arXiv subjects

Alexey Golovnev

Publications and source records attributed to Alexey Golovnev.

At least 19 recordsLinked to original sources

arXiv2026

Vector modes in Type 3 New GR

Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear weak gravity equations and presented a thorough analysis with no ambiguity left. A bit later, we generalised it to linear cosmological perturbations and discussed the strong coupling issues that appear already at this level. Recently, there were claims that some dynamical modes had been missed in our work. However, the authors of the new claims did not look at the equations of motion and analysed the quadratic Lagrangian densities instead. In this paper, I take one of the most elementary cases, namely the vector modes in New GR of Type 3, and show what was their mistake that had led them to claiming that those were dynamical. The main message: Do not substitute constraint equations into a Lagrangian.

gr-qc↗

arXiv2026

Primary Constraints of Newer General Relativity

We study the primary constraint structure of Newer General Relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action is built from a scalar formed by quadratic combinations of the nonmetricity tensor, with arbitrary coefficients $c_i$ in the Lagrangian. We decompose the Lagrangian and compute the canonical momenta conjugate to the metric. We characterize the primary constraints arising from these momenta by identifying when the map between velocities and momenta becomes non-invertible, and organize the outcome through a fully nonlinear decomposition into scalar, vector and tensor sectors. Comparing with previous results in the literature, we recover five and three primary constraints associated with the tensor and vector sectors, respectively. We also identify a previously unreported degeneracy in the scalar sector, which yields either one or two scalar primary constraints depending on the conditions imposed on the parameters $c_i$. Finally, we obtain the primary constraints associated with the covariant formulation of symmetric teleparallel gravity.

gr-qc↗

arXiv2026

Non-primary square roots in massive gravity

Non-linear dRGT massive and bimetric gravities are complicated theories constructed in terms of square roots of matrices. Apart from the technical issues of successfully working with such square roots, there is also a problem of their non-uniqueness. There are claims in the literature that one should better use the principal root. This is a very reasonable conclusion. However, the motivation they give for it is that otherwise there would be non-primary square roots violating the general covariance. In this paper, I would like to show that, if properly understood, the non-primary square roots are also perfectly covariant. At the same time, I recall the relatively old observation that the real problem with such square roots lies in perturbation theory around them. In terms of matrices, it simply does not exist. In terms of the elementary symmetric polynomials used in the Lagrangian density, it is not analytic. Moreover, the non-principal square roots are more prone to getting into the complex domain.

hep-th↗

arXiv2026

Bianchi IX dynamics with a phantom field

We consider Bianchi IX dynamics of a Universe filled with a massless phantom field. Such an exotic matter source enables regimes impossible in vacuum or with a standard scalar field. In particular, two Kasner indices of BKL oscillations can be simultaneously negative, and the absolute value of a negative index can be large. We describe the consequences of these features and explain the nature of volume oscillations recently discovered in such a system by numerical methods.

gr-qc↗

arXiv2026

Revisiting the relaxation of constraints in gauge theories

Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist gauge field quantisations respecting the constraints, and at the same time the very idea of changing the classical theory in this way has many times appeared in other works. On the other hand, what was done in the path integral approach is fixing a gauge in terms of zero-momentum variables. We would like to show that this relaxation is what normally happens when one fixes such a gauge at the level of action principle in a Lagrangian theory. Moreover, there is an interesting analogy to be drawn. Namely, one of the ways to quantise a gauge theory is to build an extended Hamiltonian and then add new conditions by hand such as to make it a second class system. The constraints' relaxation occurs when one does the same at the level of the total Hamiltonian, i.e. a second class system with the primary constraints only.

hep-th↗

arXiv2026

More on Bianchi I spacetimes and f(T) gravity

Bianchi I cosmological solutions in f(T) gravity are discussed. We start from diagonal metrics and tetrads and show that their dynamical equations are pretty much tractable analytically, with a possible arena for physical applications. Then we derive a very bad unpredictability of the teleparallel connection in these configurations. Namely, even for the simple isotropic Friedmann universes, one might apply an arbitrary time-dependent spatial rotation to the standard tetrad without changing anything in the cosmological equations.

gr-qc↗

arXiv2025

Weak Gravity Limit in Newer General Relativity

We analyse linearised field equations around the Minkowski metric with its standard flat parallel transport in models of Newer GR, that is quadratic actions in terms of nonmetricity tensor. We show that half of the freedom in choosing the model parameters is immediately fixed by asking for reasonable properties of tensors and vectors, defined with respect to spatial rotations, and accurately describe the much more complicated sector of scalars. In particular, we show that, from the teleparallel viewpoint, the model of STEGR with addition of a gradient squared of the metric determinant exhibits three halves new dynamical modes, and not just one like it was previously claimed.

gr-qc↗

arXiv2024

Is there any Trinity of Gravity, to start with?

In recent years, it has been rather fashionable to talk about geometric trinity of gravity. The main idea is that one can formally present the gravity equations in different terms, those of either torsion or nonmetricity instead of curvature. It starts from a very erroneous claim that the Levi-Civita connection, and therefore the (pseudo-)Riemannian geometry itself, are nothing but an arbitrary choice. The point is that, as long as we admit the need of having a metric for describing gravity, the standard approach does not involve any additional independent geometric structures on top of that. At the same time, any other metric-affine model does go for genuinely new stuff. In particular, the celebrated teleparallel framework introduces a notion of yet another parallel transport which is flat. It gives us curious new ways of modifying gravity, even though very often quite problematic. However, in GR-equivalent models, we only get a new language for describing the same physics, in terms of absolutely unobservable and unpredictable geometrical inventions. For sure, one can always safely create novel constructions which do not influence the physical equations of motion, but in itself it does not make much sense and blatantly goes against the Occam's razor.

gr-qc↗

arXiv2024

On the degrees of freedom count on singular phase space submanifolds

I discuss singular loci in the phase spaces of theories which lack globally well-defined numbers of dynamical modes. This is a topic which appears quite often in the recent literature on modified gravity. In particular, there were discussions about $R^2$ gravity around Minkowski space. It is a relatively simple case, and still there were some confusions. It clearly shows that one should be very accurate when trying to understand a potentially problematic theory through perturbations around a simply looking background. At the same time, many modern teleparallel approaches are laden with even more severe issues. Therefore, it is a topic which is certainly worth carefully thinking about.

hep-th↗

arXiv2024

Degrees of Freedom in modified Teleparallel Gravity

I discuss the issue of degrees of freedom in modified teleparallel gravity. These theories do have an extra structure on top of the usual (pseudo)Riemannian manifold, that of a flat parallel transport. This structure is absolutely abstract and unpredictable (pure gauge) in GR-equivalent models, however it becomes physical upon modifications. The problem is that, in the most popular models, this local symmetry is broken but not stably so, hence the infamous strong coupling issues. The Hamiltonian analyses become complicated and with contradictory results. A funny point is that what we see in available linear perturbation treatments of $f(T)$ gravity is much closer to the analysis with less dynamical degrees of freedom which has got a well-known mistake in it, while the more accurate work predicts much more of dynamics than what has ever been seen up to now. I discuss possible reasons behind this puzzle, and also argue in favour of studying the most general New GR models which are commonly ignored due to suspicion of ghosts.

gr-qc↗

arXiv2024

Conformal Transformations and Cosmological Perturbations in New General Relativity

We study conformal transformations in the most general parity-preserving models of the New General Relativity type. Then we apply them to analysis of cosmological perturbations in the (simplest) spatially flat cosmologies. Strong coupling issues around Minkowski spacetime are seen for many special cases of these models. At the same time, the behaviour of the most general three-parameter case seems to be very robust, presumably always with only the eight first-class constraints coming from diffeomorphisms. Also the case of the so-called 1-parameter New GR doesn't show any discontinuity between Minkowski and the cosmology, though without showing any deviations from GR which would be observable at this level either.

gr-qc↗

arXiv2024

Contemplating the fate of modified gravity

Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same time, available experimental evidence is limited for testing gravity as a force beyond the regimes in which the theory of general relativity has proven to be successful. This situation leads researchers to look for ``the simplest modification'' to general relativity in a certain class of models, which is enough to solve one or more problems. As a result, we are lost amid a variety of theories with no deeper guiding principle. We give a general review of existing approaches and discuss the current state of the art.

gr-qc↗

arXiv2024

Geometry and covariance of symmetric teleparallel theories of gravity

We present the geometric foundations and derivations of equations of motion for symmetric teleparallel theories of gravity in the coincident gauge and covariant frameworks. We discuss the theoretical challenges introduced by the auxiliary fields responsible for the covariantisation procedure. We elucidate a tetradic structure interpretation behind this covariant formulation. Regarding the effect of covariantisation at the level of the equations of motion, we explicitly show that the only physical change, in case of setting an arbitrary energy-momentum tensor to the right hand side, resides in the requirement of the fulfillment of the covariant conservation laws. Also, we have explicitly introduced the fundamental covariantly-conserved teleparallel tetrad for the symmetric teleparallel frameworks.

gr-qc↗

arXiv2024

Geometry of teleparallel theories

I give a brief introduction to and explain the geometry of teleparallel models of modified gravity. In particular I explain why, in my opinion, the covariantised approaches are not needed and the Weitzenböck connection is the most natural representation of the parallel transport structure. An interesting point is that it also applies to the symmetric teleparallel case. I also share my thoughts on why the teleparallel framework does not seem to be a next rung in the ladder of understanding the real worlds' gravity. At the same time, these theories do have a clear and justified academic interest to them.

gr-qc↗

arXiv2023

More on the fact that Rastall = GR

Rastall gravity is the same as General Relativity, with a simple algebraic redefinition of what is called the energy-momentum tensor. Despite it having been very clearly explained by M. Visser several years go, there are still many papers claiming big differences between the two formulations of gravitational equations and trying to use them for problems of physics. When going this way, the totally ignored task is to explain why the conserved energy-momentum quantities and the quantities used for other purposes are different from each other. Moreover, when researchers are using the non-conserved energy density and pressure for determining the sound speed, it is just inconsistent with the Rastall gravity. I carefully explain all this, and also show how one could construct a variational principle for producing equations in the Rastall form.

gr-qc↗

arXiv2023

Gravitational Waves in New General Relativity

The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary constraints in the Hamiltonian analysis. However, it is by far not enough for counting their degrees of freedom or judging whether they are any good and viable. In this paper we study linearised equations in vacuum around the trivial Minkowski tetrad. By taking the approach of cosmological perturbation theory we show that the numbers of primary constraints are very easily seen without any need of genuine Hamiltonian techniques, and give the full count of linearised degrees of freedom in the weak field limit of each and every version of New General Relativity without matter.

gr-qc↗

arXiv2023

A Pamphlet against The Energy

It is a well-known fact that there is no well-defined notion of conserved energy in gravity. In my opinion, it is not a big deal. As a conserved quantity, energy is a rather artificial invention which works perfectly well as long as we have a natural symmetry with respect to translations in time, however not when there ceases to be any notion of an objective time, rather than a mere coordinate. However, recently we have got an essential progress in teleparallel models of gravity, with emerging opinions of having solved the problem of energy. I explain why I think it simply makes no good sense to go for solving a non-existent problem, and the correct answer is just that in general there is no such thing as The Energy. (It has just been presented online at the Conference on Geometric Foundations of Gravity 2023 in Tartu, Estonia.)

gr-qc↗

arXiv2023

The geometrical meaning of the Weitzenböck connection

In the current literature, there are many discussions about the local Lorentz invariance of modified teleparallel gravity. This symmetry is obviously violated in the classical "pure tetrad" formulation of the theory, while it gets restored in the "fully covariant" approach. My claim is that, despite many heated discussions, the two formulations are just equivalent. And the purpose of this note is to argue that the local Lorentz invariance is not natural for the modified teleparallel theories at all, making the pure tetrad approach more fundamentally justified.

gr-qc↗