Flat Space Cosmology

A New Model of the Universe Incorporating Astronomical Observations of Black Holes, Dark Energy and Dark Matter

Eugene Terry Tatum, Seshavatharam

• Publisher: Universal Publishers
• Year: 2021
• ISBN:
  9781627343404
• Topic: Physical Sciences
• Subtopic: Cosmology

This compilation based upon recent peer-reviewed journal publications encapsulates how the Flat Space Cosmology model (FSC) has become the primary competitor to the inflationary standard model of cosmology. New ideas concerning black holes, dark energy an

Chapter 1

A Heuristic Model of the Evolving Universe Inspired by Hawking and Penrose

Abstract: A heuristic model of universal expansion is presented which uses, as its founding principle, Stephen Hawking’s singularity theorem. All assumptions of this model are intrinsically linked to Hawking’s theorem and its implications with respect to the time-symmetric properties of general relativity. This is believed to be the first mathematical model constructed in such a way, and it is remarkably accurate with respect to current astrophysical observations. The model’s origin, basic assumptions and selected observational correlations are presented in this chapter, including its accurate derivation of the observed Hubble parameter value.*

Keywords: Flat Space Cosmology; Cosmology Theory; Hubble Parameter; Cosmic Flatness; Cosmic Entropy; Black Holes; Rh = ct Model

1.INTRODUCTION AND BACKGROUND

A heuristic mathematical model of the evolving universe, for the purpose of this chapter, is one which tracks its global parameters (Hubble parameter, radius, mass, energy, entropy, average temperature, temperature anisotropy, etc.) as a function of cosmic time. For it to be useful, such a model should be consistent with everything we currently observe about the universe as a global object, and extend these parameters indefinitely into the past and future. In assembling such a model, it is particularly useful to start with a founding principle on which some or, preferably, all of the starting assumptions can be based. For this particular model, the founding principle is based upon the groundbreaking work of Roger Penrose [1] and Stephen Hawking [2][3] concerning the similar theoretical nature of astrophysical and cosmological singularities. This founding principle is Hawking’s singularity theorem.

Hawking’s singularity theorem implies that our universe, following time-symmetric properties of general relativity, could be treated mathematically as if it were a cosmological black hole-like object moving backwards in time (i.e., expanding from a singularity state as opposed to collapsing to a singularity state). Unfortunately, although Hawking’s theorem was rigorously logical, he never actually put together a predictive mathematical cosmological model based upon his theorem. What is presented in this chapter is believed to be the first such model.

This author (E.T.T.) was sufficiently intrigued by the initial Planck satellite survey results and the potential implications of Hawking’s singularity theorem that he teamed up with two Indian physicists (U.V.S. Seshavatharam and S. Lakshminarayana) in 2015 to publish the seminal papers [4][5][6] on this model. For reasons to be discussed below, this model is called ‘Flat Space Cosmology’ (FSC). The current five basic assumptions of FSC are presented below.

2.Five basic assumptions of flat space cosmology

1. The cosmic model is an ever-expanding sphere such that the cosmic horizon always translates at speed of light c with respect to its geometric center at all times t. The observer is operationally-defined to be at this geometric center at all times t.
2. The cosmic radius Rt and total mass Mt follow the Schwarzschild formula Rt ≅ 2GMt/c2 at all times t.
3. The cosmic Hubble parameter is defined by Ht ≅ c/Rt at all times t.
4. Incorporating our cosmological scaling adaptation of Hawking’s black hole temperature formula, at any radius Rt, cosmic temperature Tt is inversely proportional to the geometric mean of cosmic total mass Mt and the Planck mass Mpl. Rpl is defined as twice the Planck length (i.e., as the Schwarzschild radius of the Planck mass black hole). With subscript t for any time stage of cosmic evolution and subscript pl for the Planck scale epoch, and, incorporating the Schwarzschild relationship between Mt and Rt,

   (1)

5. Total cosmic entropy follows the Bekenstein-Hawking black hole entropy formula [7][8]:

   $$S_t\cong \frac{\pi R_t^2}{L_p^2}$$

   (2)

The rationale for these basic assumptions is closely tied to Hawking’s singularity theorem as it might pertain to a time-reversed Schwarzschild cosmological black hole-like object. From the centrally-located observer’s point of view, outwardly-moving photons traveling along geodesics at the cosmic boundary (i.e., the fastest-moving ‘...