A Small Patch Hypothesis in Cosmology

Abstract

If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; we occupy a small causal domain of a much larger causally-connected and possibly non-flat spacetime. A sufficiently large positive cosmological constant, $\Lambda$, sets the future asymptotic horizon scale of the observable Universe, $\sim$$\Lambda^{-1/2}$, thereby implying that the observable Universe may simply be a minute patch of a far larger pre-existing one, hereafter a Small Patch Hypothesis. Importantly, this observational bound is purely geometric; regardless of when the Universe is observed, the maximum accessible scale is finite and fixed by $\Lambda$, independent of inflationary dynamics, anthropic arguments, or assumptions about the global hosting spacetime. In this sense, inflation becomes one viable realization of the proposed Small Patch Hypothesis. Here, one particular non-inflationary alternative is considered for illustrative purposes in which a primordial spectrum grows logarithmically toward large scales, and in fact diverges at some finite $k_{c}$. If $k_{c}\ll \Lambda^{-1/2}$, then our local cosmic patch probes only the linear regime and appears exceptionally smooth. Over the comparatively narrow observable window, this power spectrum mimics a slightly red-tilted, inflation-like spectrum. Rather than introducing high-energy new fields, this perspective frames large-scale homogeneity, isotropy, Gaussianity, adiabaticity, and the observed thermodynamic Arrow of Time as possible consequences of restricted observational access to a much larger Universe in equilibrium, rather than signatures of a unique early-Universe mechanism. [abridged]