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arxiv: 2606.03408 · v1 · pith:SEMK7TEJnew · submitted 2026-06-02 · 🌀 gr-qc

Models of exponential and power-law acceleration of the Universe in Horndeski theory without ghosts and Laplace instabilities

Ruslan K. Muharlyamov , Tatiana N. Pankratyeva , Shehabaldeen O.A. Bashir This is my paper

Pith reviewed 2026-06-28 09:07 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Horndeski theoryghostsLaplace instabilitiesexponential inflationpower-law accelerationdesigner methodFRW spacetimescalar-tensor theory
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The pith

Designer method finds Horndeski subclasses for stable exponential and power-law cosmic acceleration.

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

The paper presents a designer method for flat FRW spacetimes in Horndeski scalar-tensor theory. The method constructs subclasses of the theory that admit cosmological solutions matching given expansion histories while remaining free of ghosts and Laplace instabilities. Concrete examples are constructed for exponential inflation and power-law acceleration of the universe. A sympathetic reader would care because these examples demonstrate how to build healthy modified gravity models that reproduce observed cosmic acceleration without introducing unphysical instabilities.

Core claim

The authors introduce a designer method within Horndeski's scalar-tensor theory for flat FRW spacetimes. This allows selection of theory functions such that cosmological solutions for exponential and power-law inflation exist without ghosts and Laplace instabilities, providing explicit subclasses of the theory free from these pathologies.

What carries the argument

The designer method applied to flat FRW spacetimes to select Horndeski functions ensuring no ghosts or Laplace instabilities for target expansion histories.

If this is right

  • Subclasses of Horndeski theory support exponential inflation without ghosts or Laplace instabilities.
  • Subclasses support power-law inflation models without these instabilities.
  • The method provides a systematic way to build stable cosmological solutions in Horndeski theory for flat universes.

Where Pith is reading between the lines

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

  • The derived models may be used to study how scalar field dynamics affects the duration of inflation.
  • Similar designer techniques could be applied to other spacetime symmetries beyond flat FRW.
  • Observational constraints on the expansion history could further restrict the allowed Horndeski functions.

Load-bearing premise

The designer method succeeds in selecting Horndeski functions that eliminate ghosts and Laplace instabilities for the desired flat FRW expansion histories.

What would settle it

An explicit computation for one of the constructed models showing that the no-ghost condition fails or that the Laplacian instability appears at some epoch during the expansion.

read the original abstract

We present a designer method for flat Friedman-Robertson-Walker space-times within the framework of Horndeski's scalar-tensor theory. As a result, one can find subclasses of Horndeski's scalar-tensor theory within which cosmological solutions exist without ghosts and Laplace instabilities. As an example, we found subclasses of Horndeski's theory for exponential and power-law inflation models of the Universe without pathologies.

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

0 major / 1 minor

Summary. The manuscript introduces a designer method to construct subclasses of Horndeski scalar-tensor theory supporting flat FRW solutions with prescribed exponential or power-law expansion histories that are free of ghosts and Laplace instabilities, and supplies explicit examples of such subclasses for inflation models.

Significance. If the constructions are verified to satisfy the no-ghost and no-gradient conditions along the target trajectories, the work supplies concrete, stable Horndeski models for cosmic acceleration. The designer approach itself is a reproducible tool for generating healthy modified-gravity cosmologies, which strengthens its utility beyond the specific exponential and power-law cases presented.

minor comments (1)
  1. The abstract is terse; a brief statement in the introduction or conclusion summarizing the explicit G_i(φ,X) forms obtained would improve accessibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of the designer method, and recommendation to accept. No major comments were raised that require addressing.

Circularity Check

0 steps flagged

No significant circularity; designer construction is self-contained

full rationale

The paper applies the standard designer approach: prescribe a(t) for exponential or power-law expansion, solve the background equations for the Horndeski G_i(φ,X) functions, then impose the independent no-ghost and no-Laplace-instability conditions on the quadratic action for perturbations. This is a constructive existence proof with external stability criteria that do not reduce to the input a(t) by definition. No self-citations, fitted parameters renamed as predictions, or ansatz smuggling are indicated in the provided text. The derivation chain remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. Typical Horndeski constructions involve arbitrary functions of the scalar field and its derivatives that are constrained by the designer method.

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Reference graph

Works this paper leans on

68 extracted references · 4 canonical work pages · 2 internal anchors

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