Fri - 03/21/25

**Title:

      Primodial power spectrum in loop quantum cosmology for different regularizations**  - **Authors:** Maciej Kowalczyk, Guillermo A. Mena Marugán, Tomasz Pawłowski  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and, consequently, to different physical predictions. In this work, we explore the impact of this regularization on the primordial power spectrum of cosmological perturbations. More specifically, we study this power spectrum for the conventional regularization used in Loop Quantum Cosmology and for two alternative prescriptions suggested in the literature. We set initial conditions for the perturbations at the bounce corresponding to a recently proposed vacuum state, optimally adapted to the background dynamics. This choice of vacuum is based on an asymptotic Hamiltonian diagonalization in the ultraviolet sector of the perturbations which provides a non-oscillating power spectrum. Employing a suitable approximation to the propagation equations of the perturbations around the bounce, we are able to obtain an analytic expression for the primordial power spectrum of this vacuum for all the discussed regularizations. We compare the results and prove that the main relevant distinction between the corresponding spectra is the scale where power suppression occurs. The associated wavenumber scale is proportional to the square root of the critical density in Loop Quantum Cosmology, density which is different for each of the studied regularizations.

**Title:

      Anisotropic Topological Field Theory**  - **Authors:** Emil Albrychiewicz, Andrés Franco Valiente  - **Subjects:** Subjects: High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  We study anisotropic scaling limits of topological field theories using tropical geometry. The resulting topological field theories are characterized by foliated geometries and are invariant under foliation-preserving gauge transformations. We demonstrate the tropicalization for the 2D BF theory and generalize the prescription to topological Yang-Mills and Chern-Simons theories. We call the tropical limit of the BF theory, the \textit{TBF} theory, which is an anisotropic generalization of the BF theory with an additional adjoint-valued field $T$ that enforces a projectability condition onto the leaves of the foliation. The TBF theory localizes onto the moduli space of tropicalized flat connections $\mathcal{M}(\Sigma_g,G)$ on a foliated Riemann surface $\Sigma_g$ of genus $g$. The tropical connections exhibit anisotropic behavior; their holonomy is sensitive only to the leaves of the foliation. We analyze this moduli space two distinct ways, Firstly, they are classified by leaf-wise holonomy whose dimension can be explicitly calculated for the case of tropical projective space $\mathbb{TP}^1$ by the moduli space isomorphism $\mathcal{M}\left(\mathbb{TP} ^1, G\right) \cong \operatorname{Hom}(\mathbb{Z}, G) / G$. The second way is through Kodaira-Spencer theory which gives a twisted cohomology argument to argue that $\operatorname{dim} \mathcal{M}\left(\mathbb{T} P^1, G\right)=\operatorname{rank}(\mathfrak{g})$ and we demonstrate their equivalence for the case of $SU(N)$. We show that we can glue together several $\mathbb{TP}^1$ to obtain $\operatorname{dim} \mathcal{M}\left(\Sigma_g, G\right)=(g-1)\operatorname{rank}(\mathfrak{g})$ through a foliated refinement of the Atiyah-Segal axioms. We leave several open questions such as potential connections to JT gravity and anisotropic conformal field theory.

Thu - 03/20/25

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There is no new related paper today

  1. [] - Title: Covariant effective spacetimes of spherically symmetric electro-vacuum with a cosmological constant - Jinsong Yang, Cong Zhang, Yongge Ma

Wed - 03/19/25

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  1. [] - Title: Regular black holes and their singular families - Hyat Huang, Xiao-Pin Rao

Tue - 03/18/25

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  1. [] - Title: Origin of time and probability in quantum cosmology - Leonardo Chataignier, Claus Kiefer, Mritunjay Tyagi

Mon - 03/17/25

There is no new related paper today

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  1. [] - Title: Origin of time and probability in quantum cosmology - Leonardo Chataignier, Claus Kiefer, Mritunjay Tyagi

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