical galaxy like ours (consisting of about 10¹¹ stars like our sun) were to distribute its mass over a certain radius, and have the latter density, its radius (3M/4πρ)^1/3 would be about 3.34 the size of our galaxy.

5. Discussion

In our earlier work [1]-[3] regarding realistic non-singular cosmology, and viewing the microwave background (whose temperature is 2.726 K) as a true measure of the photonic background of the universe, a general picture had emerged depicting the state of the universe at minimal scale as that of space packed with stars, that may have been whole and active with a background temperature of ~ 30,298 K. The stars were considered as the main protagonists in an oscillating universe whose turning points are determined by the photonic and the gravitonic densities. However, in this article we have been able to show that the main protagonists in such an oscillating universe would rather be the galaxies, and the state of the universe at minimal scale would be very cold, with a background temperature of ~ 192 K only!

Recall that our basic starting point depends on the assumption that the present average temperature of cosmic photons is ~ 16 K, an illustrative value higher than that associated with the microwave background, but still lower than ~ 30 K, the upper bound for an expanding scenario in our scheme for realistic non-singular cosmology based on a Friedmann equation. We have shown that our choice for the photonic and the gravitonic densities yield remarkable agreement with the supernovae data for magnitudes and redshifts provided a Hubble fraction of ~ 0.55 is adopted. We have also remarked that our implemented minimal scale yields an upper bound on observable redshifts z ~ 11. The latter fact could and should be a decisive observational constraint in any future scrutinizing of our theory.

Whether the main protagonists of a realistic non-singular cosmology are the stars or the galaxies is a question that may demand further investigation, although we tend towards adopting the more realistic colder scenario introduced in the present work. This means that the global motion of the universe (expanding and contracting) is just a very cold superficial phenomenon engaging the galaxies. Whatever will be the final form of a realistic non-singular cosmology, it would always provide a more acceptable alternative than the conventional singular cosmology and the outrageous ever-accelerating counterparts.

Appendix: Supernovae Magnitudes Data List

The following is a collected list [15], [16], [17] of items of the form {z‚M}, where z is the redshift and M is the corresponding supernova magnitude:

{{0.0104,33.21},{0.0104,33.56},{0.0104,33.73},{0.0116,32.96},{0.0121,34.05},{0.0132,34.02},{0.0136,33.73},{0.0141,34.12},{0.0141,34.13},{0.0141,34.43},{0.015,34.118},{0.0152,34.11},{0.0157,34.58},{0.016,34.071},{0.016,34.083},{0.016,34.129},{0.016,34.405},{0.0161,34.5},{0.0162,34.13},{0.0164,34.41},{0.0164,34.47},{0.0165,33.82},{0.0166,34.54},{0.0167,34.21},{0.017,34.162},{0.017,34.216},{0.017,34.319},{0.017,34.452},{0.017,34.18},{0.017,34.47},{0.0171,34.68},{0.0175,34.52},{0.0178,34.7},{0.018,34.489},{0.018,34.576},{0.018,34.29},{0.0186,34.96},{0.0193,34.59},{0.02,34.494},{0.0218,35.06},{0.0219,34.7},{0.022,34.941},{0.023,35.146},{0.0233,35.14},{0.0234,35.36},{0.024,35.228},{0.024,35.25},{0.0244,35.09},{0.0247,35.33},{0.025,34.931},{0.025,35.192},{0.0251,35.09},{0.0257,35.41},{0.026,35.342},{0.026,35.353},{0.026,35.565},{0.026,35.62},{0.0262,35.06},{0.0265,35.64},{0.0266,35.36},{0.0276,35.9},{0.028,35.15},{0.0286,35.53},{0.029,35.7},{0.0297,36.12},{0.03,35.822},{0.03,35.994},{0.0307,35.9},{0.031,35.532},{0.031,35.558},{0.0316,35.85},{0.032,35.789},{0.0327,36.08},{0.0331,35.54},{0.0348,36.17},{0.035,35.837},{0.036,36.113},{0.036,36.17},{0.036,36.01},{0.036,36.39},{0.038,36.67},{0.039,36.284},{0.04,36.38},{0.043,36.276},{0.043,36.53},{0.045,36.728},{0.045,36.97},{0.046,36.35},{0.049,36.383},{0.049,36.52},{0.049,36.9},{0.05,36.632},{0.05,36.827},{0.05,36.84},{0.05,37.08},{0.051,36.67},{0.052,37.16},{0.053,36.794},{0.053,36.97},{0.053,37.17}, {0.054,36.606},{0.056,37.31},{0.058,37.13},{0.061,37.3},{0.063,37.54},{0.063,37.67},{0.067,37.54},{0.071,37.604},{0.071,37.78},{0.075,37.642},{0.075,37.77},{0.079,37.465},{0.079,37.94},{0.088,38.07},{0.088,38.121},{0.089,38.5},{0.101,38.437},{0.101,38.73},{0.124,39.2},{0.125,38.885},{0.16,39.08},{0.172,39.79},{0.18,39.98},{0.216,40.33},{0.216,40.33},{0.23,40.44},{0.24,40.68},{0.249,40.571},{0.263,40.682},{0.278,41.},{0.285,40.731},{0.291,40.999},{0.3,40.76},{0.3,41.01},{0.32,41.45},{0.331,40.946},{0.334,40.92},{0.337,41.259},{0.34,40.71},{0.34,41.323},{0.346,41.367},{0.357,41.441},{0.358,41.474},{0.359,41.23},{0.369,41.485},{0.369,41.62},{0.371,41.488},{0.38,42.02},{0.388,42.07},{0.397,40.89},{0.4,42.04},{0.415,41.772},{0.416,42.1},{0.42,40.79},{0.42,41.76},{0.422,42.02},{0.425,41.7},{0.43,41.776},{0.43,41.99},{0.43,42.33},{0.43,42.36},{0.44,42.08},{0.44,42.57},{0.449,41.866},{0.45,42.1},{0.45,42.13},{0.45,42.58},{0.451,42.038},{0.455,42.29},{0.46,41.83},{0.46,42.23},{0.46,42.56},{0.461,42.031},{0.463,42.089},{0.465,42.81},{0.468,42.708},{0.47,42.268},{0.47,42.74},{0.47,42.77},{0.472,42.46},{0.475,42.14},{0.475,42.24},{0.477,42.38},{0.478,42.48},{0.48,42.37},{0.49,42.41},{0.49,42.54},{0.49,42.58},{0.495,42.25},{0.496,42.18},{0.498,43.21},{0.5,42.74},{0.5,42.75},{0.5,42.75},{0.504,42.429},{0.508,41.64},{0.514,42.39},{0.518,42.83},{0.521,42.05},{0.521,42.439},{0.526,42.56},{0.526,42.644},{0.526,43.01},{0.526,43.08},{0.528,42.77},{0.532,42.592},{0.538,42.66},{0.54,41.96},{0.543,42.68},{0.548,42.825},{0.55,42.487},{0.552,42.461},{0.557,42.511},{0.57,42.77},{0.57,42.81},{0.57,42.88},{0.571,42.465},{0.572,43.521},{0.579,42.86},{0.58,43.04},{0.581,42.63},{0.581,42.761},{0.582,42.881},{0.592,42.562},{0.604,42.515},{0.61,42.796},{0.613,42.961},{0.615,42.85},{0.62,43.03},{0.62,43.11},{0.627,42.746},{0.63,42.62},{0.633,43.133},{0.638,42.89},{0.638,43.3},{0.64,43.07},{0.64,43.01},{0.643,43.023},{0.644,42.78},{0.657,43.27},{0.67,43.19},{0.67,43.19},{0.679,43.398},{0.688,43.046},{0.691,43.144},{0.695,43.023},{0.698,43.33},{0.707,43.237},{0.71,43.05},{0.71,43.176},{0.719,43.22},{0.721,43.209},{0.73,43.287},{0.735,43.09},{0.735,43.14},{0.74,43.35},{0.74,43.38},{0.741,43.427},{0.752,43.17},{0.756,43.453},{0.771,43.12},{0.778,43.81},{0.791,43.353},{0.798,43.88},{0.8,43.49},{0.81,43.691},{0.811,43.95},{0.811,43.97},{0.815,43.76},{0.815,44.09},{0.817,43.652},{0.818,43.532},{0.822,43.544},{0.828,43.61},{0.828,43.96},{0.83,43.85},{0.83,44.414},{0.832,43.55},{0.839,43.45},{0.839,43.86},{0.84,43.475},{0.84,43.67},{0.854,43.96},{0.86,44.03},{0.868,43.871},{0.87,44.095},{0.873,43.75},{0.882,43.9},{0.884,44.23},{0.886,42.91},{0.899,43.64},{0.9,43.64},{0.905,43.708},{0.91,44.259},{0.927,44.553},{0.93,44.43},{0.935,43.97},{0.935,43.99},{0.94,43.87},{0.949,43.507},{0.949,43.99},{0.95,44.06},{0.95,43.954},{0.95,43.98},{0.954,43.85},{0.954,44.28},{0.954,44.3},{0.96,43.622},{0.961,44.},{0.97,44.13},{0.97,44.67},{0.975,44.21},{0.977,43.91},{0.983,43.941},{1.01,44.673},{1.01,44.77},{1.02,43.99},{1.02,44.52},{1.056,44.25},{1.12,44.67},{1.14,44.44},{1.14,44.71},{1.14,44.84},{1.19,44.19},{1.19,43.64},{1.23,44.97},{1.23,45.17},{1.265,44.64},{1.265,45.2},{1.3,45.27},{1.3,45.06},{1.305,44.51},{1.305,44.7},{1.307,44.99},{1.34,44.92},{1.34,45.05},{1.37,45.23},{1.39,44.9},{1.4,45.09},{1.4,45.28},{1.551,45.07},{1.551,45.3},{1.755,45.35},{1.755,45.53}}

References

[1] N.S. Baaklini, Realistic Non-Singular Cosmology, N.S.B. Letters, NSBL-RC-011; http://www.vixra.org/abs/1312.0204

[2] N.S. Baaklini, Realistic Non-Singular Cosmology with Negative Vacuum Density, N.S.B. Letters, NSBL-RC-012; http://www.vixra.org/abs/1401.0060

[3] N.S. Baaklini, Realistic Decelerating Cosmology and the Return to Contraction, N.S.B. Letters, NSBL-RC-014; http://www.vixra.org/abs/1402.0002

[4] A.A. Penzias & R.W. Wilson, Astrophys. J., 142 (1965) 419

[5] R.H. Dicke, P.J.E. Peebles, P.G. Roll and D.T. Wilkinson, Astrophys. J., 142 (1965) 414

[6] J.C. Mather et al, Astrophys. J., 420 (1994) 439

[7] D.J. Fixen et al, Astrophys. J., 473 (1996) 576

[8] J.C. Mather et al, Astrophys. J., 512 (1999) 511

[9] A. Friedmann, Z. Phys., 10 (1922) 377

[10] J.V. Narlikar, Introduction to Cosmology, (Cambridge University Press, Cambridge, 1993)

[11] N.S. Baaklini, Introduction to Relativistic Cosmology, N.S.B. Letters, NSBL-RC-007

[12] S. Perlmutter et al, Bull. Am. Astron. Soc., 29 (1997) 1351

[13] A.G. Riess et al, Astron. J., 116 (1998) 1009;

[14] S. Perlmutter et al, Astrophys. J., 517 (1999) 565

[15] A.G. Riess et al, Type Ia Supernova Discoveries at z > 1 From the Hubble Space Telescope..., http://arXiv.org/abs/astro-ph/0402512v2, (Astrophys. J., June, 2004)

[16] P. Astier et al, The Supernova Legacy Survey Measurement of Omega ... from the First Year Data set; http://arXiv.org/abs/astro-ph/0510447v1

[17] A.G. Riess et al, New Hubble Space Telescope Discoveries of Type Ia Supernovae at z>=1 etc., http://arXiv.org/abs/astro-ph/0611572v2

Next?