“Yes, after all…

- •
**Roger Penrose**: “Friedmann-Lemaitre-Roberston-Walker (FLRW) [are] spatially homogenous and isotropic cosmological models. …each model starts with a Big Bang… for the different alternative choices of spatial curvature. In each case, the universe starts form a singularity—the so-called Big Bang—where spacetime curvatures become infinite and then it expands rapidly outwards.” [*The Road to Reality: A Complete Guide to the Laws of the Universe*(Vintage Books, 2005), 719.]

•**Stephen Hawking & George Ellis**: “We have seen there are singularities in any Roberston-Walker space-time in which µ > 0, p ≥ 0 and Λ is not too large… the fact that singularities do occur in such models gives an indication that the existence of singularities may be a property of all space-times which can be regarded as reasonable models of the universe.” [*The Large Scale Structure of Space-Time*(Cambridge, 1973), 142.]

• See also R. M. Wald,*General Relativity*(Chicago, 1984), 213-4. - To say the universe is not isotropic and homogenous is to say its not the same from all directions and all places. By way of response, however, [the Universe is expanding from a hot dense state], and the cosmic microwave background radiation is a sort of lingering afterglow. It is measured to be highly isotropic. In fact, thermal radiation temperature various by only a tenth of a thousandth of a kelvin. This is relevant because of the Ehlers-Geren-Sachs theorem[1] (and the Stoeger, Maarten, Ellis update)[2] which can use this data to prove we are therefore in an isotropic and homogenous FLRW spacetime. The relevant papers here are:

[1]Ehlers, J., Geren, P., Sachs, R. K., “Isotropic solutions of Einstein-Liouville equations.”*J. Math. Phys.*9, 1344 (1968)

[2]Stoeger, W. R.; Maartens, R; Ellis, George (2007), “Proving Almost-Homogeneity of the Universe: An Almost Ehlers-Geren-Sachs Theorem.”*Astrophys. J.*, 39: 1–5,

**(Big Bang Theory): General relativity (GR) is true, sufficiently accurately describing the full birth-growth of space.** Consider three evidences:

• …General relativity makes accurate predictions.

• …Space in fact did expand from a hot-dense space.

• …Other evidences indicate: Physical reality (spacetime) began to exist, growing from a singularity.

This is relevant because “FLRW models with ordinary matter have a singularity at a finite time in the past.” [Christopher Smeenk, “Philosophy of Cosmology,” in Batterman (ed.), *The Oxford Handbook of Philosophy of Physics* (Oxford, 2013), 612.]^{1}

**No**,

•…Space has an early quantum era (not FLRW); GR won’t apply.

•…Space is not isotropic & homogenous.^{2}

- More specifically and technically, this fate for a past tracing so-called “geodesic” is a degenerative symptom (“pathology”) associated with singularities. That is to say, while the theorem is not a singularity theorem—it entails no singularity—its conclusion is nevertheless evidentially symptomatic of a singularity, and either way fits cleanly with the longstanding most simple inflationary theory: the Standard Big Bang model. Consequently, “A model in which the inflationary phase has no end …naturally leads to this question: Can this model also be extended to the infinite past, avoiding in this way the problem of the initial singularity? …this is in fact not possible in future-eternal inflationary spacetimes as long as they obey some reasonable physical conditions: such models must necessarily possess initial singularities. …the fact that inflationary spacetimes are past incomplete forces one to address the question of what, if anything, came before. ["Eternal Inflation and the Initial Singularity," Physical Review Letters 72 (1994): 3305, 3307 (provided by Bill Craig)]

**(BGV Theorem): Any Universe eternally inflating/expanding on average requires infinitely-fast travel** Right?

After all…

• …consider Vilenkin's spacetraveler proof/illustration

This is relevant because an object traveling infinitely fast in space is impossible, producing philosophical absurdities and violating the causality principle (in Einstein’s special relativity). The fate is symptomatic of a singularity.^{1}

**So?** Couldn’t it simply be that… [All forthcoming]

•…Space contracts on average

•…Because of an infinite contraction phase

•…Space is static on average

•…Because of infinite cycling

•…Because of an infinite contraction phase (during time-reversal)

“No, after all…

**A beginningless universe (or multiverse) model is true.** This is relevant because the Standard Big Bang model under review here is not a past eternal model.

**Singularity-expansions (e.g. The Big Bang) aren’t events.** After all, “An event takes place within a space-time context. But the Big Bang has no space-time context; there is neither time prior to the Big Bang nor a space in which the Big Bang occurs.” (SEP).