arXiv subjects

Hassan Firouzjahi

Publications and source records attributed to Hassan Firouzjahi.

At least 19 recordsLinked to original sources

arXiv2026

Bound States Inside the Horizon and Black Hole Entropy

We study the bound states perturbations in the interior of the Schwarzschild black hole and examine whether or not their microstates spectrum can furnish a statistical description of the black hole entropy. These states contain a discrete set of modes characterized by the labels $(s, p,\ell,m)$, where $s$ represents the spin of the species, $p$ denotes the radial excitation number while $(\ell,m)$ are the usual angular momentum labels. Requiring that the shortest wavelength resolved by the highly excited bound states remains above the quantum gravity scale introduces an angular cutoff $\ell_{\rm max}\sim r_H/L_{\rm Pl}$. The resulting angular degeneracy therefore scales with the horizon area. We count the corresponding configurations in the microcanonical ensemble and find an entropy of the form $S_{\rm bs}=αA/\hbar G$. Demanding that the bound state sector to be in thermal equilibrium with the black hole at the Hawking temperature fixes the fraction of the bound state energy in total black hole energy. For the gravitational perturbations sector, the equilibrium bound state contribution in entropy and the energy fraction are typically small. We also examine the conditions under which the bound states could account for the full black hole entropy. Although such saturation is possible at the level of state counting, it requires an order unity fraction in the black hole energy and therefore the backreactions on the background geometry cannot be ignored.

gr-qc↗

arXiv2026

Models with Non-minimal Coupling in Primordial Universe and Cosmological Observations

A non-minimal coupling between gravity and the inflaton field is a generic contribution in inflationary cosmology. In this work, we consider models of inflation with a non-minimal coupling $-ξϕ^2 R$ and study their observational predictions for the tensor-to-scalar ratio $r$ and the spectral index $n_s$. Unlike the conventional approach of working in the Einstein frame, we perform the analysis in the Jordan frame where the underlying dynamics, particularly the competition between the potential force and the coupling-induced friction, are more transparent. For suitable values of $ξ$, the system exhibits an extended constant-roll regime, in which this friction counteracts the potential force. Focusing on monomial potentials $V(ϕ) \propto ϕ^n$, we find that negative $ξ$ systematically reduces $r$ in the $(n_s, r)$ plane, while the shift in $n_s$ depends on the power $n$: for $n \geq 4$, the spectral index increases with $|ξ|$, whereas for $n < 4$, it decreases. Notably, the quartic model $V(ϕ) = λϕ^4/4$ with $ξ\lesssim -0.1$ shows good agreement with the ACT DR6 data and exhibits a distinct $n_s(ξ)$ dependence compared to other monomial cases. Our results demonstrate that non-minimally coupled models can effectively reconcile Planck and ACT observations, providing a unified framework for interpreting current CMB constraints.

astro-ph.CO↗

arXiv2026

Regular Black Holes from Anisotropic Source with Hydrodynamic Equation of State

We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, $P= P(ρ)$, for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches $0^+$ at large distances. Consequently, the square of the sound speed of perturbations, $c_s^2$, changes sign at the point where $P$ reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on $c_s$ puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which $P$ has its root, and at which $P$ attains its maximum.

gr-qc↗

arXiv2026

Gravitational Bound State Perturbations Inside Black Holes and Isospectrality

We study the bound state solutions for the polar perturbations in the interior of the Schwarzschild black hole. It is shown that for a given value of the spherical harmonic index $\ell$, there are a total of $\ell-1$ bound states for polar perturbations. We show both analytically and numerically that the spectrum of $\ell-2$ of these perturbations coincides exactly with the spectrum of axial perturbations. Consequently, the isospectrality between the bound states of axial and polar perturbations in the interior of the black hole is preserved. Furthermore, the additional mode found in the spectrum of polar perturbations is the algebraically special mode, which also furnishes the ground state of polar perturbations. It is shown that the spectrum of the highly excited states is equally spaced, which, in the semi-classical approximation, yields the black hole area quantization $ΔA = 16 πl_{\mathrm{Pl}}^2$.

gr-qc↗

arXiv2026

Non-Perturbative Hamiltonian and Higher Loop Corrections in USR Inflation

Calculating the action and the interaction Hamiltonian at higher orders in cosmological perturbation theory is a cumbersome task. We employ the formalism of EFT of inflation in the decoupling limit for single-field ultra slow-roll (USR) inflation and obtain a non-perturbative Hamiltonian in terms of the Goldstone field $π$. To complete the dictionary, a non-linear relation between the curvature perturbations and $π$ is presented. Using these results, we compute higher-order loop corrections in USR models with a sharp transition to the attractor phase, relevant for PBHs formation. It is shown that in the idealized picture in which the transition from the USR phase to SR phase is instantaneous and sharp, the loop corrections on long CMB scales increase rapidly with the number of loops $L$ and the setup may go out of perturbative control.

astro-ph.CO↗

arXiv2026

Hamiltonians to all Orders in Perturbation Theory and Higher Loop Corrections in Single Field Inflation with PBHs Formation

We calculate the action and the interaction Hamiltonians to all orders in perturbation theory in the model of single field inflation with a transient ultra slow-roll phase. Employing the formalism of EFT of inflation, we obtain a compact non-perturbative expression for the interaction Hamiltonian in terms of the Goldstone field $π$ in the decoupling limit. In addition, we also present a non-linear relation between $π$ and the curvature perturbations to all orders in perturbation theory. These are powerful results which enable us to calculate the cosmological correlators and loop corrections to any order in perturbation theory. As a non-trivial example, we calculate the $L$-loop corrections on long CMB scale perturbations in the USR models which are used for PBHs formation. We show that the loop corrections scale like $(ΔN {\cal P}_e L) ^L$ in which ${\cal P}_e$ is the peak of the power spectrum and $ΔN$ is the duration of the USR phase. This indicates that the loop corrections grow quickly out of perturbative control for large values of $L$. In the conventional USR setup for PBHs formation with $ΔN \simeq 2.5$, this happens at $L=4$.

astro-ph.CO↗

arXiv2026

Stochastic Inflation with Interacting Noises

Stochastic $δN$ formalism is a powerful tool to calculate the cosmological correlators non-perturbatively. However, it requires the initial data for the amplitude of the noise on the initial flat hypersurface which for a free theory during inflation is fixed to be $\frac{H}{2 π}$. In this work, we study the setups where the underlying theory involves interactions and the stochastic noises inherit these interactions. We extend the stochastic $δN$ formalism to these setups and rewrite the corresponding Langevin and Fokker-Planck equations in which the QFT corrections in the amplitude of the noises are taken into account. As an example, in the three-phase SR-USR-SR setup which is employed for PBHs formation, the modification in the amplitude of noise is calculated from the one-loop corrections in power spectrum via in-in formalism. We show that in these setups the amplitude of the stochastic noise is modified to $\frac{H}{2 π} \Big(1+ \frac{ Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{ {\cal R} } }\Big)^{\frac{1}{2}}$ in which $ \frac{Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{{\cal R} } }$ is the fractional one-loop correction in power spectrum.

astro-ph.CO↗

arXiv2025

Bound State Perturbations in the Interior of Black Holes

We revisit our earlier work and investigate the bound state perturbations in the interior of the Schwarzschild black hole. The bound sates are defined as the perturbations in the interior of the black hole with an imaginary spectrum which are regular at the center of black hole while their time-dependent profile falls off exponentially on the event horizon. Using the scale factor in the expanding direction in the interior of the black hole as the clock, we rewrite the corresponding Regge-Wheeler equation and solve it semi-analytically as well as numerically. We confirm that the bound state solutions exist for scalar, vector and axial tensor perturbations. It is shown that for a given value of $\ell >s$, there are total $\ell-s$ such bound states. We obtain the universal lower bound $2 G M ω_I >1$ for the spectrum of bound state which is asymptotically saturated in the large $\ell$ limit. Furthermore, we obtain an upper bound on the spectrum of axial perturbations which for large $\ell$ scales like $2 G M ω_I \lesssim 0.04\, \ell^4 $. As observed recently, these bound states have the curious property that the profile of the total wave function has a non-zero magnitude near the future event horizon.

gr-qc↗

arXiv2025

Trispectrum in Extended USR Model with Transition to SR

We study the trispectrum in a two-phase USR-SR setup of inflation in which the USR stage is extended in the initial phase of inflation while the second stage of inflation proceeds via a slow-roll phase. A key role is played by the sharpness parameter which controls how quickly the system reaches the final attractor phase after the USR stage. We employ both $δN$ and in-in formalisms and calculate trispectrum and the corresponding dimensionless parameters $g_{NL}$ and $τ_{NL}$. We show that both approaches yield the same results and study the shapes of trispectrum in various configurations. It is shown that the maximum value of trispectrum occurs in the setup with an infinitely sharp transition to the attractor phase while much of trispectrum is washed out in the opposite limit of a mild transition.

astro-ph.CO↗

arXiv2025

Axion USR Inflation

We consider a model of inflation in which the inflaton field is a rolling axion with a potential which is flat enough to support an intermediate phase of USR inflation. Because of the Chern-Simons interaction, one polarization of the gauge field experiences the tachyonic growth during the first slow-roll stage, inducing large corrections in curvature perturbations via the inverse decay effect. A non-trivial feature of our setup is that once the system enters the USR phase, the instability parameter falls off rapidly, terminating the gauge field production efficiently. Consequently, the power spectrum involves two separate peaks, the first peak is induced by the gauge field particles production while the second peak is due to standard USR mechanism. We show that the power spectrum at the intermediate scales develops strong scale-dependence $\propto k^m$ with the index $m >4$. Calculating the bispectrum, we demonstrate that non-Gaussianities with non-trivial shapes and multiple peaks are generated in this setup.

astro-ph.CO↗

arXiv2025

Upper Bounds on the Mass of Fundamental Fields from Primordial Universe

We study the fluctuations in the vacuum zero point energy associated to quantum fields and their statistical distributions during inflation. It is shown that the perturbations in the vacuum zero point energy have large amplitudes which are highly non-Gaussian. The effects of vacuum zero point fluctuations can be interpreted as the loop corrections in primordial power spectrum and bispectrum. Requiring that the primordial curvature perturbation to remain nearly Gaussian and the loop corrections to be under perturbative control impose strong upper bounds on the mass of fundamental fields during inflation. These bounds depend on the hierarchy of the masses in the theory such as whether or not the masses are at the similar orders. While the mass of the heaviest field in the hierarchy may not be constrained but it is shown that a combination of the masses of the fields can not be much heavier than the Hubble scale during inflation, otherwise their vacuum zero point fluctuations induce large non-Gaussianities in primordial perturbations. Considering the observational upper bound on tensor to scalar ratio, we conclude that this combined mass scale is lighter than $10^{14}$ GeV.

astro-ph.CO↗

arXiv2024

Two-loop corrections in power spectrum in models of inflation with PBHs formation

We calculate the two-loop corrections in primordial power spectrum in models of single field inflation incorporating an intermediate USR phase employed for PBHs formation. Among the total eleven one-particle irreducible Feynman diagrams, we calculate the corrections from the "double scoop" two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate that the fractional two-loop correction in power spectrum scales like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase.

hep-ph↗

arXiv2024

Loop Corrections in Gravitational Wave Spectrum in Single Field Inflation

We study the one-loop corrections in power spectrum of long gravitational waves induced from small scale modes in the models of single field inflation undergoing a phase of ultra-slow-roll (USR). We show that the spectrum of long tensor perturbations are largely unaffected by the loop corrections from the short scalar modes. In particular, the spectrum of long tensor perturbations is insensitive to the sharpness of the transition from the USR phase to the final slow-roll phase. This is in contrast to the case of scalar power spectrum in which the loop corrections can be large for a sharp transition while it is slow-roll suppressed in a mild transition. We study the tensor-scalar-scalar bispectrum in the squeezed limit and demonstrate that the Maldacena consistency condition does hold.

astro-ph.CO↗

arXiv2024

Loop Corrections in Bispectrum in USR Inflation with PBHs Formation

We calculate the one-loop corrections in bispectrum of CMB scale perturbations induced from the small scale modes undergoing an intermediate phase of USR inflation in scenarios employed for PBHs formation. Using the formalism of effective field theory of inflation we calculate the cubic and quartic Hamiltonians and perform the in-in analysis for a subset of Feynman diagrams comprising both the cubic and the quartic exchange vertices. We show the one-loop corrections in bispectrum has the local shape with $f_{NL}$ having the same structure as the one-loop correction in power spectrum in their dependence on the duration of the USR phase and the sharpness of the transition to the final attractor phase. It is shown that in the models with a sharp transition the induced loop corrections in bispectrum can quickly violate the observational bounds on $f_{NL}$.

astro-ph.CO↗

arXiv2024

Quantum Fluctuations in the Interior of Black Holes and Backreactions

We study the propagation of the quantum field perturbations in the interior of the Schwarzschild black hole. The interior of the black hole is like an anisotropic cosmological background which expands in one extended direction while contracting in azimuthal directions. Solving the quantum mode functions approximately, we calculate the expectation values of physical quantities such as the energy density $\langle ρ\rangle$ and pressure $\langle P\rangle$ as measured by an observer in the interior of the black hole. We employ a combination of the $ζ$ function regularization and dimensional regularization schemes to regularize the UV divergences in the energy momentum tensor associated to these quantum perturbations. By solving the Einstein field equations, we calculate the quantum backreactions induced in the background geometry. We speculate that the effects of quantum fluctuations in the interior of the black hole can be measured by the exterior observer.

gr-qc↗

arXiv2024

Vacuum zero point energy of self-interacting quantum fields in dS background

We consider self-interacting scalar fields with a conformal coupling in the dS background and study the quantum corrections from bubble loop diagrams. Incorporating the perturbative in-in formalism, we calculate the quantum corrections in the vacuum zero point energy and pressure of self-interacting fields with the potential $V \propto Φ^n $ for even values of $n$. We calculate the equation of state corresponding to these quantum corrections and examine the scaling of the divergent terms in the vacuum zero point energy and pressure associated to the dimensional regularization scheme. In particular, we show that for quartic self-interacting scalar field the conformal invariance is respected at two-loop order at the conformal point.

gr-qc↗

arXiv2023

Revisiting Loop Corrections in Single Field USR Inflation

We revisit the one-loop corrections on CMB scale perturbations induced from small scale modes in single field models which undergo a phase of ultra slow-roll inflation. There were concerns that large loop corrections are against the notion of the decoupling of scales and they are cancelled out once the boundary terms are included in Hamiltonian. We highlight that the non-linear coupling between the long and short modes and the modulation of the short mode power spectrum by the long mode are the key physical reasons behind the large loop corrections. In particular, in order for the modulation by the long mode to be significant there should be a strong scale-dependent enhancement in power spectrum of the short mode which is the hallmark of the USR inflation. We highlight the important roles played by the would-be decaying mode which were not taken into account properly in recent works claiming the loop cancellation. We confirm the original conclusion that the loop corrections are genuine and they can be dangerous for PBHs formation unless the transition to the final attractor phase is mild.

astro-ph.CO↗

arXiv2023

Induced Gravitational Waves from Ultra Slow-Roll Inflation and Pulsar Timing Arrays Observations

The stochastic gravitational wave background (SGWB) detected recently by the pulsar timing arrays (PTAs) observations may have cosmological origins. In this work we consider a model of single field inflation containing an intermediate phase of ultra slow-roll. Fixing the amplitude of the peak of curvature perturbations by the PBHs bounds we calculate the gravitational waves (GWs) induced from the curvature perturbations enhanced during USR. The spectrum of the induced GWs depends on the sharpness of the transition from the USR phase to the final attractor phase as well as to the duration of the USR period. While the model can accommodate the current PTAs data but it has non-trivial predictions for the induced GWs on higher frequency ranges which can be tested by future observations.

gr-qc↗