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There exist two consistent theories of massless, self-interacting gravitons, which differ by their local symmetries: general relativity and Weyl transverse gravity. We show that these two theories are also the only two metric descriptions of gravity in 4 spacetime dimensions which obey the equivalence principle for test gravitational physics. We further analyse how the weaker formulations of the equivalence principle are realised in Weyl transverse gravity (and its generalisations). The analysis sheds light on the behaviour of matter fields in this theory., Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:2409.06645

Thermodynamics of local causal horizons have been shown to encode the information necessary to derive the equations governing the gravitational dynamics. We have previously shown that, in the presence of matter, this derivation further implies quantum phenomenological corrections to gravitational dynamics. Herein, we study whether similar corrections also occur in vacuum. We show that, under the assumptions of locality and local Lorentz invariance of physics, the vacuum dynamics is prescribed by the Einstein equations. We also discuss an alternative paradigm which assumes the existence of a preferred direction of time (much like in Einstein-aether or Ho\v{r}ava-Lifshitz gravity). Then, we find an modified gravitational dynamics in which Ricci curvature is sourced by Bel-Robinson super-energy., Comment: 16 pages, 1 figure

There exist two consistent theories of self-interacting gravitons: general relativity and Weyl transverse gravity. The latter has the same classical solutions as general relativity, but different local symmetries. We argue that Weyl transverse gravity also naturally arises from thermodynamic arguments. In particular, we show that thermodynamic equilibrium of local causal diamonds together with the strong equivalence principle encodes the gravitational dynamics of Weyl transverse gravity rather than general relativity. We obtain this result in a self-consistent way, verifying the validity of our initial assumptions, i.e. the proportionality between entropy and area and the different versions of the equivalence principle in Weyl transverse gravity. Furthermore, we extend the thermodynamic derivation of the equations of motion from Weyl transverse gravity to a class of modified theories of gravity with the same local symmetries. For this purpose, we employ the general expression for Wald entropy in such theories., Comment: 18 pages, 2 figures, v1 shortened and streamlined

We analyze how the presence of closed timelike curves (CTCs) characterizing a time machine can be discerned by placing a local particle detector in a region of spacetime which is causally disconnected from the CTCs. Our study shows that not only can the detector tell if there are CTCs, but also that the detector can separate topological from geometrical information and distinguish periodic spacetimes without CTCs (like the Einstein cylinder), curvature, and spacetimes with topological identifications that enable time-machines., Comment: 20 pages, 3 figures; v2: fixed typos and updated to match published version

Entertaining the possibility of time travel will invariably challenge dearly held concepts of fundamental physics. It becomes relatively easy to construct multiple logical contradictions using differing starting points from various well-established fields of physics. Sometimes, the interpretation is that only a full theory of quantum gravity will be able to settle these logical contradictions. Even then, it remains unclear if the multitude of problems could be overcome. Yet as definitive as this seems to the notion of time travel in physics, such a recourse to quantum gravity comes with its own, long-standing challenge to most of these counter-arguments to time travel: These arguments rely on time, while quantum gravity is (in)famously stuck with and dealing with the problem of time. One attempt to answer this problem within the canonical framework resulted in the Page-Wootters formalism, and its recent gauge-theoretic re-interpretation - as an emergent notion of time. Herein, we will begin a programme to study toy models implementing the Hamiltonian constraint in quantum theory, with an aim towards understanding what an emergent notion of time can tell us about the (im)possibility of time travel., Comment: v1: 19 pages, 2 figures; v2: 20 pages, 2 figures, added references, minor text changes, no physics changes. Closely matches published version, but retains authors' preferred style choices

We investigate the primordial power spectrum of cosmological tensor perturbations in the dressed metric approach to Loop Quantum Cosmology. We compute the background-dependent effective mass that affects their propagation using the effective description of Loop Quantum Cosmology and show that this mass can be approximated in different cosmological epochs by appropriate analytic functions. Moreover, in each of those epochs we can analytically solve the propagation of the perturbations, then obtaining the general solution globally by continuity requirements. On the other hand, since there are regimes far away from slow roll in the considered background evolution, the Bunch-Davies state does not provide a privileged choice of vacuum that would pick out a specific solution for the perturbations. Instead, we select the state of these perturbations by a recently proposed criterion that removes unwanted oscillations in the power spectrum. We compute the spectrum of this vacuum and compare it with other spectra obtained in the literature, especially with one corresponding to the hybrid approach to Loop Quantum Cosmology. Finally, we notice that the same type of background dynamics is found in a phenomenological approach to quantum gravity based on thermodynamics, allowing in this case a free value for the tantamount of the critical density. Extending the dressed metric proposal to this phenomenological model, one might expect a similar form for the associated primordial power spectrum., Comment: 19 pages, 8 figures

The thermodynamics of local causal horizons has been shown to imply gravitational dynamics. In this essay, we discuss the principles underlying this observation, and its significance in our understanding of (quantum) gravity. We also show why the local thermodynamic methods cannot by themselves recover general relativity. Instead, they lead to the so-called Weyl transverse gravity. Because of this, local thermodynamic approaches avoid huge vacuum energy contributions to the cosmological constant. They even suggest a possible source for its small observed value. We also outline a way in which thermodynamics allows us to study low energy quantum gravitational effects. We arrive at quantum corrections to the gravitational equations which are suppressed by the Planck length squared., Comment: 10 pages. Essay received Honorable Mention at the Gravity Research Foundation 2023 Awards for Essays on Gravitation. Matches the version accepted in IJMPD

In this work we present a derivation of modified Raychaudhuri and Friedmann equations from a phenomenological model of quantum gravity based on the thermodynamics of spacetime. Starting from general gravitational equations of motion which encode low-energy quantum gravity effects, we found its particular solution for homogenous and isotropic universes with standard matter content, obtaining a modified Raychaudhuri equation. Then, we imposed local energy conservation and used a perturbative treatment to derive a modified Friedmann equation. The modified evolution in the early universe we obtained suggests a replacement of the Big Bang singularity by a regular bounce. Lastly, we also briefly discuss the range of validity of the perturbative approach and its results., Comment: 8 pages, 2 figures, text matches the version published in PLB

In this work, we derive the linearised equations of quadratic gravity from entanglement equilibrium of local causal diamonds. Rather than starting from the Wald entropy prescription (which depends on the gravitational Lagrangian), we employ a model independent approach based on the logarithmic corrections to horizon entanglement entropy. In this way, we are able to show the emergence of linearised quadratic gravity from entanglement equilibrium without using any a priori knowledge about gravitational dynamics. If the logarithmic correction to entropy has a negative sign, as predicted by replica trick calculations of entanglement entropy, we find that the quadratic gravity correction terms have the sign necessary to avoid tachyonic instabilities of the theory., Comment: 8 pages, 1 figure. Matches the version accepted in PRD

Gravitational theories invariant under transverse diffeomorphisms and Weyl transformations have the same classical solutions as the corresponding fully diffeomorphism invariant theories. However, they solve some of the problems related to the cosmological constant and in principle allow local energy non-conservation. In the present work, we obtain the Noether charge formalism for these theories. We first derive expressions for the Noether currents and charges corresponding to transverse diffeomorphisms and Weyl transformations, showing that the latter vanish identically. We then use these results to obtain an expression for a perturbation of a Hamiltonian corresponding to evolution along a transverse diffeomorphism generator. From this expression, we derive the first law of black hole mechanics, identifying the total energy, the total angular momentum, the Wald entropy, and the contributions of the cosmological constant perturbations and energy non-conservation. Lastly, we extend our formalism to derive the first law of causal diamonds., Comment: 20 pages

Weyl transverse gravity is a gravitational theory that is invariant under transverse diffeomorphisms and Weyl transformations. It is characterised by having the same classical solutions as general relativity while solving some of its issues with the cosmological constant. In this work, we first find the Noether currents and charges corresponding to local symmetries of Weyl transverse gravity as well as a prescription for the symplectic form. We then employ these results to derive the first law of black hole mechanics in Weyl transverse gravity (both in vacuum and in the presence of a perfect fluid), identifying the total energy, the total angular momentum, and the Wald entropy of black holes. We further obtain the first law and Smarr formula for Schwarzschild-anti-de Sitter and pure de Sitter spacetimes, discussing the contributions of the varying cosmological constant, which naturally appear in Weyl transverse gravity. Lastly, we derive the first law of causal diamonds in vacuum., Comment: 36 pages

In this review we discuss emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation., Comment: 19 pages, 2 figures. Review prepared for a Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity 2021. Version accepted by IJGMMP

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder., Comment: 17 pages, 2 Appendices, RevTex4-2; v2: accepted to JHEP, updated to match the upcoming published version. Added one figure for the conformal diagram

Motivated by exploring the interface between thermodynamics of spacetime and quantum gravity effects, we develop a heuristic derivation of Hawking temperature and Bekenstein entropy from the existence of a minimal resolvable area. Moreover, we find leading order quantum gravity corrections to them that are in qualitative agreement with results obtained by other methods, both heuristic and rigorous. In this way, we recover, as a particular case, the corrections heuristically obtained from the existence of minimal length. We also show that the size of minimal area is constrained from above by well understood results of semiclassical black hole physics, specifically by the entropy content of Hawking radiation. The minimal area derivation we introduce is also applied to finding the Unruh temperature associated with causal diamonds and to establish a new relation between this temperature and the entropy of the causal diamond's horizon., Comment: 11 pages, 3 figures. Version accepted to Physical Review D

The Belinski-Khalatnikov-Lifshitz (BKL) conjecture predicts a chaotic alternation of Kasner epochs in the evolution of generic classical spacetimes towards a spacelike singularity. As a first step towards understanding the full quantum BKL scenario, we analyze a vacuum Bianchi II model with local rotational symmetry, which presents just one Kasner transition. During the Kasner epochs, the quantum state is coherent and it is thus characterized by constant values of the different quantum fluctuations, correlations and higher-order moments. By computing the constants of motion of the system we provide, for any peaked semiclassical state, the explicit analytical transition rules that relate the parametrization of the asymptotic coherent state before and after the transition. In particular, we obtain the modification of the transition rules for the classical variables due to quantum back-reaction effects. This analysis is performed by considering a high-order truncation in moments (the full computations are performed up to fifth-order, which corresponds to neglecting terms of an order $\hbar^3$), providing a solid estimate about the quantum modifications to the classical model. Finally, in order to understand the dynamics of the state during the transition, we perform some numerical simulations for an initial Gaussian state, that show that the initial and final equilibrium values of the quantum variables are connected by strong and rapid oscillations., Comment: Version accepted in PRD. Minor typos corrected

In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity modifications to it. Quantum gravity effects are considered via modification of Bekenstein entropy by an extra logarithmic term in the area. This modification is predicted by several approaches to quantum gravity, including loop quantum gravity, string theory, AdS/CFT correspondence and generalised uncertainty principle phenomenology, giving our result a general character. The derived equations generalise classical equations of motion of unimodular gravity, instead of the ones of general relativity, and they contain at most second derivatives of the metric. We provide two independent derivations of the equations based on thermodynamics of local causal diamonds. First one uses Jacobson's maximal vacuum entanglement hypothesis, the second one Clausius entropy flux. Furthermore, we consider questions of diffeomorphism and local Lorentz invariance of the resulting dynamics and discuss its application to a simple cosmological model, finding a resolution of the classical singularity., Comment: Extended discussions, extra references added. 31 pages, 1 figure

We analyze the Generalized Uncertainty Principle (GUP) impact onto the nonextensive black hole thermodynamics by using R\'enyi entropy. We show that when introducing GUP effects, both R\'enyi entropy and temperature associated to black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with R\'enyi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into R\'enyi temperature., Comment: 9 pages, 5 figures, extended introduction, results and conclusion, added new references, accepted in Phys. Rev. D

We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynamics implied by thermodynamics of spacetime, in fact, corresponds to unimodular gravity rather than general relativity., Comment: 19 pages, 1 figure Version accepted in PRD. Few typos corrected and some references added

The approach of a quantum state to a cosmological singularity is studied through the evolution of its moments in a simple version of a Bianchi I model. In spite of the simplicity, the model exhibits several instructive and unexpected features of the moments. They are investigated here both analytically and numerically in an approximation in which anisotropy is assumed to vary slowly, while numerical methods are also used to analyze the case of a rapidly evolving anisotropy. Physical conclusions are drawn mainly regarding two questions. First, quantum uncertainty of anisotropies does not necessarily eliminate the existence of isotropic solutions, with potential implications for the interpretation of minisuperspace truncations as well as structure-formation scenarios in the early universe. Secondly, back-reaction of moments on basic expectation values is found to delay the approach to the classical singularity., Comment: minor changes, version accepted for publication

The current debate about a possible change of paradigm from a single universe to a multiverse scenario could have deep implications on our view of cosmology and of science in general. These implications therefore deserve to be analyzed from a fundamental conceptual level. We briefly review the different multiverse ideas, both historically and within contemporary physics. We then discuss several positions within philosophy of science with regard to scientific progress, and apply these to the multiverse debate. Finally, we construct some key concepts for a physical multiverse scenario and discuss the challenges this scenario has to deal with in order to provide a solid, testable theory.