Abstracts

Soner Albayrak - Perturbative Unitarity and the Wavefunction of the Universe

Middle East Technical University, Department of Physics

Abstract: Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: 1) the role of the iε-prescription and its compatibility with the requirement of unitarity; 2) the origin of the different "cutting rules"; 3) the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the iε-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name optical polytope. The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones.

Reference:

[1] S. Albayrak, P. Benincasa, C. D. Pueyo, "Perturbative Unitarity and the Wavefunction of the Universe", 2023, arXiv: 2305.19686 [hep-th].

Keremcan Doğan - How to Geometrize Non-geometry?

İstanbul Technical University, Department of Mathematics

Abstract: M theory as one of the most promising candidates for a theory of quantum gravity requires extra dimensions. In the spirit of Kaluza-Klein, these additional dimensions somewhat unify the geometry and matter, while bringing several consistency conditions. For example, fluxes which appear in the lower dimensional effective actions should obey Bianchi identities. These fluxes, as possible sources for branes, come as two types: geometric (f, H) and non-geometric (Q, R). The latter pair cannot be explained in the framework of usual differential geometry, while R flux is non-geometric even locally. In order to solve this issue, one needs to extend the notion of geometry. Algebroid structures offer such geometric generalizations, where they geometrize various seemingly non-geometric features appearing in string theories. For example Lie bialgebroids, in which f and Q fluxes appear, constitute the necessary geometric set up for T-duality, which relates several different string theories. One needs to extend this notion to a proto Lie bialgebroid in order to explain the remaining H and R fluxes. Both of these structures are constructed on a pair of vector bundles which are dual to each other. On the other hand, U-duality requires extensions of these ideas to pairs which are not dual in the usual sense. In this talk, we extend the notion of proto Lie bialgebroids to “proto bialgebroids” on such non-dual pairs in which both H and R fluxes appear as a part of the exceptional geometric structures. We achieve this by examining the calculus framework on algebroids we introduced previously in the presence of twists. We present various compatibility conditions for algebroid axioms, and analyze the effects of such twists. We also discuss the most general form of a twist procedure in terms of a vector bundle automorphism which produces such fluxes. We conclude the talk with a concrete example: SL(5) M theory and SL(5) exceptional Drinfel’d algebra.

References:

[1] A. Çatal-Özer, K. Doğan, C. Yetişmişoğlu, “Drinfel’d Doubles, Twists and All That... in Stringy Geometry and M Theory”, coming soon.

[2] A. Çatal-Özer, K. Doğan, C. Yetişmişoğlu, “Drinfel'd Double of Bialgebroids for String and M Theories: Dual Calculus Framework”, to be published in Journal of High Energy Physics, 2024, arXiv: 2312.06584 [hep-th].

[3] A. Çatal-Özer, T. Dereli, K. Doğan, “Metric-Bourbaki Algebroids: Cartan Calculus for M-Theory”, Journal of Geometry and Physics 199, 2024, arXiv: 2210.00548 [math.DG].

Cem Eröncel - Axion-like Particle Dark Matter: Beyond the Standard Paradigm

İstanbul Technical University, Department of Physics

Abstract: Axions and axion-like particles (ALPs) are among the most popular candidates that explain the origin of the mysterious dark matter. The most  popular ALP production mechanism studied in the literature is the misalignment  mechanism, where an ALP field with a quadratic or cosine potential has negligible  kinetic energy initially, and it starts oscillating when its mass becomes comparable to  the Hubble scale. Recently, there has been an interest in models that go beyond  the standard assumptions. These models not only extend the ALP dark matter parameter space, but also provide a rich phenomenology which is absent in the standard scenario. In particular, the ALP fluctuations grow exponentially via parametric resonance and tachyonic instabilities. In this talk, after giving an overview of the alternative production mechanisms, I will discuss the observational consequences  of this exponential growth and show that a sizable region of the ALP parameter  space becomes testable even if ALPs have only gravitational interactions.

Reference:

[1] A. Chatrchyan, C. Eröncel, M. Koschnitzke, G. Servant, "ALP Dark Matter with Non-periodic Potentials: Parametric Resonance, Halo Formation and Gravitational Signatures", Journal of Cosmology and Astroparticle Physics, 2023, arXiv: 2305.03756 [hep-th].

Yaghoub Heydarzade - Geometric Perfect Fluids and Dark Side of the Universe

Bilkent University, Department of Mathematics

Abstract: Recently we showed that in FLRW cosmology, the contribution from higher curvature terms in any generic metric gravity theory to the energy-momentum tensor is of the perfect fluid form. Such a geometric perfect fluid can be interpreted as a fluid remaining from the beginning of the universe where the string theory is thought to be effective. Just a short time after the beginning of the Universe, it is known that the Einstein-Hilbert action is assumed to be modified by adding all possible curvature invariants. We propose that the observed late-time accelerating expansion of the Universe can be solely driven by this geometric fluid. To support our claim, we specifically study the quadratic gravity field equations in D-dimensions. We show that the field equations of this theory for the FLRW metric possess a geometric perfect fluid source containing two critical parameters σ1 and σ2. To analyze this theory concerning its parameter space (σ1, σ2), we obtain the general second-order nonlinear differential equation governing the late-time dynamics of the deceleration parameter q. Hence using some present-day cosmological data as our initial conditions, our findings for the σ2=0 case are as follows: (i) In order to have a positive energy density for the geometric fluid ρg, the parameter σ1 must be negative for all dimensions up to D=11, (ii) For a suitable choice of σ1, the deceleration parameter experiences signature changes in the past and future, and in the meantime it lies within a negative range which means that the current observed accelerated expansion phase of the Universe can be driven solely by the curvature of the spacetime, (iii) q experiences a signature change and as the dimension D of spacetime increases, this signature change happens at earlier and later times, in the past and future, respectively.

Reference:

[1] M. Gürses, Y. Heydarzade, Ç. Şentürk, "Geometric Perfect Fluids and Dark Side of the Universe", 2024, arXiv: 2401.09784 [gr-qc].

Çağlar Pala - General Teleparallel Metrical Geometries

Pamukkale University, Department of Physics & Erciyes University, Department of Physics

Abstract: In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity. These so called general teleparallel geometries may also have applications in material physics, such as the study of crystal defects. In this work, we explore the general teleparallel geometry in the language of differential forms. We discuss the special cases of metric and symmetric teleparallelisms, clarify the relations between formulations with different gauge fixings and without gauge fixing, and develop a method of recasting Riemannian into teleparallel geometries. As illustrations of the method, exact solutions are presented for the generic quadratic theory in 2, 3 and 4 dimensions.

Reference:

[1] M. Adak, T. Dereli, T. S. Koivisto, Ç. Pala, "General Teleparallel Metrical Geometries", International Journal of Geometric Methods in Modern Physics 20, 2023, arXiv: 2303.17812 [gr-qc].

Aritra Saha - Black Holes in Supergravity for Arbitrary Values of Couplings

Feza Gürsey Institute for Physics and Mathematics & Boğaziçi University, Department of Mathematics

Abstract: Black holes, now known to be ubiquitously present in our universe, have their mathematical origin as solutions to the Einstein equation of General Relativity. In this talk, we aim to find such black hole solutions in a theory of General Relativity coupled to additional fields, namely a scalar and a vector (the so called Einstein-Maxwell-Dilaton system) in four dimensions. Such a theory is governed by a real parameter known as the coupling of the vector field to gravity, and we ask whether black holes exist in this theory for an arbitrary value of this coupling. Intriguingly, it turns out that although one cannot find the explicit closed form of the metric for arbitrary coupling, there is a novel way of expressing the physical properties of black holes such elusive metrics would describe, namely their mass and charges, via a first order non-linear ODE, and capture the entire spectrum of black holes which are possible in such a theory (for any value of the coupling). If time permits, we will discuss the same technique in a modified theory, where a topological F \wedge F term is added to the Einstein-Maxwell-Dilaton system.

Çetin Şentürk - Minimal Einstein-Aether Theory

University of Turkish Aeronautical Association, Department of Aeronautical Engineering

Abstract: We show that there is a minimal Einstein-Aether theory, obtained as a phenomenologically and theoretically consistent limit from the generic Einstein-Aether theory, that supports Einstein metrics as solutions with a reduced cosmological constant. The minimal theory is obtained by taking three of the coupling constants to be zero but keeping the expansion coupling constant to be nonzero. The square of the expansion of the unit-timelike aether field depletes the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar systems tests and black hole physics including gravitational waves.

Reference:

[1] M. Gürses, Ç. Şentürk, B. Tekin, "Minimal Einstein-Aether Theory", 2024, arXiv: 2402.07068 [gr-qc].

Kıvanç İbrahim Ünlütürk - Crossing the Singularity of a Gravitational Wave Collision

Koç University, Department of Physics

Abstract: A reformulation of general relativity was introduced by Ashtekar, Henderson and Sloan, inspired by the Belinski-Khalatnikov-Lifshitz conjecture. This reformulation is grounded in variables closely linked to those of loop quantum gravity, offering a means to analyze spacetime singularities classically, with potential application to quantum theory. These variables are expected to remain regular at spacelike singularities in general, which is supported by various examples, notably by cosmological spacetimes. In this talk, we shall show that this is also the case with singularities arising from gravitational wave collisions. We shall focus on two specific examples and explicitly confirm the regularity of these variables at the singularity.

Reference:

[1] T. Dereli, Ö. Gürtuğ, K. İ. Ünlütürk, "Crossing the Singularity of a Gravitational Wave Collision", Physical Review D 109, 2024, arXiv: 2401.11975 [gr-qc].