<p>We present a quantum quadratic gravity inflationary scenario that can accommodate the new cosmological constraints, which have disfavored Starobinsky inflation. The theory is asymptotically free in the ultraviolet, but 1-loop running is found to dynamically lead to slow-roll inflation toward the infrared. When a large number of matter fields contribute to the beta functions, the spectral index and the tensor-to-scalar ratio can be phenomenologically viable. We find that as inflation ends, the theory approaches its strong coupling regime and general relativity must emerge, as an effective field theory, as the universe must reheat and enter its standard radiation era. In order to avoid strong coupling, a minimum tensor-to-scalar ratio of 0.01 is predicted for this theory. Our framework offers a laboratory for connecting a concrete ultraviolet completion (quantum quadratic gravity) with inflationary dynamics, reheating, and precise cosmological observations.</p>

Canada

Ruolin Liu

Jerome Quintin

Niayesh Afshordi

Ultraviolet Completion of the Big Bang in Quadratic Gravity

In analogue gravity studies, the goal is to replicate black hole phenomena, such as Hawking radiation, within controlled laboratory settings. In the realm of condensed matter systems, this may happen in 2D tilted Dirac cone materials based on honeycomb lattices. In particular, we compute the entropy of this system, and find it has the same form as black hole Bekenstein-Hawking entropy, if an analogue horizon forms. Hence, these systems can be potential analogues of quantum black holes. We show that this entropy is primarily concentrated in the region where the tilt parameter is close to one, which corresponds to the location of the analogue black hole horizon. Additionally, when nonlinear effects are taken into account, the entropy is peaked in a small pocket of the Fermi sea that forms behind the analogue event horizon, which we call the $\textit{Fermi puddle}$. We further refer to this new type of analogue black hole as a $\textit{smart hole}$, since, in contrast to dumb holes, it can simulate both the correct temperature $\textit{and}$ entropy of general relativistic black holes. These results provide an opportunity to illuminate various quantum facets of black hole physics in a laboratory setting.

Jiayue Yang

Mahdi Torabian

Germany

Seyed Jafari

India

G. Baskaran

Smart holes: analogue black holes with the right temperature and entropy

<p>We explore the possibility that quadratic gravity, as a renormalizable theory, describes the interior of quantum black holes. We find new exact power-law solutions to pure quadratic gravity under spherical symmetry, which are complex valued. The resulting solutions, dubbed powerballs, are horizonless compact objects that become Schwarzschild-like a small distance (of the order of the Planck length) outside the would-be Schwarzschild horizon. We present a description of the global eternal geometry, whose right and left exteriors are Lorentzian and Euclidean Schwarzschild-like regions, respectively, while the complex interior is a form of spiraling spacetime. We compute the total on-shell action integral as a saddle point to a gravitational path integral and discuss the Lorentzian and Euclidean interpretations thereof.</p>

Conformal cores of quantum black holes in quadratic gravity

Cuscuton field theory is an extension of general relativity that does not introduce additional propagating degrees of freedom, or violate relativistic causality. We construct a general geometric description of the cuscuton field theory by introducing curvature corrections to both the volume (potential) and the surface (kinetic) terms in the original cuscuton action. Our assumptions involve a stack of spacelike branes, separated by 4-dimensional bulks. We conjecture that the cuscuton, initially a discrete field, becomes continuous in the limit, there are many such transitions. From this we derive an effective action for the cuscuton theory and show that at the quadratic level our theory propagates only the two tensorial degrees of freedom.

Japan

South Korea

Maria Mylova

Effective cuscuton theory

We estimate the canonical entropy of a quantum black hole by counting its quasi-normal modes. We first show that the partition function of a classical black hole, evaluated by counting the quasi-normal modes with a thermodynamic Boltzmann weight, leads to a small entropy of order unity due to the small contribution from higher angular modes. We then discuss how this will be modified when taking into account dissipation effects near the horizon due to interaction with the quantum black hole microstates. The structure of quasi-normal modes drastically changes, yielding a fundamental frequency of the inverse of <math><msub><mrow><mi>t</mi></mrow><mrow><mi>echo</mi></mrow></msub><mo>∼</mo></math> log(Entropy)/Temperature. This is the time-scale for reflection from the microstates (or the quantum time limit of silence, followed by echoes), independent of the strength of dissipation, and is comparable to the scrambling time proposed by Sekino &amp; Susskind. Setting the dissipation constant to Planck time, we reproduce the Bekenstein-Hawking entropy of ∼ (Horizon area)/(Planck area). This result suggests the possibility of simulating black hole entropy in analog horizons realized in condensed matter systems.

Naritaka Oshita

From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence

We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, <math><mi>Λ</mi></math>, and the energy scale for the emergence of cosmological classicality. The fact that <math><mi>Λ</mi></math> and unimodular time are complementary quantum variables implies a perennially quantum Universe should <math><mi>Λ</mi></math> be zero (or, indeed, fixed at any value). Likewise, the smallness of <math><mi>Λ</mi></math> puts an upper bound on its uncertainty, and thus a lower bound on the unimodular clock’s uncertainty or the cosmic time for the emergence of classicality. Far from being the Planck scale, classicality arises at around <math><mn>7</mn><mo>×</mo><msup><mn>10</mn><mn>11</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> for the observed <math><mi>Λ</mi></math>, and taking the region of classicality to be our Hubble volume. We confirm this argument with a direct evaluation of the wave function of the Universe in the connection representation for unimodular theory. Our argument is robust, with the only leeway being in the comoving volume of our cosmological classical patch, which should be bigger than that of the observed last scattering surface. Should it be taken to be the whole of a closed Universe, then the constraint depends weakly on <math><msub><mi>Ω</mi><mi>k</mi></msub></math>: for <math><mo>−</mo><msub><mi>Ω</mi><mi>k</mi></msub><mo>&lt;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, classicality is reached at <math><mo>&gt;</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>12</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. If it is infinite, then this energy scale is infinite, and the Universe is always classical within the minisuperspace approximation. It is a remarkable coincidence that the only way to render the Universe classical just below the Planck scale is to define the size of the classical patch as the scale of nonlinearity for a red spectrum with the observed spectral index <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>0.967</mn><mo>(</mo><mn>4</mn><mo>)</mo></math> (about <math><msup><mn>10</mn><mn>11</mn></msup></math> times the size of the current Hubble volume). In the context of holographic cosmology, we may interpret this size as the scale of confinement in the dual 3D quantum field theory, which may be probed (directly or indirectly) with future cosmological surveys.

United Kingdom

João Magueijo

Lower bound on the cosmological constant from the classicality of the early Universe

Recent advances in AdS/CFT holography have suggested that the near-horizon dynamics of black holes can be described by random matrix systems. We study how the energy spectrum of a system with a generic random Hamiltonian matrix affects its early and late time thermalization behaviour using the spectral form factor (which captures the time-dependence of two-point correlation functions). We introduce a simple statistical framework for generating random spectra in terms of the nearest neighbor spacing statistics of energy eigenvalues, enabling us to compute the averaged spectral form factor in a closed form. This helps to easily illustrate how the spectral form factor changes with different choices of nearest neighbor statistics ranging from the Poisson to Wigner surmise statistics. We suggest that it is possible to have late time oscillations in random matrix models involving β-ensembles (generalizing classical Gaussian ensembles). We also study the form factor of randomly coupled oscillator systems and show that at weak coupling, such systems exhibit regular decaying oscillations in the spectral form factor making them interesting toy models for gravitational wave echoes. We speculate on the holographic interpretation of a system of coupled oscillators, and suggest that they describe the thermalization behaviour of a black hole geometry with a membrane that cuts off the geometry at the stretched horizon.

Krishan Saraswat

Spacing statistics of energy spectra: random matrices, black hole thermalization, and echoes

We compute the albedo (or reflectivity) of electromagnetic waves off the electron-positron Hawking plasma that surrounds the horizon of a Quantum Black Hole. We adopt the “modified firewall conjecture” for fuzzballs [1, 2], where we consider significant electromagnetic interaction around the horizon. While prior work has treated this problem as an electron-photon scattering process, we find that the incoming quanta interact collectively with the fermionic excitations of the Hawking plasma at low energies. We derive this via two different methods: one using relativistic plasma dispersion relation, and another using the one-loop correction to photon propagator. Both methods find that the reflectivity of long wavelength photons off the Hawking plasma is significant, contrary to previous claims. This leads to the enhancement of the electromagnetic albedo for frequencies comparable to the Hawking temperature of black hole horizons in vacuum. We comment on possible observable consequences of this effect.

United States

Wan Chua

Electromagnetic albedo of Quantum Black Holes

We study how the evaporation rate of spherically symmetric black holes is affected through the extraction of radiation close to the horizon. We adopt a model of extraction that involves a perfectly absorptive screen placed close to the horizon and show that the evaporation rate can be changed depending on how close to the horizon the screen is placed. We apply our results to show that the scrambling time defined by the Hayden-Preskill decoding criterion, which is derived in Pennington’s work (arXiv:1905.08255) through entanglement wedge reconstruction is modified. The modifications appear as logarithmic corrections to Pennington’s time scale which depend on where the absorptive screen is placed. By fixing the proper distance between the horizon and screen we show that for small AdS black holes the leading order term in the scrambling time is consistent with Pennington’s scrambling time. However, for large AdS black holes the leading order Log contains the Bekenstein-Hawking entropy of a cell of characteristic length equal to the AdS radius rather than the entropy of the full horizon. Furthermore, using the correspondence between the radial null energy condition (NEC) and the holographic c-theorem, we argue that the screen cannot be arbitrarily close to the horizon. This leads to a holographic argument that black hole mining using a screen cannot significantly alter the lifetime of a black hole.

Extracting Hawking radiation near the horizon of AdS black holes

The Kerr/CFT correspondence is a possible route to gain insight into the quantum theory of gravity in the near-horizon region of a Kerr black hole via a dual holographic conformal field theory (CFT). Predictions of the black hole entropy, scattering cross section and the quasinormal modes from the dual holographic CFT corroborate this proposed correspondence. More recently, it has been suggested that quantum gravitational effects in the near-horizon region of a black hole may drastically modify the classical general relativistic description, leading to potential observable consequences. In this paper, we study the absorption cross section and quasinormal modes of a horizonless Kerr-like exotic compact object (ECO) in the dual CFT picture. Our analysis suggests that the near-horizon quantum modifications of the black hole can be understood as finite size and/or finite <math><mi>N</mi></math> effects in the dual CFT. Signature of the near-horizon modification to a black hole geometry manifests itself as delayed echoes in the ringdown (i.e., the postmerger phase) of a binary black hole coalescence. From our dual CFT analysis we show how the length of the circle, on which the dual CFT lives, must be related to the echo time-delay that depends on the position of the near-horizon quantum structure. We further derive the reflectivity of the ECO membrane in terms of the CFT modular parameters, showing that it takes the Boltzmann form.