13. Cosmology: what is established, what is extrapolated, what is speculative

A map of an expanding universe #

The scale factor a(t) describes expansion; normalize its present value to one. A redshift z is dimensionless and relates emission to observation. An expansion history is inferred through a cosmological model and data. A Hubble radius, particle horizon and event horizon have different definitions; none is a rigid wall in space.

13.1 The hot Big Bang does not mean “physics proved creation from nothing” #

The well-tested hot-Big-Bang framework says that the observable universe evolved from an earlier hotter and denser state. It successfully organizes cosmic expansion, primordial nucleosynthesis, the cosmic microwave background (CMB), and large-scale structure. It does not by itself establish that the universe emerged from philosophical “absolute nothing.” Questions about an initial singularity or pre-Big-Bang state require physics beyond the regime where classical general relativity can be trusted.

The CMB mean temperature is

and Planck’s baseline $\Lambda$CDM analysis gives a cosmic age close to

within the assumptions of that cosmological model. Cosmic Microwave Background (2025) · Planck 2018 results. VI. Cosmological parameters (2020)

13.2 The observable universe is larger than $ct_0$ #

Because space expanded while light propagated, the present proper distance to objects whose ancient light we see can greatly exceed $ct_0$. One must distinguish particle horizon, event horizon, Hubble radius, comoving distance, and proper distance. Statements such as “everything beyond 62 billion light-years expands faster than light and can never affect us” depend on cosmological model and on which horizon is meant; they should not be used without definitions.

13.3 Inflation #

Inflation was introduced to address the horizon and flatness problems by a period of accelerated expansion in the early universe. Inflationary universe: A possible solution to the horizon and flatness problems (1981) Many inflationary models generate nearly scale-invariant primordial perturbations, consistent with key features of CMB data, but the identity of the inflaton and the detailed microphysics remain unknown. Inflation is therefore well-motivated and phenomenologically successful as a framework, but not a directly observed particle-physics sector.

13.4 Multiverse ideas: label the evidence level #

Several very different ideas are often grouped under “multiverse”:

1. Spatial regions beyond our observable horizon in a sufficiently large universe.
2. Eternal-inflation scenarios with many thermalized regions. Eternally existing self-reproducing chaotic inflationary universe (1986)
3. Everett’s relative-state interpretation of quantum mechanics, later popularly associated with “many worlds.” Relative State Formulation of Quantum Mechanics (1957)
4. String-landscape constructions with many metastable vacua. Quantization of four-form fluxes and dynamical neutralization of the cosmological constant (2000)

These concepts do not have the same theoretical assumptions and do not have the same empirical status. None should be presented as an experimentally established fact comparable to the Higgs boson or the CMB.

The intellectually responsible rule is:

The farther an idea is from direct observation, the more explicitly we must state which assumptions carry us there.

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