arXiv subjects

Sotirios Karamitsos

Publications and source records attributed to Sotirios Karamitsos.

At least 19 recordsLinked to original sources

arXiv2026

Frame invariant diffusive formulation of scalar-tensor gravity

Thermodynamics provides a useful interpretation of scalar-tensor gravity, in which the effective imperfect fluid admitted by the nonminimal coupling features a temperature that is associated with the departure from general relativity. However, in this construction, certain thermodynamical quantities are defined with respect to a particular conformal frame. In the present work, we show that the originally proposed effective temperature assigned to nonminimally coupled scalar field theories is not frame invariant, and can thus be arbitrarily tuned by a change of frame. This raises the question of whether temperature can be viewed as an intrinsic property of a scalar-tensor theory rather than a particular representation of it. Working instead with the frame invariant formulation of scalar-tensor gravity, we find that the frame invariant effective fluid is perfect with identically vanishing temperature. The departure from general relativity is then governed not by temperature, but rather by a frame invariant chemical potential, similar to minimal theories. Therefore, general relativity can be interpreted as a state of diffusive equilibrium for any scalar-tensor theory, regardless of whether it is minimal or nonminimal.

gr-qc↗

arXiv2026

From Frame Covariance to the Swampland Distance Conjecture

Field space geometry plays a central role within the Swampland Programme, most notably in the various Distance Conjectures. However, for gravitational EFTs, this geometry is not uniquely defined: one can cast the action in many synonymous descriptions related by Weyl transformations, in which the field space metric transforms non-trivially across conformal frames. This raises a crucial question of how we are meant to think of the field space metric in view of employing the Swampland Conjectures. In this work we resolve this ambiguity by developing a fully frame-covariant framework for studying gravitational EFTs. We show that all conformal frames arise as distinct foliations of a singular higher-dimensional auxiliary geometry. Applying ADM formalism to the augmented field space, it is clear how Weyl- and unit transformations can be understood from a geometric point of view. Using this framework, we revisit the Species Scale Distance Conjecture and Sharpened Distance Conjecture, and show how the bounds derive from universal properties of gravitational EFTs under Weyl transformations. This strongly suggests that aspects of these conjectures apply to a much broader class of scalar-tensor theories and are consequences of frame covariance, rather than constraints imposed by quantum gravity.

hep-th↗

arXiv2025

Pole inflation from extended metric-affine gravity

We study inflation in the framework of extended metric-affine F(R) gravity, where all even-parity quadratic invariants of torsion and non-metricity are included in the Lagrangian alongside the F(R) term. The extended theory admits a scalar-tensor description with a non-canonical kinetic term featuring poles. As a result, the inflationary dynamics and predictions for observables of this model are insensitive to the specific form of F(R), since they are dominated by the structure of the poles (order and residue). We analyze both a simplified version analytically and the full eleven-parameter theory, and we classify the models based on whether they feature second-order poles, whether they are free from ghosts, and whether they predict a sufficiently small tensor-to-scalar ratio. By relaxing the ghost-free requirement to only exclude ghosts near the pole (where inflation occurs), we demonstrate that we can significantly enlarge the set of viable models. We thus show that extended metric-affine F(R) gravity can act as a robust framework for inflation, reproducing the attractor predictions for the spectral index and tensor-to-scalar ratio.

gr-qc↗

arXiv2025

Quasi-Palatini Formulation of Scalar-Tensor Gravity

The Palatini formulation has been successful in the development of several alternative theories of gravity. It is well understood that the Palatini and metric formulations are equivalent in minimally coupled scalar-tensor models, but nonminimal scalar-tensor models can lead to physically distinct theories depending on the underlying formulation. Once a model has been selected, the choice of formulation is a discrete one, and so promoting it to be continuous is expected to give rise to a wider class of actions. To this end, we propose the "quasi-Palatini" formulation, a method for interpolating between the metric and Palatini formulations for a given model that gives rise to a continuous family of models. We apply the quasi-Palatini formulation to Higgs inflation, induced gravity inflation, and Starobinsky inflation, and demonstrate how this leads to a deformation of the potential, studying its impact on observables. We also discuss how the interpolation between different actions can be extended to scalar-torsion and scalar-nonmetricity models.

gr-qc↗

arXiv2024

Global Portraits of Nonminimal Inflation: Metric and Palatini

In this paper, we study the global phase space dynamics of single nonminimally coupled scalar field inflation models in the metric and Palatini formalisms. Working in the Jordan frame, we derive the scalar-tensor general field equations and flat FLRW cosmological equations, and present the Palatini and metric equations in a common framework. We show that inflation is characterized by a "master" trajectory from a saddle-type de Sitter fixed point to a stable node fixed point, approximated by slow roll conditions (presented for the first time in the Palatini formalism). We show that, despite different underlying equations, the fixed point structure and properties of many models are congruent in metric and Palatini, which explains their qualitative similarities and their suitability for driving inflation. On the other hand, the global phase portraits reveal how even models which predict the same values for observable perturbations differ, both to the extent of the phase space physically available to their trajectories, as well as their past asymptotic states. We also note how the slow roll conditions tend to underestimate the end of inflationary accelerated expansion experienced by the true nonlinear "master" solution. The explicit examples we consider range from the metric and Palatini induced gravity quintic potential with a Coleman-Weinberg correction factor to Starobinsky, metric and Palatini nonminimal Higgs, second order pole, and several nontrivial Palatini models.

gr-qc↗

arXiv2022

Pole inflation from non-minimal coupling to gravity

Transforming canonical scalars to the Einstein frame can give a multi-field generalization of pole inflation (namely, a scalar with a divergent kinetic term) at vanishing field-dependent Planck mass. However, to obtain an attractor, the scalar potential must obey certain non-generic conditions. These are automatically satisfied in Quantum Field Theories with dimension-less couplings. The resulting models of pole inflation have special inflationary predictions determined by the full RG running of couplings. Acceptable predictions for the tensor/scalar ratio arise for perturbative but moderately large couplings, so we explore the possible QFT runnings: to confinement, to an IR fixed point, and to a UV fixed point.

hep-th↗

arXiv2022

Geometrising the Micro-Cosmos on a Supermanifold

For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT). After a brief historic overview of the major scientific achievements using these methods, we will focus on the covariant and differential geometric formalism originally proposed by Vilkovisky and DeWitt (VDW). We discuss recent developments made in addressing the uniqueness of the path-integral measure of the VDW effective action, and so address the problem of quantum frame dependence in cosmologically relevant scalar-tensor theories beyond the classical approximation. Particular attention will be drawn to a long-standing problem concerning the obstacles that the VDW formalism was facing from its original conception in describing generic QFTs that include fermions. We show how in addition to bosons the VDW effective action can be extended to supermanifolds to include fermions. The so-extended formulation appears to be very promising for a complete geometrisation of realistic theories of micro-cosmos, such as the Standard Model and its gravitational sector.

hep-th↗

arXiv2021

Frame Covariant Formalism for Fermionic Theories

We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

hep-th↗

arXiv2021

Gravitational Vector Dark Matter

A new dark sector consisting of a pure non-abelian gauge theory has no renormalizable interaction with SM particles, and can thereby realise gravitational Dark Matter (DM). Gauge interactions confine at a scale $Λ_{\rm DM}$ giving bound states with typical lifetimes $τ\sim M_{\rm Pl}^4/Λ^5_{\rm DM}$ that can be DM candidates if $Λ_{\rm DM} $ is below 100 TeV. Furthermore, accidental symmetries of group-theoretical nature produce special gravitationally stable bound states. In the presence of generic Planck-suppressed operators such states become long-lived: SU$(N)$ gauge theories contain bound states with $τ\sim M_{\rm Pl}^8/Λ^9_{\rm DM}$; even longer lifetimes $τ= (M_{\rm Pl}/Λ_{\rm DM})^{2N-4}/Λ_{\rm DM}$ arise from SO$(N)$ theories with $N \ge 8$, and possibly from $F_4$ or $E_8$. We compute their relic abundance generated by gravitational freeze-in and by inflationary fluctuations, finding that they can be viable DM candidates for $Λ_{\rm DM} \gtrsim 10^{10}$ GeV.

hep-ph↗

arXiv2021

$β$-function reconstruction of Palatini inflationary attractors

Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are most often considered in the metric formulation of gravity. However, non-minimal models may not necessarily maintain their attractor nature in the Palatini formalism where the connection is independent of the metric. In this work, we employ the $β$-function formalism to classify the strong coupling limit of inflationary models in both the metric and the Palatini approaches. Furthermore, we determine the range of values for the non-minimal coupling that lead to theories being observationally indistinguishable in metric and Palatini within current accuracy. Finally, we reconstruct the Jordan frame potential for $ξ$-attractors by imposing an explicit form for the $β$-function, demonstrating the effect that the choice of metric or Palatini has on the inflationary observables of the theory.

gr-qc↗

arXiv2021

Dimensional analysis and the correspondence between classical and quantum uncertainty

Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons, one of which is dimensional analysis. Since $\hbar$ is a dimensionful constant, we may always work in natural units in which $\hbar = 1$. Dimensional analysis teaches us that all physical laws can be expressed purely in terms of dimensionless quantities. This indicates that the existence of a dimensionally consistent constraint on $Δx Δp$ requires the existence of a dimensionful parameter with units of action, and that any definition of the classical limit must be formulated in terms of dimensionless quantities (such as quantum numbers). Therefore, bounds on classical uncertainty (formulated in terms of statistical ensembles) can only be written in terms of dimensionful scales of the system under consideration, and can be readily compared to their quantum counterparts after being non-dimensionalized. We compare the uncertainty of certain coupled classical systems and their quantum counterparts (such as harmonic oscillators and particles in a box), and show that they converge in the classical limit. We find that since these systems feature additional dimensionful scales, the uncertainty bounds are dependent on multiple dimensionless parameters, in accordance with dimensional considerations.

quant-ph↗

arXiv2021

Quantizing the Eisenhart Lift

The classical Eisenhart lift is a method by which the dynamics of a classical system subject to a potential can be recreated by means of a free system evolving in a higher-dimensional curved manifold, known as the lifted manifold. We extend the formulation of the Eisenhart lift to quantum systems, and show that the lifted manifold recreates not only the classical effects of the potential, but also its quantum mechanical effects. In particular, we find that the solutions of the Schrodinger equations of the lifted system reduce to those of the original system after projecting out the new degrees of freedom. In this context, we identify a conserved quantum number, which corresponds to the lifted momentum of the classical system. We further apply the Eisenhart lift to Quantum Field Theory (QFT). We show that a lifted field space manifold is able to recreate both the classical and quantum effects of a scalar field potential. We find that, in the case of QFT, the analogue of the lifted momentum is a quantum charge that is conserved not only in time, but also in space. The different possible values for this charge label an ensemble of Fock spaces that are all disjoint from one another. The relevance of these extended Fock spaces to the cosmological constant and gauge hierarchy problems is considered.

hep-th↗

arXiv2020

Frame Covariance in Quantum Gravity

We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the Vilkovisky-DeWitt formalism, treating both the scalar fields and the components of the gravitational tensor field as coordinates describing a manifold. By using tensors covariant under diffeomorphisms of this manifold, we show that scalar-tensor theories can be written in a form that is manifestly frame invariant at both classical and quantum levels. In~the same context, we show that in order to maintain manifest frame invariance, we must modify the Feynman rules of theories with a non-trivial field space. We show that one such theory is General Relativity by demonstrating explicitly that it has a non-zero field-space Riemann tensor. Thus, when constructing theories of quantum gravity, we must deal not only with curved spacetime, but also with a curved field space. Finally, we address the cosmological frame problem by tracing its origin to the existence of a new model function that appears in the path integral measure. Once this function is fixed, we find that frame transformations have no effect on the quantisation of the theory. The uniqueness of our improved quantum effective action is discussed.

hep-th↗

arXiv2020

T-Model Inflation and Bouncing Cosmology

We examine the dynamics of a closed cosmology whose matter source is that of a conformally coupled scalar field with a broken ${\rm SO}(1,1)$ symmetry, which correspond to the $α$-attractors proposed by Linde and Kallosh. Following a field redefinition, such models give rise to "T-model" inflationary potentials, whose dynamics provide both an inflationary phase and a classical bounce. We show that the universe can undergo bounces far from the regime of quantum gravity. We analyse perturbations on this background with particular attention given to the effects of a double-bouncing scenario (with rapid recollapse between bounces) on the long wavelength modes. We demonstrate that the predictions of such models agree well with observations and might explain the suppression of power in the low multiples of the CMB.

gr-qc↗

arXiv2019

Beyond the Poles in Attractor Models of Inflation

We offer a geometric interpretation of attractor theories with singular kinetic terms as a union of multiple canonical models. We demonstrate that different domains (separated by poles) can drastically differ in their phenomenology. We illustrate this with the help of a "master model" that leads to distinct predictions depending on which side of the pole the field evolves before examining the more realistic example of $α$-attractor models. Such models lead to quintessential inflation within the poles when featuring an exponential potential. However, beyond the poles, we discover a novel behaviour: the scalar field responsible for the early-time acceleration of the Universe may reach the boundary of the field-space manifold, indicating that the theory is incomplete and that a boundary condition must be imposed in order to determine its late-time behaviour. If the evolution of the field is arrested before this happens, however, we discover that quintessence can be achieved without a potential offset. Turning to multifield models with singular kinetic terms, we see that poles generalise straightforwardly to singular curves, which act as "model walls" between distinct pole-free inflationary models. As an example, we study a simple two-field $α$-attractor-inspired model, whose evolution of isocurvature perturbations is sensitive to where the non-canonical field begins its trajectory. We finally discuss initial conditions in attractor theories, where the existence of multiple disconnected canonical models implies that we must make a fundamental choice: in which domain we impose a distribution for the inflaton in order to then determine the likelihood of inflation.

hep-th↗

arXiv2019

A Finite Measure for the Initial Conditions of Inflation

We investigate whether inflation requires finely tuned initial conditions in order to explain the degree of flatness and homogeneity observed in the Universe. We achieve this by using the Eisenhart lift, which can be used to write any scalar field theory in a purely geometric manner. Using this formalism, we construct a manifold whose points represent all possible initial conditions for an inflationary theory. After equipping this manifold with a natural metric, we show that the total volume of this manifold is finite for a wide class of inflationary potentials. Hence, we identify a natural measure that enables us to distinguish between generic and finely tuned sets of initial conditions without the need for a regulator, in contrast to previous work in the literature. Using this measure, we find that the initial conditions that allow for sufficient inflation are indeed finely tuned. The degree of fine-tuning also depends crucially on the value of the cosmological constant at the time of inflation. Examining the example potential $V=λφ^4+Λ$, we find that we require percent-level fine tuning if we allow the cosmological constant during inflation to be much larger than it is today. However, if we fix the cosmological constant to its presently observed value, the degree of fine tuning required is of order $10^{-29}$.

gr-qc↗

arXiv2018

The Eisenhart Lift for Field Theories

We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalised coordinate. As an illustrative example in Classical Mechanics, we apply this formalism to simple harmonic motion. We extend the Eisenhart lift to homogeneous field theories by adding one new field. Unlike an auxiliary field, this field is fully dynamical and is therefore termed fictitious. We show that the Noether symmetries of a theory with a potential are solutions of the Killing equations in the lifted field space. We generalise this approach to field theories in four and higher spacetime dimensions by virtue of a mixed vielbein that links the field space and spacetime. Possible applications of the extended Eisenhart-lift formalism including the gauge hierarchy problem and the initial conditions problem in inflation are briefly discussed.

physics.class-ph↗

arXiv2018

On the Cosmological Frame Problem

We introduce a fully-frame covariant formalism for inflation by taking into account conformal transformations in addition to field reparametrizations. We begin by providing a brief overview of frame problems in the history of science before outlining the crux of the frame problem in inflationary cosmology. After introducing the concept of frame tensors in curved field space, we demonstrate how the quantum perturbations and the observables sourced by them can be made frame covariant. We then specialize to two-field models, examining the impact of isocurvature effects on the inflationary observables in a frame-covariant manner. We study the phenomenology of two particular models, a minimal polynomial model and a nonminimal model inspired by Higgs inflation. We observe that in the latter scenario, isocurvature effects are greatly enhanced. Moving beyond the tree-level approximation, we outline how our approach may be extended at the quantum level through the Vilkovisky--De Witt formalism and the generalization of frame tensors to configuration space, leading to a fully frame-invariant effective action. Finally, we summarize our findings and present possible future directions of research on the topic of frame covariance.

hep-th↗