Holographic Theories of Inflation and Fluctuations

TL;DR

Holographic Space-time (HST) provides a quantum-mechanical framework in which causal diamonds carry finite-dimensional operator algebras and space-time geometry emerges from observer overlaps, tying SUSY to Poincaré invariance in large-$N$ limits and eliminating continuous moduli via fuzzy compactifications. The paper develops a holographic model of inflation (HEI) with no fundamental inflaton, where $e^{3N_e}$ copies of horizon-volume degrees of freedom generate approximately scale-invariant, near-Bunch-Davies fluctuations, and a subsequent transition to a final de Sitter phase; bulk EFT is emergent and thermodynamic rather than fundamental. It further constructs a DBHF-to-dS cosmology, embedding a dS interior within a larger FRW universe, and shows how localized excitations and fluctuations arise from horizon dynamics and transition timings. The framework offers an anthropic/thermodynamic account of the observed small cosmological constant and low initial entropy, while addressing Boltzmann brain concerns within a finite, time-dependent Hamiltonian theory, and lays out a path toward connecting early-universe holography with late-time dS physics. Overall, the work presents a self-consistent holographic cosmology that integrates inflation, fluctuations, gravity, and entropy bounds without invoking a fundamental inflaton field or spacetime quantization at the Planck scale.

Abstract

The theory of holographic space-time (HST) generalizes both string theory and quantum field theory. It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of non-commutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite dimensional unitary representations of super- algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-Poincare invariant limits in which the number of holographic degrees of freedom goes to infinity. Finite radius de Sitter (dS) spaces have no moduli, and break SUSY with a gravitino mass scaling like $Λ^{1/4}$. We present a holographic theory of inflation and fluctuations. The inflaton field is an emergent concept, describing the geometry of an underlying HST model, rather than "a field associated with a microscopic string theory". We argue that the phrase in quotes is meaningless in the HST formalism.

Figures (1)

• Figure 1: Schematic relation between the different cosmological models. The left chart shows 3 models satisfying all the rules of HST. The infinite DBHF and HEI models, and the black hole in the DBHF, with a dS interior. The right chart is our heuristic idea of how these models are put together to make a more realistic cosmology in which an early era of inflation generates localized excitations in a dS universe, which is embedded in a DBHF-dS multiverse.