arXiv subjects

Peter K. S. Dunsby

Publications and source records attributed to Peter K. S. Dunsby.

At least 19 recordsLinked to original sources

arXiv2026

Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies

We develop a harmonic framework for spherically symmetric Friedmann-like geometries with constant scalar curvature but non-zero trace-free Ricci curvature. This preserves Friedmann-type isotropic expansion while introducing a radially varying tidal field and supporting anisotropic stress. We formulate the scalar Laplace-Beltrami operator as a Sturm-Liouville problem and establish its self-adjoint domains and regularity at minimal spheres. Robertson-Walker harmonics are recovered in the maximally symmetric limit. Trace-free curvature terms are expressed as spectral projection kernels. Rotational symmetry preserves angular labels and parity, while the tidal profile couples different radial eigenmodes. A finite-shell calculation displays this off-diagonal structure, verifies consistency between radial representations, and confirms the expected weak-field scaling. A minimally coupled scalar field remains diagonal in the exact basis, indicating operator-dependent mixing rather than mixing solely due to inhomogeneity. We formulate transverse-traceless kernels, whose dynamical application requires a specified model for the supporting anisotropic matter. This converts curvature-induced mode mixing into a spectral problem for perturbations beyond maximally symmetric cosmologies.

gr-qc↗

arXiv2026

Cosmological structure growth in energy-momentum squared gravity

We investigate the cosmological evolution of matter perturbations in the modified gravity model $f(R,T^2)$, where $T^2=T_{μν}T^{μν}$ denotes the quadratic contraction of the energy--momentum tensor. Using the gauge-invariant 1+3 covariant formalism, we study the evolution of the matter density contrast and analyze several growth observables, including the growth factor, the growth index, and the weighted growth rate $fσ_8$. We consider representative values $n=1/2$ and $n=1/4$, which probe different regimes of the matter--geometry coupling. We show that the growth index decreases with increasing redshift and approaches the standard matter-dominated behavior at early times, while mild scale-dependent deviations from the $Λ$CDM model emerge at late times. The model predicts small departures from General Relativity for $n=1/4$, whereas stronger deviations appear for $n=1/2$ and larger values of the coupling parameter $α$. We further compare the theoretical predictions for $fσ_8$ with current observational data and find that viable parameter choices remain within the observational $\pm2σ$ bounds. These results indicate that $f(R,T^2)$ gravity can provide a viable description of late-time cosmic acceleration and large-scale structure formation while remaining consistent with current growth observations.

astro-ph.CO↗

arXiv2026

Reconstructing the slope of a nearly flat quintessence potential from cosmography

We revisit thawing quintessence models with nearly flat scalar-field potentials using a cosmographic framework. Earlier work indicates that the cosmographic reconstruction of the slope $λ=-(dV/dϕ)/V$ of the quintessence potential in the general case requires the knowledge of the cosmographic paremeters up to the jerk parameter $j$. In this work we show that the slow-roll conditions $[(dV/dϕ)/V]^2 \ll 1$ and $|(d^2V/dϕ^2)/V| \ll 1$ allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter $q$ (and the density parameter $Ω_ϕ$). Confronting the assumption of near-flatness with the cosmographic data after DESI DR2, however, reveals possible tension between the two. We further show that these models exhibit attractor behaviour in the $w$--$Ω_ϕ$ and $w$--$w'$ phase planes, corresponding to a universal thawing evolution with $w \approx -1$ at early times. We also derive the corresponding relation in the cosmographic $q$--$j$ plane and show that different cosmological expansion histories can produce the same thawing evolution. Nevertheless, all viable trajectories remain close to the $Λ$CDM limit $j=1$.

gr-qc↗

arXiv2026

Covariant Tolman-Oppenheimer-Volkoff equations in Energy-Momentum Squared Gravity

We study static, spherically symmetric stellar configurations in an extended class of Energy--Momentum Squared Gravity using the covariant $1+1+2$ semi-tetrad formalism. For perfect physical fluids, we show that the nonlinear matter corrections can be reinterpreted as an effective perfect fluid, so that the stellar equilibrium equations retain the standard Tolman--Oppenheimer--Volkoff form when written in terms of effective variables. The resulting covariant structure equations are formulated in both metric and dimensionless variables and, whenever an effective closure relation exists, reduce to an autonomous planar dynamical system. This provides a global qualitative description of the stellar phase space in terms of finite and asymptotic critical points. Specializing to linear physical equations of state, we recover the general relativistic benchmark and identify sectors that are exactly, asymptotically, or piecewise equivalent to general relativity, as well as sectors -- particularly dust configurations -- for which the planar reduction breaks down and the full three-dimensional covariant flow must be considered. We further recover the standard metric Tolman--Oppenheimer--Volkoff equation in terms of effective variables and show that, although the exterior spacetime remains Schwarzschild, the natural matching condition at the stellar surface is $p_{\rm eff}(R)=0$, which need not coincide with $p(R)=0$ for self-bound matter.

gr-qc↗

arXiv2026

Cosmological perturbations in Energy-Momentum Squared Gravity

We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor modes on FLRW backgrounds, in the case of radiation and dust. Two representative subclasses are examined in detail, in which non-linearity enters through $\mathcal{O}(ηρ^2)$ corrections or modifications in the equation-of-state parameter and the sound speed. For scalar perturbations, the density contrast can be enhanced or reduced relative to General Relativity, depending on the coupling parameter and the wavelength regime. A similar behaviour occurs for vector modes, allowing for a non-trivial vorticity at early-times. Tensor modes, described by the magnetic part of the Weyl tensor and the shear tensor propagate as damped waves with slowly varying effective masses. All sectors reduce continuously to their GR limits as $η\!\to\!0$. The framework isolates robust signatures - early-time scalar tilts, tensor damping shifts, and altered vorticity decay - that can be confronted with CMB and large-scale-structure observations to constrain these theories of gravity.

gr-qc↗

arXiv2026

Covariant Dynamical Systems Formulation of the Tolman-Oppenheimer-Volkoff Equations

We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the $1+1+2$ semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff system can be expressed as a covariant first-order dynamical system and, after suitable normalization, reformulated as a three-dimensional autonomous flow for a general equation of state (EoS). In the case of a linear EoS, the system reduces further to a planar dynamical system whose finite and asymptotic equilibrium points, together with their stability properties, admit a clear geometrical interpretation in terms of covariant variables. For more general equations of state, such as the polytropic case, the dynamics naturally acquire a genuinely three-dimensional character. Beyond providing a compact, covariant, and physically transparent reformulation of the relativistic stellar problem, the present analysis clarifies how the standard metric description is encoded within a global phase-space structure constructed from geometrically meaningful covariant variables.

gr-qc↗

arXiv2026

Direct cosmographic reconstruction of the quintessence potential

We derive expressions for the first and second derivatives of the quintessence potential $V(ϕ)$, in terms of $λ= -V^{\prime}/V$ and $Γ= (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $Ω_ϕ$ and the cosmographic parameters $q$, $j$, and $s$. Our mapping is not explicitly a function of the equation of state parameter $w$. We use these results, along with recent observational data, to derive expansions of $V(ϕ)$ about the present-day value of the scalar field, $ϕ_0$.

gr-qc↗

arXiv2025

Dynamical dark energy in models with evolution close to $Λ$CDM

In this communication we address whether or not there is an equivalence between the kinematical and dynamical descriptions of the spatially flat $Λ$CDM model. We address this by investigating whether an almost $Λ$CDM expansion history ($j(z)\approx1$) corresponds to an almost $Λ$CDM model ($w_{\rm DE}(z)\approx-1$) by considering two particular explicit examples. At least for the cases considered, this turns out not to be the case. Instead, what we find is that an almost $Λ$CDM cosmic evolution rather corresponds to an \emph{almost unified dark fluid model}. Considering that one never gets the exact condition $j(z)=1$ from any cosmographic data sets, this raises further questions on whether the $Λ$CDM model is the best candidate for the standard model of the evolution of the universe.

gr-qc↗

arXiv2025

Some exact relativistic star solutions in $f(R)$ gravity

We present a covariant description of non-vacuum static spherically symmetric spacetimes in $f(R)$ gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman-Oppenheimer-Volkoff (TOV) equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case $f(R)=R+αR^{2}$, which have the correct thermodynamic properties for standard matter.

gr-qc↗

arXiv2024

A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity

Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to specify not a particular functional form of f(R) a-priori, but rather a particular cosmological evolution, which fixes the cosmography. In a sense, our approach is the way around the reconstruction method. This is shown using both non-compact and compact dynamical variables. The focus in this paper is on the compact analysis since we demonstrate the applicability of this formulation using examples of bouncing and cyclic cosmology. In particular, our analysis reveals, in a model-independent manner, the problem of achieving such cosmologies when the universe is globally spatially flat and devoid of matter.

gr-qc↗

arXiv2024

A dynamical systems formulation for inhomogeneous LRS-II spacetimes

We present a dynamical system formulation for inhomogeneous LRS-II spacetimes using the covariant 1+1+2 decomposition approach. Our approach describes the LRS-II dynamics from the point of view of a comoving observer. Promoting the covariant radial derivatives of the covariant dynamical quantities to new dynamical variables and utilizing the commutation relation between the covariant temporal and radial derivatives, we were able to construct an autonomous system of first-order ordinary differential equations along with some purely algebraic constraints. Using our dynamical system formulation we found several interesting features in the LRS-II phase space with dust, one of them being that the homogeneous solutions constitute an invariant submanifold. For the particular case of LTB, we were also able to recover the previously known result that an expanding LTB tends to Milne in the absence of a cosmological constant, providing a potential validation of our formalism.

gr-qc↗

arXiv2024

Bouncing cosmologies in the presence of a Dirac-Born-Infeld field

We perform a detailed dynamical system analysis for the behaviour of a Dirac-Born-Infeld (DBI) field in a spatially closed Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. The DBI field is characterised by a potential and brane tension. We study power-law or exponential functions for the potential and tension. We find that in a spatially closed FLRW cosmology, a DBI field in the ultra-relativistic limit allows for a broader range of initial conditions resulting in a bouncing universe than in the non-relativistic limit. We further note that the range of initial conditions allowing for a bounce is larger if we consider power-law functions for the potential and tension, compared to the exponential case. Our dynamical analysis shows that a DBI field does not exhibit stable cyclical behaviour, including the case in which a negative cosmological constant is present.

gr-qc↗

arXiv2024

Causal dynamics of null horizons under linear perturbations

We study the causal dynamics of an embedded null horizon foliated by marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric background spacetime subjected to linear perturbations. We introduce a simple procedure which characterizes the transition of the causal character of the null horizon. We apply our characterization scheme to non-dissipative perturbations of the Schwarzschild and spatially homogeneous backgrounds. For the latter, a linear equation of state was imposed. Assuming a harmonic decomposition of the linearized field equations, we clarify the variables of a formal solution to the linearized system that determine how the null horizon evolves. For both classes of backgrounds, the shear and vorticity 2-vectors are essential to the characterization, and their roles are made precise. Finally, we discuss aspects of the relationship between the characterizing conditions. Various properties related to the self-adjointness of the MOTS stability operator are extensively discussed.

gr-qc↗

arXiv2024

Double polytropic cosmic acceleration from the Murnaghan equation of state

We consider a double polytropic cosmological fluid and demonstrate that, when one constituent resembles a bare cosmological constant while the other emulates a generalized Chaplygin gas, a good description of the Universe's large-scale dynamics is obtained. In particular, our double polytropic reduces to the Murnaghan equation of state, whose applications are already well established in solid state physics and classical thermodynamics. Intriguingly, our model approximates the conventional $Λ$CDM paradigm while reproducing the collective effects of logotropic and generalized Chaplygin fluids across different regimes. To check the goodness of our fluid description, we analyze first order density perturbations, refining our model through various orders of approximation, utilizing $σ_8$ data alongside other cosmological data sets. Encouraging results suggest that our model, based on the Murnaghan equation of state, outperforms the standard cosmological background within specific approximate regimes and, on the whole, surpasses the standard phenomenological reconstruction of dark energy.

gr-qc↗

arXiv2023

Unifying the dark sector through a single matter fluid with non-zero pressure

We explore a generalised unified dark energy model that incorporates a non-minimal interaction between a tachyonic fluid and an additional scalar field. Specifically, we require that the second field possesses a vacuum energy, introducing an ineliminable offset due to a symmetry-breaking mechanism. After the transition (occurring as due to the symmetry-breaking mechanism of the second field), the corresponding equation of state (EoS) takes the form of a combination between a generalised Chaplygin gas (GCG) component and a cosmological constant contribution. We reinterpret this outcome by drawing parallels to the so-called Murnaghan EoS, widely-employed in the realm of solid-state physics to characterise fluids that, under external pressure, counteract the pressure's effect. We examine the dynamic behaviour of this model and highlight its key distinctions compared to the GCG model. We establish parameter bounds that clarifies the model's evolution across cosmic expansion history, showing that it, precisely, exhibits behaviour akin to a logotropic fluid that eventually converges to the $Λ$CDM model in the early universe, while behaving as a logotropic or Chaplygin gas at intermediate and late times respectively. We explain our findings from a thermodynamic perspective, and determine the small perturbations in the linear regime. At very early times, the growth factor flattens as expected while the main departures occur at late times, where the Murnagham EoS results in a more efficient growth of perturbations. We discuss this deviation in view of current observations and conclude that our model is a suitable alternative to the standard cosmological paradigm, introducing the concept of a matter-like field with non-zero pressure.

gr-qc↗

arXiv2023

Horizon area bound and MOTS stability in locally rotationally symmetric solutions

In this paper, we study the stability of marginally outer trapped surfaces (MOTS), foliating horizons of the form $r=X(τ)$, embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ``outside" of and homologous to $\mathcal{S}$. Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ``growth" of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.

gr-qc↗

arXiv2022

A note on the dynamical system formulations in $f(R)$ gravity

A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting them in chronological order as they appeared in the history of the relevant scientific literature. In this way, we illuminate how the shortcoming(s) of an existing formulation encouraged the development of an alternative formulation. Whenever possible, a 2-dimensional phase portrait is given for a better visual representation of the dynamics of phase space. We also touch upon how cosmological perturbations can be analyzed using the phase space language.

gr-qc↗

arXiv2021

Conformal geometry on a class of embedded hypersurfaces in spacetimes

In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^μ$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper conformal transformation. To ensure a non-vanishing positivity scalar curvature of the induced metric, we impose that the scalar curvature of the conformal metric is non-negative and that the associated conformal factor satisfies $\hatφ^2+2\hat{\hatφ}>0$, where $\hat{\ast}$ denotes derivative along $e^μ$. Firstly, it is demonstrated that such hypersurface is either Einstein or the twist vanishes on it, and that the scalar curvature of the induced metric is constant. It is then proved that if the hypersurface is compact and of Einstein, and admits a proper conformal transformation, then the hypersurface must be isomorphic to the $3$-sphere, where we make use of well known results on Riemannian manifolds admitting conformal transformations. If the hypersurface is not Einstein and has nowhere vanishing sheet expansion, we show that this conclusion fails. However, with the additional conditions that the scalar curvatures of the induced metric and the conformal metric coincide, the associated conformal factor is strictly negative and the third and higher order derivatives of the conformal factor vanish, the conclusion follows. Furthermore, additional results are obtained under the conditions that the scalar curvature of a metric conformal to the induced metric is also constant. Finally, we consider some of our results in context of locally rotationally symmetric spacetimes and show that, if the hypersurfaces are compact and not of Einstein type, then under specified conditions the hypersurface is isomorphic to the $3$-sphere, where we constructed explicit examples of proper conformal Killing vector fields along $e^μ$.

math.DG↗