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Big-Bang Problem

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Classical and Quantum Cosmology

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Abstract

The big-bang problem is an open issue in theoretical physics. In this and the next chapters, we will review some of the proposals, few of which successful or completely satisfactory, advanced to solve it. Let us first explain why the big bang is a problem at the classical level.

Vaccha, the speculative view that the world is eternal…that the world is not eternal…that the world is finite…that the world is infinite is a thicket of views, a wilderness of views, a contortion of views, a vacillation of views, a fetter of views. It is beset by suffering, by vexation, by despair, and by fever, and it does not lead to disenchantment, to dispassion, to cessation, to peace, to direct knowledge, to enlightenment, to Nibbāna.

— Aggivacchagotta Sutta, Majjhima Nikāya 72.14 [1]

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Notes

  1. 1.

    In Chap. 2, we used the symbol u μ for a generic unit time-like vector. Here and in the following, we reserve it for congruences.

  2. 2.

    Null congruences will be defined and employed in Sect. 7.7

  3. 3.

    We refer the interested reader to [4] for a complete review of older results and [2] for a concise proof of the following theorem by Hawking and Penrose [38].

  4. 4.

    For Theravāda cosmology and the creation-destruction myth, see Dı̄gha Nikāya 27.10-31 [53], Majjhima Nikāya 28.7,12 [1], Aṅguttara Nikāya 4:156, 7:66 [54]. A comprehensive account can be found in the Visuddhimagga, XIII 13, 28–65 [55].

  5. 5.

    The co-tetrad e a  μ is often denoted as ω a  μ in the literature.

  6. 6.

    Sum and product indices range from 1 to D − 1 unless stated otherwise. Sums or products with subscript i < j run both on j and on i < j.

  7. 7.

    In nine spatial dimensions, the maximum p i​j k is zero at p 1 = p 2 = p 3 = −1∕3, p 4 = … = p 9 = 1∕3.

  8. 8.

    This name was given by Misner [82] after a famous mechanical kitchen mixer, produced by an American brand of electric home appliances. Reference to this tool is due to the fact that, after a large number of eras, all parts of the whole universe are in causal contact with one another, along all directions: the texture of a cream or a dough is homogenized after enough mixing cycles. In fact, the BKL model was a candidate solution to the horizon problem well before inflation was proposed. This can be roughly seen from (2.188) and the discussion at the end of Sect. 5.2.2 In a given Kasner era, τ plays the role of conformal time along the direction expanding (forward in time) monotonically. Inflation, as we have seen, does much more than addressing the horizon problem.

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    Gianluca Calcagni

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Calcagni, G. (2017). Big-Bang Problem. In: Classical and Quantum Cosmology. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-41127-9_6

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