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arxiv: 2604.25918 · v2 · submitted 2026-04-28 · ✦ hep-th

Recognition: unknown

de Sitter in String Theory vs. Gibbons & Hawking

Yoav Zigdon
Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:32 UTC · model grok-4.3

classification ✦ hep-th
keywords de Sitter spacetimestring theoryGibbons-Hawking entropysphere partition functioneffective actionEuclidean quantum gravityperturbative expansion
0
0 comments X

The pith

Perturbative string theory forbids de Sitter times closed manifold solutions to all orders under the Gibbons-Hawking assumption

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that perturbative string theory admits no solution whose metric is de Sitter times a closed manifold, and that this holds through every order in the alpha-prime and string-coupling expansions. The argument rests on the fact that the tree-level effective action vanishes for any closed Euclidean target space, a result obtained by several independent routes to the same effective action. A reader would care because the conclusion implies that the universe cannot settle into an asymptotically de Sitter state at late times. The link to the Gibbons-Hawking proposal enters through the assumption that the logarithm of the sphere partition function acquires a nonzero term proportional to one over Newton's constant in the saddle-point approximation.

Core claim

Perturbative string theory does not admit a solution whose spacetime metric is de Sitter times a closed manifold, to all orders in the α' and g_s expansions, under the assumption that the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to 1/G_N in a saddle-point approximation. Evidence comes from independent approaches to the effective action of string theory, all of which agree that the tree-level action vanishes for closed Euclidean target-space solutions. One possible implication is that the state of the Universe will depart from an asymptotically de Sitter spacetime.

What carries the argument

The tree-level term in the string effective action, which vanishes for any closed Euclidean target space, together with the saddle-point contribution to the sphere partition function.

If this is right

  • The prohibition on de Sitter times closed manifold holds at every order in the α' and g_s expansions.
  • Several independent derivations of the string effective action all yield the same vanishing tree-level term for closed Euclidean targets.
  • The late-time state of the universe must depart from an asymptotically de Sitter spacetime.
  • The result stands or falls with the Gibbons-Hawking relation between horizon area and entropy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the assumption fails, de Sitter solutions could still appear once non-perturbative effects are included.
  • The same vanishing action may constrain other constant-curvature backgrounds in string theory.
  • Late-time cosmology would then require a dynamical mechanism that drives the universe away from de Sitter.

Load-bearing premise

The logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to 1/G_N in the saddle-point approximation.

What would settle it

A direct evaluation of the sphere partition function that finds no term in its logarithm proportional to 1/G_N, or an explicit construction of a de Sitter times closed manifold solution whose tree-level effective action does not vanish.

read the original abstract

This paper corroborates a statement that perturbative string theory does not admit a solution whose spacetime metric is de Sitter times a closed manifold, to all orders in the $\alpha'$ and $g_s$ expansions, under the assumption that the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to $\frac{1}{G_N}$ in a saddle-point approximation. This assumption is related to the Gibbons-Hawking proposal that the entropy of the cosmological horizon of the static patch is $\frac{A}{4G_N}$. Evidence for the statement comes from independent approaches to the effective action of string theory, all of which agree that the tree-level action vanishes for closed Euclidean target-space solutions. One possible implication is that the state of the Universe will depart from an asymptotically de Sitter spacetime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that perturbative string theory does not admit a solution whose spacetime metric is de Sitter times a closed manifold, to all orders in the α' and g_s expansions, under the assumption that the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to 1/G_N in a saddle-point approximation (related to the Gibbons-Hawking entropy proposal A/4G_N). Evidence is drawn from independent effective-action derivations agreeing that the tree-level action vanishes for closed Euclidean target-space solutions. One possible implication is that the state of the Universe will depart from an asymptotically de Sitter spacetime.

Significance. If the central claim holds, the result would constitute a conditional no-go theorem for de Sitter compactifications in perturbative string theory, with direct relevance to string cosmology and the viability of de Sitter backgrounds. It synthesizes existing tree-level calculations across approaches and could sharpen discussions on whether string theory permits stable late-time acceleration under the stated partition-function assumption. The conditional framing and external assumption limit broader impact unless the assumption is independently validated.

major comments (1)
  1. Abstract and introduction: the all-orders claim (no de Sitter × closed manifold solutions in α' and g_s expansions) rests on tree-level vanishing of the effective action, but the manuscript provides no explicit argument or derivation showing why α' corrections (e.g., curvature-squared terms) or g_s loop effects cannot produce a nonzero on-shell action whose saddle satisfies the assumed nonzero log Z ~ 1/G_N contribution. The tree-level agreement alone does not preclude such terms from yielding a consistent nonzero saddle.
minor comments (2)
  1. The abstract refers to 'independent approaches' without naming them or citing the specific calculations; adding explicit references in the introduction would improve traceability.
  2. Notation for the partition-function assumption (log Z proportional to 1/G_N) could be introduced with a brief equation in §1 to make the saddle-point approximation precise for readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and will revise the manuscript to clarify the scope of our claims.

read point-by-point responses

  1. Referee: Abstract and introduction: the all-orders claim (no de Sitter × closed manifold solutions in α' and g_s expansions) rests on tree-level vanishing of the effective action, but the manuscript provides no explicit argument or derivation showing why α' corrections (e.g., curvature-squared terms) or g_s loop effects cannot produce a nonzero on-shell action whose saddle satisfies the assumed nonzero log Z ~ 1/G_N contribution. The tree-level agreement alone does not preclude such terms from yielding a consistent nonzero saddle.

    Authors: We agree that the manuscript's all-orders claim rests on the tree-level vanishing of the effective action for closed Euclidean target-space solutions, as established by multiple independent derivations, without an explicit argument showing why α' corrections or g_s loop effects cannot produce a nonzero on-shell action consistent with the log Z assumption. In the revised version, we will update the abstract and introduction to qualify the claim: the no-go holds at tree level, with the extension to all orders being conditional on higher-order terms not generating a saddle that satisfies the nonzero 1/G_N contribution to log Z. This makes the conditional framing explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: central claim is conditional on external assumption with independent tree-level evidence

full rationale

The paper explicitly conditions its no-de-Sitter statement on the external Gibbons-Hawking-related assumption that log Z receives a nonzero 1/G_N saddle contribution. Supporting evidence is drawn from multiple independent approaches to the string effective action agreeing that the tree-level action vanishes for closed Euclidean solutions. No derivation step reduces a claimed prediction to a fitted parameter by construction, renames a known result, or relies on a self-citation chain whose load-bearing content is unverified within the paper. The all-orders extension in α' and g_s is presented as following from the tree-level agreement under the stated assumption rather than from any internal redefinition or smuggling of ansatze.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The entire claim rests on one external domain assumption about the sphere partition function; no free parameters are fitted and no new entities are postulated.

axioms (1)
  • domain assumption the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to 1/G_N in a saddle-point approximation
    This is the explicit assumption on which the no-de-Sitter statement is conditioned and is tied directly to the Gibbons-Hawking entropy proposal.

pith-pipeline@v0.9.0 · 5424 in / 1351 out tokens · 61998 ms · 2026-05-07T15:32:36.891567+00:00 · methodology

discussion (0)

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Reference graph

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