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Inflation and Holography in String Theory

Bruno Carneiro da Cunha

TL;DR

The paper investigates whether inflationary patches and cosmological horizons can be encoded holographically within string theory via Bousso's covariant holographic screens. Using deformations of AdS/CFT backgrounds (notably D1-D5 with AdS$_3\times$S$^3$, and AdS$_5\times$S$^5$ and AdS$_7\times$S$^4$ cases), it derives lower-dimensional effective theories and analyzes horizon formation through dynamics akin to the Raychaudhuri equation. The central finding is that these symmetric backgrounds do not produce inflationary horizons; the evolution tends toward AdS with no cosmological horizon, implying that a dual description for bulk regions behind horizons may require density matrices rather than pure states. The results underscore the tension between holographic descriptions and cosmological inflation in standard string constructions and motivate exploration of less symmetric or non-perturbative backgrounds to realize holographic inflation.

Abstract

The encoding of an inflating patch of space-time in terms of a dual theory is discussed. Following Bousso's interpretation of the holographic principle, we find that those are generically described not by states in the dual theory but by density matrices. We try to implement this idea on simple deformations of the AdS/CFT examples, and an argument is given as to why inflation is so elusive to string theory.

Inflation and Holography in String Theory

TL;DR

The paper investigates whether inflationary patches and cosmological horizons can be encoded holographically within string theory via Bousso's covariant holographic screens. Using deformations of AdS/CFT backgrounds (notably D1-D5 with AdSS, and AdSS and AdSS cases), it derives lower-dimensional effective theories and analyzes horizon formation through dynamics akin to the Raychaudhuri equation. The central finding is that these symmetric backgrounds do not produce inflationary horizons; the evolution tends toward AdS with no cosmological horizon, implying that a dual description for bulk regions behind horizons may require density matrices rather than pure states. The results underscore the tension between holographic descriptions and cosmological inflation in standard string constructions and motivate exploration of less symmetric or non-perturbative backgrounds to realize holographic inflation.

Abstract

The encoding of an inflating patch of space-time in terms of a dual theory is discussed. Following Bousso's interpretation of the holographic principle, we find that those are generically described not by states in the dual theory but by density matrices. We try to implement this idea on simple deformations of the AdS/CFT examples, and an argument is given as to why inflation is so elusive to string theory.

Paper Structure

This paper contains 7 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Holographic Screens
  3. Deformations of the background
  4. Inflation?
  5. Other Examples
  6. $\hbox{AdS}_5\times\hbox{S}^5$
  7. $\hbox{AdS}_7\times\hbox{S}^4$

Figures (2)

  • Figure 1: The Penrose diagram for the maximally extended Schwarzchild-AdS solution. The thicker vertical lines represent the holographic screens. Holography tells us that a state $P$ inside the black hole can be immersed into either Hilbert space ${\cal H}_1$ or ${\cal H}_2$.
  • Figure 2: The birth of a child-universe in AdS space. A domain wall separates the expanding region (to the left) to the vacuum Schwarzchild solution (right). The holographic screens are represented in thicker lines.