arxiv: 2603.04712 · v3 · submitted 2026-03-05 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Emergent inflation in fractional cosmology

S. M. M. Rasouli

Authors on Pith no claims yet

Pith reviewed 2026-05-15 16:16 UTC · model grok-4.3

classification 🌀 gr-qc

keywords fractional cosmologyemergent inflationgeneralized measurespre-inflationary regimestable attractore-foldsgraceful exitradiation domination

0 comments

The pith

A fractional potential in generalized cosmology lets inflation emerge dynamically from a non-singular pre-inflationary phase as a stable attractor without any external scalar field.

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

The paper constructs a fractional potential inside a generalized measure framework to drive the early universe. Cosmological evolution begins in a non-singular pre-inflationary regime, after which inflation appears naturally and remains stable, resembling plateau-type models. The dynamics fix the end of inflation and tie the number of e-folds directly to the fractional parameter alpha, satisfying observational constraints and resolving the horizon problem. The model then exits inflation into an exact radiation-dominated phase whose time dependence is standard but whose normalization depends on alpha.

Core claim

Within the emergent fractional cosmological framework rooted in generalized measures, a suitably chosen fractional potential produces non-singular pre-inflationary evolution; inflation then arises dynamically without an external scalar field, functions as a stable attractor with plateau-like behavior, yields an alpha-dependent e-fold count consistent with observations, solves the horizon problem, and permits a graceful exit into radiation domination with standard time dependence but alpha-dependent normalization.

What carries the argument

The fractional potential constructed inside the generalized measure framework, which supplies the dynamical mechanism that turns inflation into a stable attractor.

If this is right

Inflation ends at a definite time set by the dynamics and hands over to radiation domination with standard time scaling.
The total number of e-folds is fixed by the value of the fractional parameter alpha.
The horizon problem is solved because the pre-inflationary phase plus the attractor behavior stretches causal regions sufficiently.
The radiation era that follows has the usual a proportional to t to the 1/2 scaling but carries an alpha-dependent prefactor.

Where Pith is reading between the lines

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

If the fractional parameter alpha can be linked to measurable late-time quantities, the model might predict new relations between early-universe observables and present-day cosmology.
The same construction could be tested by checking whether the predicted exit from inflation produces the observed amplitude of primordial perturbations for a narrow range of alpha.
Extending the framework to include spatial curvature or matter fields would show whether the non-singular start remains robust.

Load-bearing premise

A suitable fractional potential can be chosen inside the generalized measure framework so that inflation becomes a stable attractor whose e-fold count follows directly from the dynamics.

What would settle it

A concrete calculation or numerical integration showing that no choice of the fractional potential produces both a stable inflationary attractor and an alpha-dependent e-fold number that matches the observed horizon scale.

Figures

Figures reproduced from arXiv: 2603.04712 by S. M. M. Rasouli.

**Figure 1.** Figure 1: The α-dependent potential Φα(a) (left panel) and the corresponding effective force F (a) (right panel) as functions of the scale factor. The solid and the dashed curves correspond to Φ0 = 1/6 and Φ0 = 1/12, respectively, and we have set p = 4, ac = 1. Let us be more precise. In order to propose a suitable form of F (a) that satisfies the criteria mentioned above, we assume a constant characteristic scale f… view at source ↗

read the original abstract

In this paper, we investigate the evolution of the early universe within an emergent fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal geometries and scale-dependent effective dimensions. By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor, exhibiting similarities with plateau-type inflationary scenarios. By analyzing the dynamical transition, we determine the end of inflation and establish a meaningful relation between the number of e-folds and the fractional parameter $\alpha$, ensuring consistency with observations and addressing the horizon problem. Moreover, the model admits a graceful exit from inflation, followed by an exact radiation-dominated solution with the standard time dependence and an $\alpha$-dependent normalization.

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.

Desk Editor's Note private letter to a colleague

The paper gets inflation as a stable attractor from a fractional potential in generalized measures without an external scalar, and ties e-folds to α, but the potential is constructed to produce those features rather than fixed by the framework.

read the letter

The main takeaway is that this work builds a fractional potential inside a generalized measure to drive early-universe evolution from a non-singular phase, with inflation emerging as an attractor that resembles plateau models. It then links the number of e-folds directly to the fractional parameter α and shows a clean exit to radiation with standard time dependence but α-dependent normalization. That gives a single-parameter handle on the horizon problem and avoids adding a separate inflaton field, which is the concrete novelty here. The dynamical transition and the exact post-inflation solution are worked out explicitly enough to be testable in principle. The soft spot is the potential itself. The abstract and setup describe it as “constructed” to achieve the attractor and the α-e-fold relation, so it is not obvious whether the form follows uniquely from the fractional measure or is chosen to make the desired behavior happen. If the latter, the “emergent” and “natural” language overstates what is shown, and the observational consistency may rest on that choice rather than on the measure alone. No uniqueness argument or first-principles derivation of the potential is indicated, which leaves the stability claim and graceful exit harder to assess without the full equations. This is worth a look for people already working on fractional or fractal-inspired cosmologies who want an alternative to scalar-driven inflation. A reader looking for new mechanisms with few free parameters could extract the α-e-fold relation and check it against data. The internal logic holds together on the surface, but the derivations need referee scrutiny for robustness. Send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper explores emergent inflation within a fractional cosmological model based on generalized measure constructions related to fractal geometries. By constructing a suitable fractional potential, it claims that the cosmological evolution originates from a non-singular pre-inflationary regime, with inflation arising dynamically as a stable attractor without an external scalar field and exhibiting similarities to plateau-type scenarios. The work derives a relation between the number of e-folds and the fractional parameter α that addresses the horizon problem consistently with observations, and demonstrates a graceful exit to an exact radiation-dominated solution with standard time dependence but α-dependent normalization.

Significance. If the fractional potential follows from the generalized measure rather than being an ad-hoc choice, and if the attractor behavior and e-fold relation are derived directly from the dynamics, this could represent a meaningful alternative to standard scalar-field inflation by naturally incorporating non-singularity and graceful exit. The link to scale-dependent effective dimensions offers a potentially novel perspective on early-universe dynamics. The significance hinges on demonstrating that these features are not engineered into the potential but emerge from the framework.

major comments (2)

[Section defining the fractional potential] In the section defining the fractional potential, the potential is introduced as 'constructed' to achieve the non-singular pre-inflationary regime and stable attractor behavior. The manuscript should explicitly show whether this specific form is uniquely fixed by the generalized measure (e.g., via the modified action or measure) or selected as an ansatz to produce the desired dynamics; without this, the claims of 'natural' emergence and 'dynamical' origin of inflation rest on a potentially circular construction.
[Analysis of dynamical transition and e-folds] In the analysis of the dynamical transition and e-fold count, the relation between the number of e-folds and α is presented as following from the equations and ensuring observational consistency. It must be demonstrated that this relation is derived independently from the fractional dynamics rather than adjusted to fit the horizon-problem resolution; otherwise the central claim that inflation 'addresses the horizon problem' risks being an artifact of the potential choice.

minor comments (2)

[Introduction] A short recap of the generalized measure framework and its relation to fractional derivatives would improve accessibility for readers outside the immediate subfield.
[Figures and dynamical systems analysis] Phase-space plots and potential figures should explicitly indicate the range of α values shown and label the attractor fixed points for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and valuable comments. We have carefully considered the points raised regarding the motivation of the fractional potential and the derivation of the e-fold relation. We provide point-by-point responses below and indicate the revisions we plan to make.

read point-by-point responses

Referee: In the section defining the fractional potential, the potential is introduced as 'constructed' to achieve the non-singular pre-inflationary regime and stable attractor behavior. The manuscript should explicitly show whether this specific form is uniquely fixed by the generalized measure (e.g., via the modified action or measure) or selected as an ansatz to produce the desired dynamics; without this, the claims of 'natural' emergence and 'dynamical' origin of inflation rest on a potentially circular construction.

Authors: The fractional potential is selected as an ansatz within the generalized measure framework to realize the desired non-singular pre-inflationary behavior and stable attractor. It is not claimed to be the unique form fixed by the measure, but rather a physically motivated choice consistent with the scale-dependent dimensions in fractional cosmology. In the revised manuscript, we will add a dedicated subsection explaining the rationale for this potential form, referencing how it aligns with the modified action and fractal geometry considerations. This will clarify that the emergence is dynamical once the potential is set, without circularity. revision: partial
Referee: In the analysis of the dynamical transition and e-fold count, the relation between the number of e-folds and α is presented as following from the equations and ensuring observational consistency. It must be demonstrated that this relation is derived independently from the fractional dynamics rather than adjusted to fit the horizon-problem resolution; otherwise the central claim that inflation 'addresses the horizon problem' risks being an artifact of the potential choice.

Authors: We agree that it is important to show the independence of the derivation. The relation N(α) is obtained by solving the fractional Friedmann equations and integrating the Hubble parameter over the inflationary epoch, as detailed in our dynamical analysis. The value of α is then chosen to yield sufficient e-folds (N > 60) to solve the horizon problem, which is a standard procedure in inflationary models. In the revision, we will include the explicit integral expression for N in terms of α and the potential parameters to demonstrate that it follows directly from the dynamics. This makes the addressing of the horizon problem a consequence of the model parameters rather than an ad hoc adjustment. revision: yes

Circularity Check

1 steps flagged

Suitable fractional potential constructed to enforce attractor and e-fold relation

specific steps

self definitional [Abstract]
"By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor, exhibiting similarities with plateau-type inflationary scenarios. By analyzing the dynamical transition, we determine the end of inflation and establish a meaningful relation between the number of e-folds and the fractional parameter α, ensuring consistency with observations and addressing the horizon problem."

The potential is introduced as 'suitable' precisely to generate the non-singular regime, attractor behavior, and α–e-fold relation that 'ensures consistency with observations.' The claimed first-principles emergence therefore reduces to the input choice of potential form; the subsequent dynamical analysis and 'meaningful relation' are then computed from that same choice.

full rationale

The derivation begins by positing a generalized measure framework but then explicitly constructs a 'suitable' fractional potential chosen to produce non-singular pre-inflationary evolution, dynamic inflation as a stable attractor without external scalar, and an α-dependent e-fold count that matches observations. This makes the emergence and the e-fold–α relation artifacts of the potential choice rather than independent outputs of the measure equations. The graceful exit to radiation is shown after this choice, but the load-bearing step remains the tailored ansatz. No self-citation chain or external uniqueness theorem is invoked in the provided text, so circularity is partial rather than total.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the existence of a suitable fractional potential inside a generalized measure framework; α functions as a free parameter that is adjusted for observational consistency.

free parameters (1)

fractional parameter α
Controls the number of e-folds and the normalization of the radiation era; chosen to ensure consistency with observations.

axioms (1)

domain assumption Generalized measure constructions closely related to fractal geometries and scale-dependent effective dimensions form the underlying formulation.
Stated as the conceptual root of the fractional cosmological framework.

invented entities (1)

fractional potential no independent evidence
purpose: To drive the non-singular pre-inflationary evolution and produce inflation as a stable attractor.
Introduced by the authors to realize the claimed dynamics.

pith-pipeline@v0.9.0 · 5426 in / 1346 out tokens · 47807 ms · 2026-05-15T16:16:32.366493+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

?

contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration contradicts

?

contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

the fractional parameter α ... |α-1| ≪ 1 ... N ≃ 50-60

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Evolution of density perturbations in fractional cosmology
gr-qc 2026-03 unverdicted novelty 6.0

Fractional cosmology modifies density perturbation growth via parameter α, yielding a new upper bound α ≲ 1.07 from σ8 normalization and Sachs-Wolfe constraints.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · cited by 1 Pith paper · 4 internal anchors

[1]

Inflationary universe: A possible solution to the horizon and flatness prob- lems.Physical Review D, 23(2):347, 1981

Alan H Guth. Inflationary universe: A possible solution to the horizon and flatness prob- lems.Physical Review D, 23(2):347, 1981

work page 1981
[2]

The inflationary universe.Scientific American, 250(5): 116–129, 1984

Alan H Guth and Paul J Steinhardt. The inflationary universe.Scientific American, 250(5): 116–129, 1984

work page 1984
[3]

Classical and quantum cosmology of the starobinsky inflationary model.Physical Review D, 32(10):2511, 1985

Alexander Vilenkin. Classical and quantum cosmology of the starobinsky inflationary model.Physical Review D, 32(10):2511, 1985

work page 1985
[4]

Hybrid inflation.Physical Review D, 49(2):748, 1994

Andrei Linde. Hybrid inflation.Physical Review D, 49(2):748, 1994

work page 1994
[5]

k-inflation

Christian Armendariz-Picon, Thibault Damour, and VF1999PhLB Mukhanov. k-inflation. Physics Letters B, 458(2-3):209–218, 1999

work page 1999
[6]

Inflation and eternal inflation.Physics Reports, 333:555–574, 2000

Alan H Guth. Inflation and eternal inflation.Physics Reports, 333:555–574, 2000

work page 2000
[7]

Inflationary cosmology.Physica Scripta, 2000(T85):168–176, 2000

Andrei Linde. Inflationary cosmology.Physica Scripta, 2000(T85):168–176, 2000

work page 2000
[8]

On natural inflation.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 70(8):083512, 2004

Katherine Freese and William H Kinney. On natural inflation.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 70(8):083512, 2004

work page 2004
[9]

New models of chaotic inflation in supergravity.journal of Cosmology and Astroparticle Physics, 2010(11):011–011, 2010

Renata Kallosh and Andrei Linde. New models of chaotic inflation in supergravity.journal of Cosmology and Astroparticle Physics, 2010(11):011–011, 2010

work page 2010
[10]

Inflation and fractional quantum cosmology.Fractal and Fractional, 6(11): 655, 2022

Seyed Meraj Mousavi Rasouli, Emanuel W de Oliveira Costa, Paulo Moniz, and Shahram Jalalzadeh. Inflation and fractional quantum cosmology.Fractal and Fractional, 6(11): 655, 2022

work page 2022
[11]

Encyclopædia inflationaris: Opi- parous edition.Physics of the Dark Universe, 46:101653, 2024

Jerome Martin, Christophe Ringeval, and Vincent Vennin. Encyclopædia inflationaris: Opi- parous edition.Physics of the Dark Universe, 46:101653, 2024

work page 2024
[12]

A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems.Physics Letters B, 108 (6):389–393, 1982

Andrei D Linde. A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems.Physics Letters B, 108 (6):389–393, 1982

work page 1982
[13]

Eternal extended inflation and graceful exit from old inflation without jordan- brans-dicke.Physics Letters B, 249(1):18–26, 1990

Andrei Linde. Eternal extended inflation and graceful exit from old inflation without jordan- brans-dicke.Physics Letters B, 249(1):18–26, 1990

work page 1990
[14]

Horizon problem remediation via deformed phase space.General Relativity and Gravitation, 43(10):2895–2910, 2011

SMM Rasouli, Mehrdad Farhoudi, and Nima Khosravi. Horizon problem remediation via deformed phase space.General Relativity and Gravitation, 43(10):2895–2910, 2011

work page 2011
[15]

About jordan and einstein frames: a study in inflationary magnetogenesis.Universe, 10(9):350, 2024

Joel Velásquez, Héctor J Hortua, and Leonardo Castañeda. About jordan and einstein frames: a study in inflationary magnetogenesis.Universe, 10(9):350, 2024

work page 2024
[16]

Cosmological perturbations from inflation.Journal of Physics A: Math- ematical and Theoretical, 40(25):6561–6572, 2007

Slava Mukhanov. Cosmological perturbations from inflation.Journal of Physics A: Math- ematical and Theoretical, 40(25):6561–6572, 2007

work page 2007
[17]

Evolution of gravitational perturbations in non- commutative inflation.Journal of Cosmology and Astroparticle Physics, 2007(11):013– 013, 2007

Seoktae Koh and Robert H Brandenberger. Evolution of gravitational perturbations in non- commutative inflation.Journal of Cosmology and Astroparticle Physics, 2007(11):013– 013, 2007. 20

work page 2007
[18]

TASI Lectures on Inflation

Daniel Baumann. Tasi lectures on inflation.arXiv preprint arXiv:0907.5424, 2009

work page internal anchor Pith review Pith/arXiv arXiv 2009
[19]

Inflation and cosmological perturbations

David Langlois. Inflation and cosmological perturbations. InLectures on Cosmology: Accelerated Expansion of the Universe, pages 1–57. Springer, 2010

work page 2010
[20]

Brandenberger

Robert H. Brandenberger. Principles, progress and problems in inflationary cosmology. AAPPS Bull., 11:20–29, 2001

work page 2001
[21]

Inflationary paradigm in trouble after planck2013.Physics Letters B, 723(4-5):261–266, 2013

Anna Ijjas, Paul J Steinhardt, and Abraham Loeb. Inflationary paradigm in trouble after planck2013.Physics Letters B, 723(4-5):261–266, 2013

work page 2013
[22]

Gravity-Driven Acceleration and Kinetic Inflation in Noncommutative Brans-Dicke Setting

SMM Rasouli and Paulo Vargas Moniz. Gravity-driven acceleration and kinetic inflation in noncommutative brans-dicke setting.arXiv preprint arXiv:1611.00085, 2016

work page internal anchor Pith review Pith/arXiv arXiv 2016
[23]

Phase space noncommutativity, power-law inflation and quantum cosmology.Chaos, Solitons&Fractals, 187:115349, 2024

SMM Rasouli and João Marto. Phase space noncommutativity, power-law inflation and quantum cosmology.Chaos, Solitons&Fractals, 187:115349, 2024

work page 2024
[24]

Kinetic inflation in de- formed phase space brans–dicke cosmology.Physics of the Dark Universe, 24:100269, 2019

Seyed Meraj Mousavi Rasouli, João Marto, and P Vargas Moniz. Kinetic inflation in de- formed phase space brans–dicke cosmology.Physics of the Dark Universe, 24:100269, 2019

work page 2019
[25]

Noncommutativity and its role in constant-roll inflation models with non-minimal coupling constrained by swampland conjectures.Chinese Physics C, 49(2):025108, 2025

Saeed Noori Gashti, Mohammad Reza Alipour, Mohammad Ali S Afshar, and Jafar Sadeghi. Noncommutativity and its role in constant-roll inflation models with non-minimal coupling constrained by swampland conjectures.Chinese Physics C, 49(2):025108, 2025

work page 2025
[26]

Chaotic inflation.Physics Letters B, 129(3-4):177–181, 1983

Andrei D Linde. Chaotic inflation.Physics Letters B, 129(3-4):177–181, 1983

work page 1983
[27]

Cosmology of the very early universe

Robert H Brandenberger. Cosmology of the very early universe. InAIP conference pro- ceedings, volume 1268, pages 3–70. American Institute of Physics, 2010

work page 2010
[28]

Inflationary spacetimes are incom- plete in past directions.Physical review letters, 90(15):151301, 2003

Arvind Borde, Alan H Guth, and Alexander Vilenkin. Inflationary spacetimes are incom- plete in past directions.Physical review letters, 90(15):151301, 2003

work page 2003
[29]

Planck 2018 results

PD Meerburg, Planck Collaboration, et al. Planck 2018 results. x. constraints on inflation. Astronomy&Astrophysics, 641:A10, 2020

work page 2018
[30]

A new type of isotropic cosmological models without singularity

Alexei A Starobinsky. A new type of isotropic cosmological models without singularity. Physics Letters B, 91(1):99–102, 1980

work page 1980
[31]

Nonlocal cosmology.Physical Review Letters, 99 (11):111301, 2007

Stanley Deser and Richard P Woodard. Nonlocal cosmology.Physical Review Letters, 99 (11):111301, 2007

work page 2007
[32]

The effective field theory of inflation.Journal of High Energy Physics, 2008(03): 014–014, 2008

Clifford Cheung, A Liam Fitzpatrick, Jared Kaplan, Leonardo Senatore, and Paolo Crem- inelli. The effective field theory of inflation.Journal of High Energy Physics, 2008(03): 014–014, 2008

work page 2008
[33]

Introduction to multifractional spacetimes

Gianluca Calcagni. Introduction to multifractional spacetimes. InAIP Conference Pro- ceedings, volume 1483, pages 31–53. American Institute of Physics, 2012

work page 2012
[34]

Classical and quantum gravity with fractional operators.Classical and Quantum Gravity, 38(16):165005, 2021

Gianluca Calcagni. Classical and quantum gravity with fractional operators.Classical and Quantum Gravity, 38(16):165005, 2021. 21

work page 2021
[35]

Constant-roll inflation in f (r) gravity.Classical and Quantum Gravity, 34(24):245012, 2017

S Nojiri, SD Odintsov, and VK Oikonomou. Constant-roll inflation in f (r) gravity.Classical and Quantum Gravity, 34(24):245012, 2017

work page 2017
[36]

Fractional einstein–hilbert action cosmology.Modern Physics Letters A, 28(14):1350056, 2013

VK Shchigolev. Fractional einstein–hilbert action cosmology.Modern Physics Letters A, 28(14):1350056, 2013

work page 2013
[37]

Broadening quantum cosmology with a frac- tional whirl.Modern Physics Letters A, 36(14):2140005, 2021

SMM Rasouli, S Jalalzadeh, and PV Moniz. Broadening quantum cosmology with a frac- tional whirl.Modern Physics Letters A, 36(14):2140005, 2021

work page 2021
[38]

Exact solutions and cosmological constraints in fractional cosmology.Fractal and Fractional, 7(5):368, 2023

Esteban González, Genly Leon, and Guillermo Fernandez-Anaya. Exact solutions and cosmological constraints in fractional cosmology.Fractal and Fractional, 7(5):368, 2023

work page 2023
[39]

Quantum fractionary cosmology: K-essence theory.Uni- verse, 9(4):185, 2023

J Socorro and J Juan Rosales. Quantum fractionary cosmology: K-essence theory.Uni- verse, 9(4):185, 2023

work page 2023
[40]

Modified friedmann equations from frac- tional entropy.Europhysics Letters, 143(5):59001, 2023

Zeynep Çoker, Özgür Ökcü, and Ekrem Aydiner. Modified friedmann equations from frac- tional entropy.Europhysics Letters, 143(5):59001, 2023

work page 2023
[41]

Quantum tunneling from family of cantor potentials in fractional quantum mechanics

Vibhav Narayan Singh, Mohammad Umar, Mohammad Hasan, and Bhabani Prasad Man- dal. Quantum tunneling from family of cantor potentials in fractional quantum mechanics. Annals of Physics, 450:169236, 2023

work page 2023
[42]

Rami Ahmad El-Nabulsi and Waranont Anukool. Constraining the fractal chern–simons modified gravity with astronomical observations and estimation of the fractal dimension of the universe.The European Physical Journal Plus, 139(4):342, 2024

work page 2024
[43]

Friedmann equations of the fractal apparent horizon.Physics of the Dark Universe, 44:101498, 2024

R Jalalzadeh, S Jalalzadeh, A Sayahian Jahromi, and H Moradpour. Friedmann equations of the fractal apparent horizon.Physics of the Dark Universe, 44:101498, 2024

work page 2024
[44]

Quantum creation of a frw universe: applying the riesz fractional derivative.arXiv preprint arXiv:2503.15348, 2025

DL Canedo, P Moniz, and G Oliveira-Neto. Quantum creation of a frw universe: applying the riesz fractional derivative.arXiv preprint arXiv:2503.15348, 2025

work page arXiv 2025
[45]

Cosmology under the fractional calculus approach.Monthly Notices of the Royal Astronomical Society, 517(4):4813–4826, 2022

Miguel A García-Aspeitia, Guillermo Fernandez-Anaya, A Hernández-Almada, Genly Leon, and Juan Magaña. Cosmology under the fractional calculus approach.Monthly Notices of the Royal Astronomical Society, 517(4):4813–4826, 2022

work page 2022
[46]

Revisiting fractional cosmology.Fractal and Fractional, 7(2):149, 2023

Bayron Micolta-Riascos, Alfredo D Millano, Genly Leon, Cristián Erices, and Andronikos Paliathanasis. Revisiting fractional cosmology.Fractal and Fractional, 7(2):149, 2023

work page 2023
[47]

Dark matter in fractional gravity

Francesco Benetti, Andrea Lapi, Giovanni Gandolfi, Paolo Salucci, and Luigi Danese. Dark matter in fractional gravity. i. astrophysical tests on galactic scales.The Astrophysical Journal, 949(2):65, 2023

work page 2023
[48]

Fractional einstein field equa- tions in 2+1 dimensional spacetime: E

Ernesto Contreras, Antonio Di Teodoro, and Miguel Mena. Fractional einstein field equa- tions in 2+1 dimensional spacetime: E. contreras et al.General Relativity and Gravitation, 57(5):85, 2025

work page 2025
[49]

Estimated age of the universe in fractional cosmology.Fractal and Fractional, 7(12):854, 2023

Emanuel Wallison de Oliveira Costa, Raheleh Jalalzadeh, Pedro Felix da Silva Júnior, Seyed Meraj Mousavi Rasouli, and Shahram Jalalzadeh. Estimated age of the universe in fractional cosmology.Fractal and Fractional, 7(12):854, 2023. 22

work page 2023
[50]

Gravitational foundations and exact solutions inn–dimensional fractional cosmology.arXiv preprint arXiv:2512.11583, 2025

SMM Rasouli, J Marto, D Oliveira, and P Moniz. Gravitational foundations and exact solutions inn–dimensional fractional cosmology.arXiv preprint arXiv:2512.11583, 2025

work page arXiv 2025
[51]

Fractional time-delayed differential equations: Applications in cosmological studies.Fractal and Fractional, 9(5):318, 2025

Bayron Micolta-Riascos, Byron Droguett, Gisel Mattar Marriaga, Genly Leon, Andronikos Paliathanasis, Luis del Campo, and Yoelsy Leyva. Fractional time-delayed differential equations: Applications in cosmological studies.Fractal and Fractional, 9(5):318, 2025

work page 2025
[52]

Fractional-order derivatives in cosmological models of accelerated expan- sion.Modern Physics Letters A, 36(14):2130014, 2021

VK Shchigolev. Fractional-order derivatives in cosmological models of accelerated expan- sion.Modern Physics Letters A, 36(14):2130014, 2021

work page 2021
[53]

Fractional scalar field cosmology.Fractal and Fractional, 8(5):281, 2024

Seyed Meraj Mousavi Rasouli, Samira Cheraghchi, and Paulo Moniz. Fractional scalar field cosmology.Fractal and Fractional, 8(5):281, 2024

work page 2024
[54]

Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action

SMM Rasouli. Emergentλcdm cosmology from a fractional extension of newtonian grav- ity.arXiv preprint arXiv:2603.03113, 2026

work page internal anchor Pith review Pith/arXiv arXiv 2026
[55]

Fractal universe and quantum gravity.Physical review letters, 104(25): 251301, 2010

Gianluca Calcagni. Fractal universe and quantum gravity.Physical review letters, 104(25): 251301, 2010

work page 2010
[56]

Quantum field theory, gravity and cosmology in a fractal universe

Gianluca Calcagni. Quantum field theory, gravity and cosmology in a fractal universe. Journal of High Energy Physics, 2010(3):120, 2010

work page 2010
[57]

Universality class in conformal inflation.Journal of Cosmology and Astroparticle Physics, 2013(07):002–002, 2013

Renata Kallosh and Andrei Linde. Universality class in conformal inflation.Journal of Cosmology and Astroparticle Physics, 2013(07):002–002, 2013

work page 2013
[58]

Evolution of density perturbations in fractional cosmology

SMM Rasouli. Evolution of density perturbations in fractional newtonian cosmology.arXiv preprint arXiv:2603.07781, 2026

work page internal anchor Pith review Pith/arXiv arXiv 2026
[59]

A newtonian expanding universe.The Quarterly Journal of Mathematics, (1):64–72, 1934

Edward A Milne. A newtonian expanding universe.The Quarterly Journal of Mathematics, (1):64–72, 1934

work page 1934
[60]

Newtonian universes and the curvature of space.The quarterly journal of mathematics, 1(1):73–80, 1934

William Hunter McCrea and Edward Arthur Milne. Newtonian universes and the curvature of space.The quarterly journal of mathematics, 1(1):73–80, 1934

work page 1934
[61]

Newtonian cosmology.Nature, 175(4454):466–466, 1955

WH McCrea. Newtonian cosmology.Nature, 175(4454):466–466, 1955

work page 1955
[62]

On the significance of newtonian cosmology.Astronomical Jour- nal, Vol

William Hunter McCrea. On the significance of newtonian cosmology.Astronomical Jour- nal, Vol. 60, p. 271, 60:271, 1955

work page 1955
[63]

Cosmology and newtonian mechanics.American Journal of Physics, 33(2):105–108, 1965

C Callan, RH Dicke, and PJE Peebles. Cosmology and newtonian mechanics.American Journal of Physics, 33(2):105–108, 1965

work page 1965
[64]

Cosmology calculations almost without general relativity.American journal of physics, 73(7):653–662, 2005

Thomas F Jordan. Cosmology calculations almost without general relativity.American journal of physics, 73(7):653–662, 2005

work page 2005
[65]

Discrete newtonian cosmology.Classical and Quantum Gravity, 31(2):025003, 2013

George FR Ellis and Gary W Gibbons. Discrete newtonian cosmology.Classical and Quantum Gravity, 31(2):025003, 2013

work page 2013
[66]

Newtonian cosmology revisited.Monthly Notices of the Royal Astronomical Society, 282(1):206–210, 1996

Frank J Tipler. Newtonian cosmology revisited.Monthly Notices of the Royal Astronomical Society, 282(1):206–210, 1996. 23

work page 1996
[67]

Turning a Newtonian analogy for FLRW cosmology into a relativistic problem.Phys

Valerio Faraoni and Farah Atieh. Turning a Newtonian analogy for FLRW cosmology into a relativistic problem.Phys. Rev. D, 102(4):044020, 2020. doi: 10.1103/PhysRevD.102. 044020

work page doi:10.1103/physrevd.102 2020
[68]

Aghanim et al

N. Aghanim et al. Planck 2018 results. VI. Cosmological parameters.Astron. Astrophys., 641:A6, 2020. doi: 10.1051/0004-6361/201833910. [Erratum: Astron.Astrophys. 652, C4 (2021)]

work page doi:10.1051/0004-6361/201833910 2018
[69]

Unity of cosmological inflation attractors.Physical review letters, 114(14):141302, 2015

Mario Galante, Renata Kallosh, Andrei Linde, and Diederik Roest. Unity of cosmological inflation attractors.Physical review letters, 114(14):141302, 2015

work page 2015
[70]

S. M. M. Rasouli and Paulo Vargas Moniz. Noncommutative minisuperspace, gravity- driven acceleration, and kinetic inflation.Phys. Rev. D, 90(8):083533, 2014. doi: 10.1103/ PhysRevD.90.083533

work page 2014
[71]

S. M. M. Rasouli and Paulo Vargas Moniz. Gravity-driven Acceleration and Kinetic Infla- tion in Noncommutative Brans-dicke Setting.Odessa Astron. Pub., 29:19–24, 2016. doi: 10.18524/1810-4215.2016.29.84956

work page doi:10.18524/1810-4215.2016.29.84956 2016
[72]

The emergent universe: Inflationary cosmology with no singularity.Classical and Quantum Gravity, 21(1):223–232, 2004

George FR Ellis and Roy Maartens. The emergent universe: Inflationary cosmology with no singularity.Classical and Quantum Gravity, 21(1):223–232, 2004

work page 2004
[73]

Galilean genesis: an alternative to inflation.Journal of Cosmology and Astroparticle Physics, 2010(11):021–021, 2010

Paolo Creminelli, Alberto Nicolis, and Enrico Trincherini. Galilean genesis: an alternative to inflation.Journal of Cosmology and Astroparticle Physics, 2010(11):021–021, 2010

work page 2010
[74]

Perturbations in a non- singular bouncing universe.Physics Letters B, 569(1-2):113–122, 2003

Massimo Gasperini, Massimo Giovannini, and Gabriele Veneziano. Perturbations in a non- singular bouncing universe.Physics Letters B, 569(1-2):113–122, 2003

work page 2003
[75]

Bouncing cosmologies: progress and problems

Robert Brandenberger and Patrick Peter. Bouncing cosmologies: progress and problems. Foundations of Physics, 47(6):797–850, 2017

work page 2017
[76]

Density perturbations in the ekpyrotic scenario.Physical Review D, 66(4):046005, 2002

Justin Khoury, Burt A Ovrut, Paul J Steinhardt, and Neil Turok. Density perturbations in the ekpyrotic scenario.Physical Review D, 66(4):046005, 2002

work page 2002
[77]

Springer, 2007

Maurizio Gasperini and Jnan Maharana.String theory and fundamental interactions: Gabriele Veneziano and theoretical physics: historical and contemporary perspectives. Springer, 2007

work page 2007
[78]

A minimal fractional deformation of newtonian gravity.arXiv preprint arXiv:2603.16009, 2026

SMM Rasouli. A minimal fractional deformation of newtonian gravity.arXiv preprint arXiv:2603.16009, 2026

work page arXiv 2026
[79]

Inflationary universe in deformed phase space scenario.Annals of Physics, 393:288– 307, 2018

Seyed Meraj Mousavi Rasouli, Nasim Saba, Mehrdad Farhoudi, João Marto, and PV Mo- niz. Inflationary universe in deformed phase space scenario.Annals of Physics, 393:288– 307, 2018

work page 2018
[80]

Noncommutativity, sáez–ballester theory and kinetic inflation.Universe, 8 (3):165, 2022

SMM Rasouli. Noncommutativity, sáez–ballester theory and kinetic inflation.Universe, 8 (3):165, 2022

work page 2022

Showing first 80 references.