Mathematical Physics, Physics and Astronomy, Applied Mathematics, Analysis
36
Scopus Publications
658
Scholar Citations
16
Scholar h-index
22
Scholar i10-index
Scopus Publications
Quintessence: Quadratic potentials Artur Alho, Claes Uggla Journal of Mathematical Physics, 2026 Arguably one can use a canonical scalar field φ, minimally coupled to gravity, with quadratic potentials V=Λ±12m2φ2 to explore some general features of slow-roll and hilltop thawing quintessence, respectively. For each of these two potentials, and pressure-free matter, we introduce a regular unconstrained dynamical system on a compact state space, where the formulation for the hilltop case is new. Together with a derivation of monotonic functions in the two global state space settings, this enables us to obtain global results and to introduce figures that illustrate the global solution spaces of these models, in which we situate the observationally viable quintessence solutions.
Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids Artur Alho, Vitor Bessa, Filipe C. Mena Journal of Dynamics and Differential Equations, 2025 Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $$V(\\phi )=\\frac{(\\lambda \\phi )^{2n}}{2n}$$ V ( ϕ ) = ( λ ϕ ) 2 n 2 n , $$\\lambda >0$$ λ > 0 , $$n\\in {\\mathbb {N}}$$ n ∈ N , interacting with a perfect fluid with linear equation of state $$p_{\\textrm{pf}}=(\\gamma _{\\textrm{pf}}-1)\\rho _{\\textrm{pf}}$$ p pf = ( γ pf - 1 ) ρ pf , $$\\gamma _{\\textrm{pf}}\\in (0,2)$$ γ pf ∈ ( 0 , 2 ) , in flat Robertson–Walker spacetimes. The interaction is a friction-like term of the form $$\\Gamma (\\phi )=\\mu \\phi ^{2p}$$ Γ ( ϕ ) = μ ϕ 2 p , $$\\mu >0$$ μ > 0 , $$p\\in {\\mathbb {N}}\\cup \\{0\\}$$ p ∈ N ∪ { 0 } . The analysis relies on the introduction of a new regular 3-dimensional dynamical systems’ formulation of the Einstein equations on a compact state space, and the use of dynamical systems’ tools such as quasi-homogeneous blow-ups and averaging methods involving a time-dependent perturbation parameter.
New simple and accurate quintessence approximations Artur Alho, Claes Uggla Physical Review D, 2025 We derive new approximations for quintessence solutions that are simpler and an order of magnitude more accurate than anything available in the literature, which from an observational perspective \\emph{makes numerical calculations superfluous}. For example, our tracking quintessence approximation yields $\\sim 0.1\\%$ maximum relative errors of $H(z)/H_0$ and $\\Omega_\\mathrm{m}(z)$ for the observationally viable inverse power law scalar field potentials, and similarly for viable thawing quintessence models using two slow-roll parameters. The approximations are trivially computed from the scalar field potential and as an application we give \\emph{analytic} expressions for the CPL parameters calculated from an arbitrary scalar field potential for thawing and tracking quintessence models.
Spherically symmetric elastic bodies in general relativity Artur Alho, José Natário, Paolo Pani, Guilherme Raposo Classical and Quantum Gravity, 2024 The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers (2022 Phys. Rev. D 105 044025, 2022 Phys. Rev. D 106 L041502) and (arXiv:2306.16584 [gr-qc]), where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physically admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.
Scale invariant elastic stars in general relativity Artur Alho, José Natário, Paolo Pani, Guilherme Raposo Physical Review D, 2024 We present a model of relativistic elastic stars featuring scale invariance. This implies a linear mass-radius relation and the absence of a maximum mass. The most compact spherically symmetric configuration that is radially stable and satisfies all energy and causality conditions has a slightly smaller radius than the Schwarzschild light ring radius. To the best of our knowledge, this is the first material compact object with such remarkable properties in General Relativity, which makes it a unique candidate for a black-hole mimicker.
Quintessential α-attractor inflation: a dynamical systems analysis Artur Alho, Claes Uggla Journal of Cosmology and Astroparticle Physics, 2023 The equations for quintessential α-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Padé approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation.
Compactness bounds in general relativity Artur Alho, José Natário, Paolo Pani, Guilherme Raposo Physical Review D, 2022 A foundational theorem due to Buchdahl states that, within General Relativity (GR), the maximum compactness C ≡ GM/ ( Rc 2 ) of a static, spherically symmetric, perfect fluid object of mass M and radius R is C = 4 / 9. As a corollary, there exists a compactness gap between perfect fluid stars and black holes (where C = 1 / 2). Here we generalize Buchdahl’s result by introducing the most general equation of state for elastic matter with constant longitudinal wave speeds and apply it to compute the maximum compactness of regular, self-gravitating objects in GR. We show that: (i) the maximum compactness grows monotonically with the longitudinal wave speed; (ii) elastic matter can exceed Buchdahl’s bound and reach the black hole compactness C = 1 / 2 continuously; (iii) however, imposing subluminal wave propagation lowers the maximum compactness bound to C ≈ 0 . 462, which we conjecture to be the maximum compactness of any static elastic object satisfying causality; (iv) imposing also radial stability further decreases the maximum compactness to C ≈ 0 . 389. Therefore, although anisotropies are often invoked as a mechanism for supporting horizonless ultracompact objects, we argue that the black hole compactness cannot be reached with physically reasonable matter within GR and that true black hole mimickers require either exotic matter or beyond-GR effects.
Cosmological global dynamical systems analysis Artur Alho, Woei Chet Lim, Claes Uggla Classical and Quantum Gravity, 2022 We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature.
Homogenization of scalar field cosmologies A. ALHO, F. C. MENA 13th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories Proceedings of the Mg13 Meeting on General Relativity 2012, 2015
Dynamics of quadratic f (R) cosmology with a perfect fluid: Jordan and Einstein frames A Alho, M Lima, FC Mena arXiv preprint arXiv:2603.09667 , 2026 2026
Quintessence: Quadratic potentials A Alho, C Uggla Journal of Mathematical Physics 67 (3) , 2026 2026 Citations: 1
Quintessence A Alho, E Bernholm, C Uggla arXiv preprint arXiv:2511.02727 , 2025 2025 Citations: 2
Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids: A. Alho et al. A Alho, V Bessa, FC Mena Journal of Dynamics and Differential Equations 37 (2), 1637-1705 , 2025 2025 Citations: 3
New simple and accurate quintessence approximations A Alho, C Uggla Physical Review D 111 (8), 083549 , 2025 2025 Citations: 7
Tracking quintessence A Alho, C Uggla, J Wainwright Physics of the Dark Universe 44, 101433 , 2024 2024 Citations: 8
Spherically symmetric elastic bodies in general relativity A Alho, J Natário, P Pani, G Raposo Classical and Quantum Gravity 41 (7), 073002 , 2024 2024 Citations: 23
Scale invariant elastic stars in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 109 (6), 064037 , 2024 2024 Citations: 13
Quintessential α-attractor inflation: A dynamical systems analysis A Alho, C Uggla Journal of Cosmology and Astroparticle Physics 2023 (11), 083 , 2023 2023 Citations: 19
Quintessence from a state space perspective A Alho, C Uggla, J Wainwright Physics of the Dark Universe 39, 101146 , 2023 2023 Citations: 17
Compactness bounds in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 106 (4), L041502 , 2022 2022 Citations: 55
Cosmological global dynamical systems analysis A Alho, WC Lim, C Uggla Classical and Quantum Gravity 39 (14), 145010 , 2022 2022 Citations: 17
Compact elastic objects in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 105 (4), 044025 , 2022 2022 Citations: 40
Self-gravitating static balls of power-law elastic matter A Alho, S Calogero, A Liljenberg arXiv preprint arXiv:2104.11131 , 2021 2021 Citations: 4
D ynamical systems in perturbative scalar field cosmology A Alho, C Uggla, J Wainwright Classical and Quantum Gravity 37 (22), 225011 , 2020 2020 Citations: 12
Static self-gravitating Newtonian elastic balls A Alho, S Calogero Archive for Rational Mechanics and Analysis 238 (2), 639-669 , 2020 2020 Citations: 7
Global dynamics of Yang–Mills field and perfect-fluid Robertson–Walker cosmologies A Alho, V Bessa, FC Mena Journal of Mathematical Physics 61 (3) , 2020 2020 Citations: 17
Perturbations of the Lambda-CDM model in a dynamical systems perspective A Alho, C Uggla, J Wainwright Journal of Cosmology and Astroparticle Physics 2019 (09), 045-045 , 2019 2019 Citations: 25
The wave equation near flat Friedmann–Lemaître–Robertson–Walker and Kasner Big Bang singularities A Alho, G Fournodavlos, AT Franzen Journal of Hyperbolic Differential Equations 16 (02), 379-400 , 2019 2019 Citations: 23
Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter A Alho, S Calogero Commun. Math. Phys. 371, 975–1004 , 2019 2019 Citations: 7
MOST CITED SCHOLAR PUBLICATIONS
On dynamical systems approaches and methods in f ( R ) cosmology A Alho, S Carloni, C Uggla Journal of Cosmology and Astroparticle Physics 2016 (08), 064-064 , 2016 2016 Citations: 77
Global dynamics and inflationary center manifold and slow-roll approximants A Alho, C Uggla Journal of Mathematical Physics 56 (1) , 2015 2015 Citations: 62
Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids A Alho, J Hell, C Uggla Classical and Quantum Gravity 32 (14), 145005 , 2015 2015 Citations: 59
Compactness bounds in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 106 (4), L041502 , 2022 2022 Citations: 55
Compact elastic objects in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 105 (4), 044025 , 2022 2022 Citations: 40
Inflationary -attractor cosmology: A global dynamical systems perspective A Alho, C Uggla Physical Review D 95 (8), 083517 , 2017 2017 Citations: 38
Perturbations of the Lambda-CDM model in a dynamical systems perspective A Alho, C Uggla, J Wainwright Journal of Cosmology and Astroparticle Physics 2019 (09), 045-045 , 2019 2019 Citations: 25
Spherically symmetric elastic bodies in general relativity A Alho, J Natário, P Pani, G Raposo Classical and Quantum Gravity 41 (7), 073002 , 2024 2024 Citations: 23
The wave equation near flat Friedmann–Lemaître–Robertson–Walker and Kasner Big Bang singularities A Alho, G Fournodavlos, AT Franzen Journal of Hyperbolic Differential Equations 16 (02), 379-400 , 2019 2019 Citations: 23
Scalar field deformations of cosmology A Alho, C Uggla Physical Review D 92 (10), 103502 , 2015 2015 Citations: 22
The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies A Alho, FC Mena, JAV Kroon Advances in Theoretical and Mathematical Physics 21 (4) , 2017 2017 Citations: 21
Quintessential α-attractor inflation: A dynamical systems analysis A Alho, C Uggla Journal of Cosmology and Astroparticle Physics 2023 (11), 083 , 2023 2023 Citations: 19
Pre-inflationary homogenization of scalar field cosmologies A Alho, FC Mena Physics Letters B 703 (5), 537-542 , 2011 2011 Citations: 19
Quintessence from a state space perspective A Alho, C Uggla, J Wainwright Physics of the Dark Universe 39, 101146 , 2023 2023 Citations: 17
Cosmological global dynamical systems analysis A Alho, WC Lim, C Uggla Classical and Quantum Gravity 39 (14), 145010 , 2022 2022 Citations: 17
Global dynamics of Yang–Mills field and perfect-fluid Robertson–Walker cosmologies A Alho, V Bessa, FC Mena Journal of Mathematical Physics 61 (3) , 2020 2020 Citations: 17
Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies A Alho, FC Mena Physical Review D 90 (4), 043501 , 2014 2014 Citations: 16
Spherical linear waves in de Sitter spacetime JL Costa, A Alho, J Natário Journal of mathematical physics 53 (5) , 2012 2012 Citations: 14
Scale invariant elastic stars in general relativity A Alho, J Natário, P Pani, G Raposo Physical Review D 109 (6), 064037 , 2024 2024 Citations: 13
The problem of a self-gravitating scalar field with positive cosmological constant JL Costa, A Alho, J Natário Annales Henri Poincaré 14 (5), 1077-1107 , 2013 2013 Citations: 13
